122-869: [REDACTED] Look up Bose-Einstein condensate or Bose-Einstein statistics in Wiktionary, the free dictionary. Bose–Einstein may refer to: Bose–Einstein condensate , a phase of matter in quantum mechanics Bose–Einstein condensation (network theory) , the application of this model in network theory Bose–Einstein condensation of polaritons Bose–Einstein condensation of quasiparticles Bose–Einstein correlations Bose–Einstein integral Bose–Einstein statistics , in particle statistics See also [ edit ] Bose (disambiguation) Einstein (disambiguation) Boson (disambiguation) Satyendra Nath Bose , Indian physicist Albert Einstein (disambiguation) Topics referred to by
244-600: A Hanukkah celebration. Einstein next traveled to California, where he met Caltech president and Nobel laureate Robert A. Millikan . His friendship with Millikan was "awkward", as Millikan "had a penchant for patriotic militarism", where Einstein was a pronounced pacifist . During an address to Caltech's students, Einstein noted that science was often inclined to do more harm than good. This aversion to war also led Einstein to befriend author Upton Sinclair and film star Charlie Chaplin , both noted for their pacifism. Carl Laemmle , head of Universal Studios , gave Einstein
366-575: A unified field theory by generalizing his geometric theory of gravitation to include electromagnetism . As a result, he became increasingly isolated from the mainstream modern physics . His intellectual achievements and originality made Einstein broadly synonymous with genius . In 1999, he was named Time 's Person of the Century . Albert Einstein was born in Ulm , in the Kingdom of Württemberg in
488-585: A BEC using sodium atoms. In 2001 Cornell, Wieman, and Ketterle shared the Nobel Prize in Physics "for the achievement of Bose–Einstein condensation in dilute gases of alkali atoms, and for early fundamental studies of the properties of the condensates". Bose first sent a paper to Einstein on the quantum statistics of light quanta (now called photons ), in which he derived Planck's quantum radiation law without any reference to classical physics. Einstein
610-521: A bill to parliament to extend British citizenship to Einstein, during which period Einstein made a number of public appearances describing the crisis brewing in Europe. In one of his speeches he denounced Germany's treatment of Jews, while at the same time he introduced a bill promoting Jewish citizenship in Palestine, as they were being denied citizenship elsewhere. In his speech he described Einstein as
732-464: A collection of enough Bose particles in thermal equilibrium will mostly be in the ground state, with only a few in any excited state, no matter how small the energy difference. Consider now a gas of particles, which can be in different momentum states labeled | k ⟩ {\displaystyle |k\rangle } . If the number of particles is less than the number of thermally accessible states, for high temperatures and low densities,
854-450: A condensate of lithium atoms only one month following the JILA work. Lithium has attractive interactions, causing the condensate to be unstable and collapse for all but a few atoms. Hulet's team subsequently showed the condensate could be stabilized by confinement quantum pressure for up to about 1000 atoms. Various isotopes have since been condensed. In the image accompanying this article,
976-740: A contract to install electric lighting in Munich, but without success—they lacked the capital that would have been required to update their technology from direct current to the more efficient, alternating current alternative. The failure of their bid forced them to sell their Munich factory and search for new opportunities elsewhere. The Einstein family moved to Italy, first to Milan and a few months later to Pavia , where they settled in Palazzo Cornazzani . Einstein, then fifteen, stayed behind in Munich in order to finish his schooling. His father wanted him to study electrical engineering , but he
1098-677: A diploma handed to him by King Alfonso XIII . (His Spanish trip also gave him a chance to meet a fellow Nobel laureate, the neuroanatomist Santiago Ramón y Cajal .) From 1922 until 1932, with the exception of a few months in 1923 and 1924, Einstein was a member of the Geneva-based International Committee on Intellectual Cooperation of the League of Nations , a group set up by the League to encourage scientists, artists, scholars, teachers and other people engaged in
1220-580: A formative event from his youth, when he was sick in bed and his father brought him a compass . This sparked his lifelong fascination with electromagnetism . He realized that "Something deeply hidden had to be behind things." Albert attended St. Peter's Catholic elementary school in Munich from the age of five. When he was eight, he was transferred to the Luitpold Gymnasium , where he received advanced primary and then secondary school education. In 1894, Hermann and Jakob's company tendered for
1342-427: A gaseous BEC. This led to the immediate pursuit of the idea by four independent research groups; these were led by Isaac Silvera ( University of Amsterdam ), Walter Hardy ( University of British Columbia ), Thomas Greytak ( Massachusetts Institute of Technology ) and David Lee ( Cornell University ). However, cooling atomic hydrogen turned out to be technically difficult, and Bose-Einstein condensation of atomic hydrogen
SECTION 10
#17327727996851464-463: A gravel sorter and an electric typewriter. His employers were pleased enough with his work to make his position permanent in 1903, although they did not think that he should be promoted until he had "fully mastered machine technology". It is conceivable that his labors at the patent office had a bearing on his development of his special theory of relativity. He arrived at his revolutionary ideas about space, time and light through thought experiments about
1586-498: A large fraction of bosons occupy the lowest quantum state , at which microscopic quantum-mechanical phenomena, particularly wavefunction interference , become apparent macroscopically . More generally, condensation refers to the appearance of macroscopic occupation of one or several states: for example, in BCS theory , a superconductor is a condensate of Cooper pairs . As such, condensation can be associated with phase transition , and
1708-513: A man can be." In 1912, Einstein entered into a relationship with Elsa Löwenthal , who was both his first cousin on his mother's side and his second cousin on his father's. When Marić learned of his infidelity soon after moving to Berlin with him in April 1914, she returned to Zürich, taking Hans Albert and Eduard with her. Einstein and Marić were granted a divorce on 14 February 1919 on the grounds of having lived apart for five years. As part of
1830-400: A minimum width velocity distribution. This width is given by the curvature of the magnetic potential in the given direction. More tightly confined directions have bigger widths in the ballistic velocity distribution. This anisotropy of the peak on the right is a purely quantum-mechanical effect and does not exist in the thermal distribution on the left. This graph served as the cover design for
1952-532: A new kind of fluid, now known as a superfluid , at temperatures less than 2.17 K (the lambda point ). Superfluid helium has many unusual properties, including zero viscosity (the ability to flow without dissipating energy) and the existence of quantized vortices . It was quickly believed that the superfluidity was due to partial Bose–Einstein condensation of the liquid. In fact, many properties of superfluid helium also appear in gaseous condensates created by Cornell, Wieman and Ketterle (see below). Superfluid helium-4
2074-446: A paper which laid the foundations for the concepts of both laser and maser , and contained a trove of information that would be beneficial to developments in physics later on. In the middle part of his career, Einstein made important contributions to statistical mechanics and quantum theory. Especially notable was his work on the quantum physics of radiation , in which light consists of particles, subsequently called photons . With
2196-664: A platform from which to promote traditional Catholic doctrine. Einstein's former physics professor Hendrik Lorentz and the Polish chemist Marie Curie were also members of the committee. In March and April 1925, Einstein and his wife visited South America, where they spent about a week in Brazil, a week in Uruguay and a month in Argentina. Their tour was suggested by Jorge Duclout (1856–1927) and Mauricio Nirenstein (1877–1935) with
2318-524: A professorial salary but with no teaching duties to burden him. Their invitation was all the more appealing to him because Berlin happened to be the home of his latest girlfriend, Elsa Löwenthal. He duly joined the Academy on 24 July 1913, and moved into an apartment in the Berlin district of Dahlem on 1 April 1914. He was installed in his Humboldt University position shortly thereafter. The outbreak of
2440-573: A proof of function, early results showed that, in the microgravity environment of the ISS, about half of the atoms formed into a magnetically insensitive halo-like cloud around the main body of the BEC. Consider a collection of N non-interacting particles, which can each be in one of two quantum states , | 0 ⟩ {\displaystyle |0\rangle } and | 1 ⟩ {\displaystyle |1\rangle } . If
2562-648: A result of Germany having driven the Jews out, they had lowered their "technical standards" and put the Allies ' technology ahead of theirs. Einstein later contacted leaders of other nations, including Turkey's Prime Minister, İsmet İnönü , to whom he wrote in September 1933, requesting placement of unemployed German-Jewish scientists. As a result of Einstein's letter, Jewish invitees to Turkey eventually totaled over "1,000 saved individuals". Locker-Lampson also submitted
SECTION 20
#17327727996852684-403: A short time after he had given the twelve year old Einstein a geometry textbook, the boy "had worked through the whole book. He thereupon devoted himself to higher mathematics ... Soon the flight of his mathematical genius was so high I could not follow." Einstein recorded that he had "mastered integral and differential calculus " while still just fourteen. His love of algebra and geometry
2806-505: A stronger condition is which defines a transition between a gas phase and a condensed phase. On the critical region it is possible to define a critical temperature and thermal wavelength: recovering the value indicated on the previous section. The critical values are such that if T < T c {\displaystyle T<T_{\text{c}}} or λ > λ c {\displaystyle \lambda >\lambda _{\text{c}}} , we are in
2928-447: A subsequent letter to physicist and friend Max Born , who had already emigrated from Germany to England, Einstein wrote, "... I must confess that the degree of their brutality and cowardice came as something of a surprise." After moving to the US, he described the book burnings as a "spontaneous emotional outburst" by those who "shun popular enlightenment", and "more than anything else in
3050-601: A tour of his studio and introduced him to Chaplin. They had an instant rapport, with Chaplin inviting Einstein and his wife, Elsa, to his home for dinner. Chaplin said Einstein's outward persona, calm and gentle, seemed to conceal a "highly emotional temperament", from which came his "extraordinary intellectual energy". Chaplin's film City Lights was to premiere a few days later in Hollywood, and Chaplin invited Einstein and Elsa to join him as his special guests. Walter Isaacson , Einstein's biographer, described this as "one of
3172-478: A twenty year old Serbian , Mileva Marić . Over the next few years, the pair spent many hours discussing their shared interests and learning about topics in physics that the polytechnic school's lectures did not cover. In his letters to Marić, Einstein confessed that exploring science with her by his side was much more enjoyable than reading a textbook in solitude. Eventually the two students became not only friends but also lovers. Historians of physics are divided on
3294-511: A visitor is the joyous, positive attitude to life ... The American is friendly, self-confident, optimistic, and without envy." In 1922, Einstein's travels were to the old world rather than the new. He devoted six months to a tour of Asia that saw him speaking in Japan, Singapore and Sri Lanka (then known as Ceylon ). After his first public lecture in Tokyo, he met Emperor Yoshihito and his wife at
3416-428: Is a liquid rather than a gas, which means that the interactions between the atoms are relatively strong; the original theory of Bose–Einstein condensation must be heavily modified in order to describe it. Bose–Einstein condensation remains, however, fundamental to the superfluid properties of helium-4. Note that helium-3 , a fermion , also enters a superfluid phase (at a much lower temperature) which can be explained by
3538-529: Is actually limited to the case of ultracold temperatures, which fits well for the most alkali atoms experiments. This approach originates from the assumption that the state of the BEC can be described by the unique wavefunction of the condensate ψ ( r → ) {\displaystyle \psi ({\vec {r}})} . For a system of this nature , | ψ ( r → ) | 2 {\displaystyle |\psi ({\vec {r}})|^{2}}
3660-433: Is different from Wikidata All article disambiguation pages All disambiguation pages Bose-Einstein condensate In condensed matter physics , a Bose–Einstein condensate ( BEC ) is a state of matter that is typically formed when a gas of bosons at very low densities is cooled to temperatures very close to absolute zero , i.e., 0 K (−273.15 °C; −459.67 °F). Under such conditions,
3782-413: Is exponential: For large N , the normalization constant C is (1 − p ) . The expected total number of particles not in the lowest energy state, in the limit that N → ∞ {\displaystyle N\rightarrow \infty } , is equal to It does not grow when N is large; it just approaches a constant. This will be a negligible fraction of the total number of particles. So
Bose–Einstein - Misplaced Pages Continue
3904-547: Is given by where: Interactions shift the value, and the corrections can be calculated by mean-field theory . This formula is derived from finding the gas degeneracy in the Bose gas using Bose–Einstein statistics . The critical temperature depends on the density. A more concise and experimentally relevant condition involves the phase-space density D = n λ T 3 {\displaystyle {\mathcal {D}}=n\lambda _{T}^{3}} , where
4026-417: Is in state | 0 ⟩ {\displaystyle |0\rangle } or in state | 1 ⟩ {\displaystyle |1\rangle } cannot be determined, so each value of K determines a unique quantum state for the whole system. Suppose now that the energy of state | 1 ⟩ {\displaystyle |1\rangle } is slightly greater than
4148-409: Is interpreted as the particle density, so the total number of atoms is N = ∫ d r → | ψ ( r → ) | 2 {\displaystyle N=\int d{\vec {r}}|\psi ({\vec {r}})|^{2}} Provided essentially all atoms are in the condensate (that is, have condensed to the ground state), and treating
4270-434: Is the thermal de Broglie wavelength . It is a dimensionless quantity. The transition to BEC occurs when the phase-space density is greater than critical value: in 3D uniform space. This is equivalent to the above condition on the temperature. In a 3D harmonic potential, the critical value is instead where n {\displaystyle n} has to be understood as the peak density. For an ideal Bose gas we have
4392-688: Is the analog of superfluidity. In 1999 condensation was demonstrated in antiferromagnetic Tl Cu Cl 3 , at temperatures as great as 14 K. The high transition temperature (relative to atomic gases) is due to the magnons' small mass (near that of an electron) and greater achievable density. In 2006, condensation in a ferromagnetic yttrium-iron-garnet thin film was seen even at room temperature, with optical pumping. Excitons , electron-hole pairs, were predicted to condense at low temperature and high density by Boer et al., in 1961. Bilayer system experiments first demonstrated condensation in 2003, by Hall voltage disappearance. Fast optical exciton creation
4514-485: The ETH Zurich , to take up a chair in theoretical physics. His teaching activities there centred on thermodynamics and analytical mechanics, and his research interests included the molecular theory of heat, continuum mechanics and the development of a relativistic theory of gravitation. In his work on the latter topic, he was assisted by his friend, Marcel Grossmann, whose knowledge of the kind of mathematics required
4636-645: The First World War in July 1914 marked the beginning of Einstein's gradual estrangement from the nation of his birth. When the " Manifesto of the Ninety-Three " was published in October 1914—a document signed by a host of prominent German thinkers that justified Germany's belligerence—Einstein was one of the few German intellectuals to distance himself from it and sign the alternative, eirenic " Manifesto to
4758-737: The German Empire , Einstein moved to Switzerland in 1895, and at the age of seventeen he enrolled in the mathematics and physics teaching diploma program at the Swiss federal polytechnic school . In 1903, he secured a permanent position at the Swiss Patent Office . In 1905, he submitted a successful PhD dissertation to the University of Zurich . In 1914, he moved to Berlin to join the Prussian Academy of Sciences and
4880-722: The Humboldt University of Berlin , becoming director of the Kaiser Wilhelm Institute for Physics in 1917. In 1933, while Einstein was visiting the United States, Adolf Hitler came to power in Germany. Horrified by the Nazi persecution of his fellow Jews, Einstein decided to remain in the US. On the eve of World War II , he endorsed a letter to President Franklin D. Roosevelt alerting him to
5002-627: The Imperial Palace , with thousands of spectators thronging the streets in the hope of catching a glimpse of him. (In a letter to his sons, he wrote that Japanese people seemed to him to be generally modest, intelligent and considerate, and to have a true appreciation of art. But his picture of them in his diary was less flattering: "[the] intellectual needs of this nation seem to be weaker than their artistic ones – natural disposition?" His journal also contains views of China and India which were uncomplimentary. Of Chinese people, he wrote that "even
Bose–Einstein - Misplaced Pages Continue
5124-509: The 1997 Nobel Prize in Physics ) and magnetic evaporative cooling . About four months later, an independent effort led by Wolfgang Ketterle at MIT condensed sodium-23 . Ketterle's condensate had a hundred times more atoms, allowing important results such as the observation of quantum mechanical interference between two different condensates. Cornell, Wieman and Ketterle won the 2001 Nobel Prize in Physics for their achievements. A group led by Randall Hulet at Rice University announced
5246-427: The 1999 textbook Thermal Physics by Ralph Baierlein. Bose–Einstein condensation also applies to quasiparticles in solids. Magnons , excitons , and polaritons have integer spin which means they are bosons that can form condensates. Magnons, electron spin waves, can be controlled by a magnetic field. Densities from the limit of a dilute gas to a strongly interacting Bose liquid are possible. Magnetic ordering
5368-414: The 2001 Nobel Prize in Physics . Bose-Einstein condensation of alkali gases is easier because they can be pre-cooled with laser cooling techniques, unlike atomic hydrogen at the time, which give a significant head start when performing the final forced evaporative cooling to cross the condensation threshold. These early studies founded the field of ultracold atoms , and hundreds of research groups around
5490-485: The British High Commissioner, welcomed him with a degree of ceremony normally only accorded to a visiting head of state, including a cannon salute. One reception held in his honor was stormed by people determined to hear him speak: he told them that he was happy that Jews were beginning to be recognized as a force in the world. Einstein's decision to tour the eastern hemisphere in 1922 meant that he
5612-653: The British capital to meet several people prominent in British scientific, political or intellectual life, and to deliver a lecture at King's College . In July 1921, he published an essay, "My First Impression of the U.S.A.", in which he sought to sketch the American character, much as had Alexis de Tocqueville in Democracy in America (1835). He wrote of his transatlantic hosts in highly approving terms: "What strikes
5734-627: The Europeans " instead. However, this expression of his doubts about German policy did not prevent him from being elected to a two-year term as president of the German Physical Society in 1916. When the Kaiser Wilhelm Institute for Physics opened its doors the following year—its foundation delayed because of the war—Einstein was appointed its first director, just as Planck and Nernst had promised. Einstein
5856-486: The German Empire, on 14 March 1879. His parents, secular Ashkenazi Jews , were Hermann Einstein , a salesman and engineer, and Pauline Koch . In 1880, the family moved to Munich 's borough of Ludwigsvorstadt-Isarvorstadt , where Einstein's father and his uncle Jakob founded Elektrotechnische Fabrik J. Einstein & Cie, a company that manufactured electrical equipment based on direct current . He often related
5978-641: The German consulate and surrendered his passport, formally renouncing his German citizenship. The Nazis later sold his boat and converted his cottage into a Hitler Youth camp. In April 1933, Einstein discovered that the new German government had passed laws barring Jews from holding any official positions , including teaching at universities. Historian Gerald Holton describes how, with "virtually no audible protest being raised by their colleagues", thousands of Jewish scientists were suddenly forced to give up their university positions and their names were removed from
6100-620: The Gross–Pitaevski equation (GPE) (also a non-linear Schrödinger equation ): where: In the case of zero external potential, the dispersion law of interacting Bose–Einstein-condensed particles is given by so-called Bogoliubov spectrum (for T = 0 {\displaystyle \ T=0} ): Albert Einstein Albert Einstein ( / ˈ aɪ n s t aɪ n / , EYEN -styne ; German: [ˈalbɛʁt ˈʔaɪnʃtaɪn] ; 14 March 1879 – 18 April 1955)
6222-464: The Indian physicist Satyendra Nath Bose , he laid the groundwork for Bose-Einstein statistics . For much of the last phase of his academic life, Einstein worked on two endeavors that proved ultimately unsuccessful. First, he advocated against quantum theory's introduction of fundamental randomness into science's picture of the world, objecting that "God does not play dice". Second, he attempted to devise
SECTION 50
#17327727996856344-725: The Investigation of the State of the Ether in a Magnetic Field". Einstein excelled at physics and mathematics from an early age, and soon acquired the mathematical expertise normally only found in a child several years his senior. He began teaching himself algebra, calculus and Euclidean geometry when he was twelve; he made such rapid progress that he discovered an original proof of the Pythagorean theorem before his thirteenth birthday. A family tutor, Max Talmud , said that only
6466-778: The Nobel award, the Royal Society 's Copley Medal , was not hung around Einstein's neck until 1925. He was elected an International Member of the American Philosophical Society in 1930. Einstein resigned from the Prussian Academy in March 1933. His accomplishments in Berlin had included the completion of the general theory of relativity, proving the Einstein–de Haas effect , contributing to
6588-561: The Nobel citation displayed a degree of doubt even about the work on photoelectricity that it acknowledged: it did not assent to Einstein's notion of the particulate nature of light, which only won over the entire scientific community when S. N. Bose derived the Planck spectrum in 1924. That same year, Einstein was elected an International Honorary Member of the American Academy of Arts and Sciences . Britain's closest equivalent of
6710-847: The Parish of Roughton, Norfolk . To protect Einstein, Locker-Lampson had two bodyguards watch over him; a photo of them carrying shotguns and guarding Einstein was published in the Daily Herald on 24 July 1933. Locker-Lampson took Einstein to meet Winston Churchill at his home, and later, Austen Chamberlain and former Prime Minister Lloyd George . Einstein asked them to help bring Jewish scientists out of Germany. British historian Martin Gilbert notes that Churchill responded immediately, and sent his friend, physicist Frederick Lindemann , to Germany to seek out Jewish scientists and place them in British universities. Churchill later observed that as
6832-574: The Sun that took place on 29 May 1919 provided an opportunity to put his theory of gravitational lensing to the test, and observations performed by Sir Arthur Eddington yielded results that were consistent with his calculations. Eddington's work was reported at length in newspapers around the world. On 7 November 1919, for example, the leading British newspaper, The Times , printed a banner headline that read: "Revolution in Science ;– New Theory of
6954-550: The Swiss authorities deemed him medically unfit for military service. He found that Swiss schools too appeared to have no use for him, failing to offer him a teaching position despite the almost two years that he spent applying for one. Eventually it was with the help of Marcel Grossmann 's father that he secured a post in Bern at the Swiss Patent Office , as an assistant examiner – level III . Patent applications that landed on Einstein's desk for his evaluation included ideas for
7076-656: The United States in 1933. In 1935, she was diagnosed with heart and kidney problems. She died in December 1936. A volume of Einstein's letters released by Hebrew University of Jerusalem in 2006 added further names to the catalog of women with whom he was romantically involved. They included Margarete Lebach (a married Austrian), Estella Katzenellenbogen (the rich owner of a florist business), Toni Mendel (a wealthy Jewish widow) and Ethel Michanowski (a Berlin socialite), with whom he spent time and from whom he accepted gifts while married to Löwenthal. After being widowed, Einstein
7198-541: The United States, drawn back to the US by the offer of a two month research fellowship at the California Institute of Technology . Caltech supported him in his wish that he should not be exposed to quite as much attention from the media as he had experienced when visiting the US in 1921, and he therefore declined all the invitations to receive prizes or make speeches that his admirers poured down upon him. But he remained willing to allow his fans at least some of
7320-535: The Universe ;– Newtonian Ideas Overthrown". With Eddington's eclipse observations widely reported not just in academic journals but by the popular press as well, Einstein became "perhaps the world's first celebrity scientist", a genius who had shattered a paradigm that had been basic to physicists' understanding of the universe since the seventeenth century. Einstein began his new life as an intellectual icon in America, where he arrived on 2 April 1921. He
7442-769: The University of Zurich, much admired by Alfred Kleiner, led to Zürich's luring him away from Bern with a newly created associate professorship. Promotion to a full professorship followed in April 1911, when he accepted a chair at the German Charles-Ferdinand University in Prague, a move which required him to become an Austrian citizen of the Austro-Hungarian Empire . His time in Prague saw him producing eleven research papers. In July 1912, he returned to his alma mater ,
SECTION 60
#17327727996857564-820: The age of sixteen, Einstein sat the entrance examination for the federal polytechnic school (later the Eidgenössische Technische Hochschule, ETH) in Zürich, Switzerland. He failed to reach the required standard in the general part of the test, but performed with distinction in physics and mathematics. On the advice of the polytechnic's principal, he completed his secondary education at the Argovian cantonal school (a gymnasium ) in Aarau , Switzerland, graduating in 1896. While lodging in Aarau with
7686-421: The bosons using mean-field theory , the energy (E) associated with the state ψ ( r → ) {\displaystyle \psi ({\vec {r}})} is: Minimizing this energy with respect to infinitesimal variations in ψ ( r → ) {\displaystyle \psi ({\vec {r}})} , and holding the number of atoms constant, yields
7808-569: The care of his mother or in temporary confinement in an asylum. After her death, he was committed permanently to Burghölzli , the Psychiatric University Hospital in Zürich. Einstein graduated from the federal polytechnic school in 1900, duly certified as competent to teach mathematics and physics. His successful acquisition of Swiss citizenship in February 1901 was not followed by the usual sequel of conscription ;
7930-558: The children are spiritless and look obtuse... It would be a pity if these Chinese supplant all other races. For the likes of us the mere thought is unspeakably dreary". ) He was greeted with even greater enthusiasm on the last leg of his tour, in which he spent twelve days in Mandatory Palestine , newly entrusted to British rule by the League of Nations in the aftermath of the First World War. Sir Herbert Samuel ,
8052-706: The configurations, about half the particles are in | 0 ⟩ {\displaystyle |0\rangle } and the other half in | 1 ⟩ {\displaystyle |1\rangle } . The balance is a statistical effect: the number of configurations is largest when the particles are divided equally. If the particles are indistinguishable, however, there are only N +1 different configurations. If there are K particles in state | 1 ⟩ {\displaystyle |1\rangle } , there are N − K particles in state | 0 ⟩ {\displaystyle |0\rangle } . Whether any particular particle
8174-449: The critical temperature and particle number corresponding to the conditions of negligible chemical potential μ {\displaystyle \mu } . In Bose–Einstein statistics distribution, μ {\displaystyle \mu } is actually still nonzero for BECs; however, μ {\displaystyle \mu } is less than the ground state energy. Except when specifically talking about
8296-496: The curriculum, allotting him a top grade of 6 for history, physics, algebra, geometry, and descriptive geometry. At seventeen, he enrolled in the four-year mathematics and physics teaching diploma program at the federal polytechnic school. Marie Winteler, a year older than him, took up a teaching post in Olsberg , Switzerland. The five other polytechnic school freshmen following the same course as Einstein included just one woman,
8418-420: The distinguishable case, for large N , the fraction in state | 0 ⟩ {\displaystyle |0\rangle } can be computed. It is the same as flipping a coin with probability proportional to p = exp(− E / T ) to land tails. In the indistinguishable case, each value of K is a single state, which has its own separate Boltzmann probability. So the probability distribution
8540-405: The divorce settlement, Einstein agreed that if he were to win a Nobel Prize, he would give the money that he received to Marić; he won the prize two years later. Einstein married Löwenthal in 1919. In 1923, he began a relationship with a secretary named Betty Neumann, the niece of his close friend Hans Mühsam. Löwenthal nevertheless remained loyal to him, accompanying him when he emigrated to
8662-400: The energy of state | 0 ⟩ {\displaystyle |0\rangle } by an amount E . At temperature T , a particle will have a lesser probability to be in state | 1 ⟩ {\displaystyle |1\rangle } by e − E / k T {\displaystyle e^{-E/kT}} . In the distinguishable case,
8784-585: The equation of state where v = V / N {\displaystyle v=V/N} is the per-particle volume, λ {\displaystyle \lambda } is the thermal wavelength , f {\displaystyle f} is the fugacity , and It is noticeable that g 3 / 2 {\displaystyle g_{3/2}} is a monotonically growing function of f {\displaystyle f} in f ∈ [ 0 , 1 ] {\displaystyle f\in [0,1]} , which are
8906-474: The fall of 1915, his reimagining of the mathematics of gravitation in terms of Riemannian geometry was complete, and he applied his new theory not just to the behavior of the Sun as a gravitational lens but also to another astronomical phenomenon, the precession of the perihelion of Mercury (a slow drift in the point in Mercury's elliptical orbit at which it approaches the Sun most closely). A total eclipse of
9028-557: The family of Jost Winteler , he fell in love with Winteler's daughter, Marie. (His sister, Maja , later married Winteler's son Paul. ) In January 1896, with his father's approval, Einstein renounced his citizenship of the German Kingdom of Württemberg in order to avoid conscription into military service . The Matura (graduation for the successful completion of higher secondary schooling), awarded to him in September 1896, acknowledged him to have performed well across most of
9150-476: The field exists. In 1911, he used the principle to estimate the amount by which a ray of light from a distant star would be bent by the gravitational pull of the Sun as it passed close to the Sun's photosphere (that is, the Sun's apparent surface). He reworked his calculation in 1913, having now found a way to model gravitation with the Riemann curvature tensor of a non-Euclidean four-dimensional spacetime . By
9272-452: The formation of bosonic Cooper pairs of two atoms (see also fermionic condensate ). The first "pure" Bose–Einstein condensate was created by Eric Cornell , Carl Wieman , and co-workers at JILA on 5 June 1995. They cooled a dilute vapor of approximately two thousand rubidium-87 atoms to below 170 nK using a combination of laser cooling (a technique that won its inventors Steven Chu , Claude Cohen-Tannoudji , and William D. Phillips
9394-483: The fraction ⟨ n 0 ⟩ N ≈ 0 {\displaystyle {\frac {\langle n_{0}\rangle }{N}}\approx 0} . At temperatures near to absolute 0, particles tend to condense in the fundamental state, which is the state with momentum p → = 0 {\displaystyle {\vec {p}}=0} . In 1938, Pyotr Kapitsa , John Allen and Don Misener discovered that helium-4 became
9516-408: The ground state, μ {\displaystyle \mu } can be approximated for most energy or momentum states as μ ≈ 0 {\displaystyle \mu \approx 0} . Nikolay Bogoliubov considered perturbations on the limit of dilute gas, finding a finite pressure at zero temperature and positive chemical potential. This leads to corrections for
9638-490: The ground state. The Bogoliubov state has pressure ( T = 0): P = g n 2 / 2 {\displaystyle P=gn^{2}/2} . The original interacting system can be converted to a system of non-interacting particles with a dispersion law. In some simplest cases, the state of condensed particles can be described with a nonlinear Schrödinger equation, also known as Gross–Pitaevskii or Ginzburg–Landau equation. The validity of this approach
9760-481: The life of the mind to work more closely with their counterparts in other countries. He was appointed as a German delegate rather than as a representative of Switzerland because of the machinations of two Catholic activists, Oskar Halecki and Giuseppe Motta . By persuading Secretary General Eric Drummond to deny Einstein the place on the committee reserved for a Swiss thinker, they created an opening for Gonzague de Reynold , who used his League of Nations position as
9882-528: The macroscopic occupation of the state is the order parameter . Bose–Einstein condensate was first predicted, generally, in 1924–1925 by Albert Einstein , crediting a pioneering paper by Satyendra Nath Bose on the new field now known as quantum statistics . In 1995, the Bose–Einstein condensate was created by Eric Cornell and Carl Wieman of the University of Colorado Boulder using rubidium atoms; later that year, Wolfgang Ketterle of MIT produced
10004-453: The most memorable scenes in the new era of celebrity". Chaplin visited Einstein at his home on a later trip to Berlin and recalled his "modest little flat" and the piano at which he had begun writing his theory. Chaplin speculated that it was "possibly used as kindling wood by the Nazis". In February 1933, while on a visit to the United States, Einstein knew he could not return to Germany with
10126-640: The number of nucleons , see #Isotopes ) such as atomic hydrogen, helium-4 , lithium-7, rubidium-87 or strontium-84. In 1938, Fritz London proposed the BEC as a mechanism for superfluidity in He and superconductivity . The quest to produce a Bose–Einstein condensate in the laboratory was stimulated by a paper published in 1976 by two program directors at the National Science Foundation (William Stwalley and Lewis Nosanow), proposing to use spin-polarized atomic hydrogen to produce
10248-764: The only values for which the series converge. Recognizing that the second term on the right-hand side contains the expression for the average occupation number of the fundamental state ⟨ n 0 ⟩ {\displaystyle \langle n_{0}\rangle } , the equation of state can be rewritten as Because the left term on the second equation must always be positive, λ 3 v > g 3 / 2 ( f ) {\displaystyle {\frac {\lambda ^{3}}{v}}>g_{3/2}(f)} , and because g 3 / 2 ( f ) ≤ g 3 / 2 ( 1 ) {\displaystyle g_{3/2}(f)\leq g_{3/2}(1)} ,
10370-399: The particle distribution will be biased slightly towards state | 0 ⟩ {\displaystyle |0\rangle } . But in the indistinguishable case, since there is no statistical pressure toward equal numbers, the most-likely outcome is that most of the particles will collapse into state | 0 ⟩ {\displaystyle |0\rangle } . In
10492-426: The particles will all be in different states. In this limit, the gas is classical. As the density increases or the temperature decreases, the number of accessible states per particle becomes smaller, and at some point, more particles will be forced into a single state than the maximum allowed for that state by statistical weighting. From this point on, any extra particle added will go into the ground state. To calculate
10614-424: The phenomena of capillarity"), in which he proposed a model of intermolecular attraction that he afterwards disavowed as worthless, was published in the journal Annalen der Physik in 1901. His 24-page doctoral dissertation also addressed a topic in molecular physics. Titled "Eine neue Bestimmung der Moleküldimensionen" ("A New Determination of Molecular Dimensions") and dedicated to his friend Marcel Grossman, it
10736-454: The potential German nuclear weapons program and recommended that the US begin similar research , though he generally viewed the idea of nuclear weapons with great dismay. In 1905, he published four groundbreaking papers , sometimes described as his annus mirabilis (miracle year). These papers outlined a theory of the photoelectric effect, explained Brownian motion , introduced his special theory of relativity, and demonstrated that if
10858-626: The presence of a Bose–Einstein condensate. Understanding what happens with the fraction of particles on the fundamental level is crucial. As so, write the equation of state for f = 1 {\displaystyle f=1} , obtaining So, if T ≪ T c {\displaystyle T\ll T_{\text{c}}} , the fraction ⟨ n 0 ⟩ N ≈ 1 {\displaystyle {\frac {\langle n_{0}\rangle }{N}}\approx 1} , and if T ≫ T c {\displaystyle T\gg T_{\text{c}}} ,
10980-455: The president of Columbia University , who described Einstein as "the ruling monarch of the mind". Harry Emerson Fosdick , pastor at New York's Riverside Church , gave Einstein a tour of the church and showed him a full-size statue that the church made of Einstein, standing at the entrance. Also during his stay in New York, he joined a crowd of 15,000 people at Madison Square Garden during
11102-409: The quantum theory of radiation, and the development of Bose–Einstein statistics . In 1907, Einstein reached a milestone on his long journey from his special theory of relativity to a new idea of gravitation with the formulation of his equivalence principle , which asserts that an observer in an infinitesimally small box falling freely in a gravitational field would be unable to find any evidence that
11224-427: The question of the extent to which Marić contributed to the insights of Einstein's annus mirabilis publications. There is at least some evidence that he was influenced by her scientific ideas, but there are scholars who doubt whether her impact on his thought was of any great significance at all. Correspondence between Einstein and Marić, discovered and published in 1987, revealed that in early 1902, while Marić
11346-560: The rise to power of the Nazis under Germany's new chancellor, Adolf Hitler . While at American universities in early 1933, he undertook his third two-month visiting professorship at the California Institute of Technology in Pasadena. In February and March 1933, the Gestapo repeatedly raided his family's apartment in Berlin. He and his wife Elsa returned to Europe in March, and during
11468-491: The rolls of institutions where they were employed. A month later, Einstein's works were among those targeted by the German Student Union in the Nazi book burnings , with Nazi propaganda minister Joseph Goebbels proclaiming, "Jewish intellectualism is dead." One German magazine included him in a list of enemies of the German regime with the phrase, "not yet hanged", offering a $ 5,000 bounty on his head. In
11590-423: The same term [REDACTED] This disambiguation page lists articles associated with the title Bose–Einstein . If an internal link led you here, you may wish to change the link to point directly to the intended article. Retrieved from " https://en.wikipedia.org/w/index.php?title=Bose–Einstein&oldid=1211917278 " Category : Disambiguation pages Hidden categories: Short description
11712-402: The special theory is correct, mass and energy are equivalent to each other. In 1915, he proposed a general theory of relativity that extended his system of mechanics to incorporate gravitation . A cosmological paper that he published the following year laid out the implications of general relativity for the modeling of the structure and evolution of the universe as a whole. In 1917, he wrote
11834-430: The statistical distribution of identical particles with integer spin , now called bosons . Bosons are allowed to share a quantum state. Einstein proposed that cooling bosonic atoms to a very low temperature would cause them to fall (or "condense") into the lowest accessible quantum state , resulting in a new form of matter. Bosons include the photon , polaritons , magnons , some atoms and molecules (depending on
11956-640: The support of several Argentine scholars, including Julio Rey Pastor , Jakob Laub , and Leopoldo Lugones . and was financed primarily by the Council of the University of Buenos Aires and the Asociación Hebraica Argentina (Argentine Hebraic Association) with a smaller contribution from the Argentine-Germanic Cultural Institution. In December 1930, Einstein began another significant sojourn in
12078-558: The time with him that they requested. After arriving in New York City, Einstein was taken to various places and events, including Chinatown , a lunch with the editors of The New York Times , and a performance of Carmen at the Metropolitan Opera , where he was cheered by the audience on his arrival. During the days following, he was given the keys to the city by Mayor Jimmy Walker and met Nicholas Murray Butler ,
12200-446: The transition temperature at any density, integrate, over all momentum states, the expression for maximum number of excited particles, p /(1 − p ) : When the integral (also known as Bose–Einstein integral ) is evaluated with factors of k B {\displaystyle k_{B}} and ℏ restored by dimensional analysis, it gives the critical temperature formula of the preceding section. Therefore, this integral defines
12322-920: The transmission of signals and the synchronization of clocks, matters which also figured in some of the inventions submitted to him for assessment. In 1902, Einstein and some friends whom he had met in Bern formed a group that held regular meetings to discuss science and philosophy. Their choice of a name for their club, the Olympia Academy , was an ironic comment upon its far from Olympian status. Sometimes they were joined by Marić, who limited her participation in their proceedings to careful listening. The thinkers whose works they reflected upon included Henri Poincaré , Ernst Mach and David Hume , all of whom significantly influenced Einstein's own subsequent ideas and beliefs. Einstein's first paper, "Folgerungen aus den Capillaritätserscheinungen" ("Conclusions drawn from
12444-589: The trip, they learned that the German Reichstag had passed the Enabling Act on 23 March, transforming Hitler's government into a de facto legal dictatorship, and that they would not be able to proceed to Berlin. Later on, they heard that their cottage had been raided by the Nazis and Einstein's personal sailboat confiscated. Upon landing in Antwerp , Belgium on 28 March, Einstein immediately went to
12566-443: The two states are equal in energy, each different configuration is equally likely. If we can tell which particle is which, there are 2 N {\displaystyle 2^{N}} different configurations, since each particle can be in | 0 ⟩ {\displaystyle |0\rangle } or | 1 ⟩ {\displaystyle |1\rangle } independently. In almost all of
12688-478: The velocity-distribution data indicates the formation of a Bose–Einstein condensate out of a gas of rubidium atoms. The false colors indicate the number of atoms at each velocity, with red being the fewest and white being the most. The areas appearing white and light blue are at the lowest velocities. The peak is not infinitely narrow because of the Heisenberg uncertainty principle : spatially confined atoms have
12810-446: The world now routinely produce BECs of dilute atomic vapors in their labs. Since 1995, many other atomic species have been condensed (see #Isotopes ), and BECs have also been realized using molecules, polaritons , other quasi-particles, and photons. This transition to BEC occurs below a critical temperature, which for a uniform three-dimensional gas consisting of non-interacting particles with no apparent internal degrees of freedom
12932-481: The world, fear the influence of men of intellectual independence". Einstein was now without a permanent home, unsure where he would live and work, and equally worried about the fate of countless other scientists still in Germany. Aided by the Academic Assistance Council , founded in April 1933 by British Liberal politician William Beveridge to help academics escape Nazi persecution, Einstein
13054-420: The year being celebrated as an annus mirabilis for physics akin to 1666 (the year in which Isaac Newton experienced his greatest epiphanies). The publications deeply impressed Einstein's contemporaries. Einstein's sabbatical as a civil servant approached its end in 1908, when he secured a junior teaching position at the University of Bern . In 1909, a lecture on relativistic electrodynamics that he gave at
13176-434: Was a German-born theoretical physicist who is widely held as one of the most influential scientists . Best known for developing the theory of relativity , Einstein also made important contributions to quantum mechanics . His mass–energy equivalence formula E = mc , which arises from special relativity , has been called "the world's most famous equation". He received the 1921 Nobel Prize in Physics . Born in
13298-622: Was a fractious pupil who found the Gymnasium's regimen and teaching methods far from congenial. He later wrote that the school's policy of strict rote learning was harmful to creativity. At the end of December 1894, a letter from a doctor persuaded the Luitpold's authorities to release him from its care, and he joined his family in Pavia. While in Italy as a teenager, he wrote an essay entitled "On
13420-528: Was able to leave Germany. He rented a house in De Haan, Belgium, where he lived for a few months. In late July 1933, he visited England for about six weeks at the invitation of the British Member of Parliament Commander Oliver Locker-Lampson , who had become friends with him in the preceding years. Locker-Lampson invited him to stay near his Cromer home in a secluded wooden cabin on Roughton Heath in
13542-406: Was born in Bern , Switzerland. Their son Eduard was born in Zürich in July 1910. In letters that Einstein wrote to Marie Winteler in the months before Eduard's arrival, he described his love for his wife as "misguided" and mourned the "missed life" that he imagined he would have enjoyed if he had married Winteler instead: "I think of you in heartfelt love every spare minute and am so unhappy as only
13664-525: Was briefly in a relationship with Margarita Konenkova, thought by some to be a Russian spy; her husband, the Russian sculptor Sergei Konenkov , created the bronze bust of Einstein at the Institute for Advanced Study at Princeton. Following an episode of acute mental illness at about the age of twenty, Einstein's son Eduard was diagnosed with schizophrenia . He spent the remainder of his life either in
13786-401: Was completed on 30 April 1905 and approved by Professor Alfred Kleiner of the University of Zurich three months later. (Einstein was formally awarded his PhD on 15 January 1906.) Four other pieces of work that Einstein completed in 1905— his famous papers on the photoelectric effect , Brownian motion , his special theory of relativity and the equivalence of mass and energy —have led to
13908-558: Was elected a Foreign Member of the Royal Netherlands Academy of Arts and Sciences in 1920, and a Foreign Member of the Royal Society in 1921 . In 1922, he was awarded the 1921 Nobel Prize in Physics "for his services to Theoretical Physics, and especially for his discovery of the law of the photoelectric effect". At this point some physicists still regarded the general theory of relativity skeptically, and
14030-438: Was greater than his own. In the spring of 1913, two German visitors, Max Planck and Walther Nernst , called upon Einstein in Zürich in the hope of persuading him to relocate to Berlin. They offered him membership of the Prussian Academy of Sciences , the directorship of the planned Kaiser Wilhelm Institute for Physics and a chair at the Humboldt University of Berlin that would allow him to pursue his research supported by
14152-508: Was impressed, translated the paper himself from English to German and submitted it for Bose to the Zeitschrift für Physik , which published it in 1924. (The Einstein manuscript, once believed to be lost, was found in a library at Leiden University in 2005. ) Einstein then extended Bose's ideas to matter in two other papers. The result of their efforts is the concept of a Bose gas , governed by Bose–Einstein statistics , which describes
14274-487: Was only realized in 1998. On 5 June 1995, the first gaseous condensate was produced by Eric Cornell and Carl Wieman at the University of Colorado at Boulder NIST – JILA lab, in a gas of rubidium atoms cooled to 170 nanokelvins (nK). Shortly thereafter, Wolfgang Ketterle at MIT produced a Bose–Einstein Condensate in a gas of sodium atoms. For their achievements Cornell, Wieman, and Ketterle received
14396-496: Was so great that at twelve, he was already confident that nature could be understood as a "mathematical structure". At thirteen, when his range of enthusiasms had broadened to include music and philosophy, Talmud introduced Einstein to Kant 's Critique of Pure Reason . Kant became his favorite philosopher; according to Talmud, "At the time he was still a child, only thirteen years old, yet Kant's works, incomprehensible to ordinary mortals, seemed to be clear to him." In 1895, at
14518-483: Was unable to go to Stockholm in the December of that year to participate in the Nobel prize ceremony. His place at the traditional Nobel banquet was taken by a German diplomat, who gave a speech praising him not only as a physicist but also as a campaigner for peace. A two-week visit to Spain that he undertook in 1923 saw him collecting another award, a membership of the Spanish Academy of Sciences signified by
14640-599: Was used to form condensates in sub-kelvin Cu 2 O in 2005 on. Polariton condensation was first detected for exciton-polaritons in a quantum well microcavity kept at 5 K. In June 2020, the Cold Atom Laboratory experiment on board the International Space Station successfully created a BEC of rubidium atoms and observed them for over a second in free-fall. Although initially just
14762-510: Was visiting her parents in Novi Sad , she gave birth to a daughter, Lieserl . When Marić returned to Switzerland it was without the child, whose fate is uncertain. A letter of Einstein's that he wrote in September 1903 suggests that the girl was either given up for adoption or died of scarlet fever in infancy. Einstein and Marić married in January 1903. In May 1904, their son Hans Albert
14884-617: Was welcomed to New York City by Mayor John Francis Hylan , and then spent three weeks giving lectures and attending receptions. He spoke several times at Columbia University and Princeton , and in Washington, he visited the White House with representatives of the National Academy of Sciences . He returned to Europe via London, where he was the guest of the philosopher and statesman Viscount Haldane . He used his time in
#684315