Misplaced Pages

#52947

33-597: FMO may refer to: Fenna-Matthews-Olson complex Fish Marketing Organisation , a statutory body of Hong Kong Flavin-containing monooxygenase Flexible macroblock ordering Fragment molecular orbital Frontier molecular orbital theory Münster Osnabrück Airport in North Rhine-Westphalia, Germany Netherlands Development Finance Company (Dutch: Nederlandse Financierings-Maatschappij voor Ontwikkelingslanden N.V. ) Topics referred to by

66-405: A linear transformation , a Fourier transformation . This transformation is itself a quantum superposition and every position wave function can be represented as a superposition of momentum wave functions and vice versa. These superpositions involve an infinite number of component waves. Other transformations express a quantum solution as a superposition of eigenvectors , each corresponding to

99-521: A computational device, improving computational speeds at room temperature, yielding 100-1000x efficiency. Quantum superposition Quantum superposition is a fundamental principle of quantum mechanics that states that linear combinations of solutions to the Schrödinger equation are also solutions of the Schrödinger equation. This follows from the fact that the Schrödinger equation

132-543: A possible result of a measurement on the quantum system. An eigenvector ψ i {\displaystyle \psi _{i}} for a mathematical operator, A ^ {\displaystyle {\hat {A}}} , has the equation A ^ ψ i = λ i ψ i {\displaystyle {\hat {A}}\psi _{i}=\lambda _{i}\psi _{i}} where λ i {\displaystyle \lambda _{i}}

165-437: A qubit with both position and spin, the state is a superposition of all possibilities for both: where we have a general state Ψ {\displaystyle \Psi } is the sum of the tensor products of the position space wave functions and spinors. Successful experiments involving superpositions of relatively large (by the standards of quantum physics) objects have been performed. In quantum computers ,

198-649: A sum or superposition of the eigenstates of an Hermitian operator, like the Hamiltonian, because the eigenstates form a complete basis: where | n ⟩ {\displaystyle |n\rangle } are the energy eigenstates of the Hamiltonian. For continuous variables like position eigenstates, | x ⟩ {\displaystyle |x\rangle } : where ϕ α ( x ) = ⟨ x | α ⟩ {\displaystyle \phi _{\alpha }(x)=\langle x|\alpha \rangle }

231-591: Is a linear differential equation in time and position. More precisely, the state of a system is given by a linear combination of all the eigenfunctions of the Schrödinger equation governing that system. An example is a qubit used in quantum information processing . A qubit state is most generally a superposition of the basis states | 0 ⟩ {\displaystyle |0\rangle } and | 1 ⟩ {\displaystyle |1\rangle } : where | Ψ ⟩ {\displaystyle |\Psi \rangle }

264-503: Is different from Wikidata All article disambiguation pages All disambiguation pages Fenna-Matthews-Olson complex Since the structure is available, calculating structure-based optical spectra is possible for comparison with experimental optical spectra. In the simplest case only the excitonic coupling of the BChls is taken into account. More realistic theories consider pigment-protein coupling. An important property

297-569: Is made up of a superposition of energy eigenstates. Now consider the more concrete case of an electron that has either spin up or down. We now index the eigenstates with the spinors in the z ^ {\displaystyle {\hat {z}}} basis: where | ↑ ⟩ {\displaystyle |{\uparrow }\rangle } and | ↓ ⟩ {\displaystyle |{\downarrow }\rangle } denote spin-up and spin-down states respectively. As previously discussed,

330-425: Is not possible. Because energy can exist in a superposition of states, it can travel all routes within a material at the same time. When a photon finds the correct destination, the superposition collapses, making the energy available. However, no purely quantum process can be wholly responsible, because some quantum processes slow down the movement of quantized objects through networks. Anderson localization prevents

363-541: Is one possible measured quantum value for the observable A {\displaystyle A} . A superposition of these eigenvectors can represent any solution: Ψ = ∑ n a i ψ i . {\displaystyle \Psi =\sum _{n}a_{i}\psi _{i}.} The states like ψ i {\displaystyle \psi _{i}} are called basis states. Important mathematical operations on quantum system solutions can be performed using only

SECTION 10

#1732775399053

396-542: Is still debated in literature with the suggestion that the original experiments were interpreted incorrectly assigning the spectral oscillations to electronic coherences instead of ground-state vibrational coherences, which will naturally be expected to live longer due to the narrower spectral width of vibrational transitions. The problem of finding a reaction centre in a protein matrix is formally equivalent to many problems in computing. Mapping computing problems onto reaction center searches may allow light harvesting to work as

429-399: Is sufficient to destroy the interference pattern, if the path information is accessible in principle from the experiment or even if it is dispersed in the environment and beyond any technical possibility to be recovered, but in principle still ‘‘out there.’’ The absence of any such information is the essential criterion for quantum interference to appear. Any quantum state can be expanded as

462-625: Is the quantum state of the qubit, and | 0 ⟩ {\displaystyle |0\rangle } , | 1 ⟩ {\displaystyle |1\rangle } denote particular solutions to the Schrödinger equation in Dirac notation weighted by the two probability amplitudes c 0 {\displaystyle c_{0}} and c 1 {\displaystyle c_{1}} that both are complex numbers. Here | 0 ⟩ {\displaystyle |0\rangle } corresponds to

495-497: Is the local transition energy (site energy) of the BChls, different for each, due to their individual local protein environment. The site energies of the BChls determine the direction of the energy flow. Some structural information on the FMO-RC super complex is available, which was obtained by electron microscopy and linear dichroism spectra measured on FMO trimers and FMO-RC complexes. From these measurements, two orientations of

528-495: Is the projection of the state into the | x ⟩ {\displaystyle |x\rangle } basis and is called the wave function of the particle. In both instances we notice that | α ⟩ {\displaystyle |\alpha \rangle } can be expanded as a superposition of an infinite number of basis states. Given the Schrödinger equation where | n ⟩ {\displaystyle |n\rangle } indexes

561-400: Is very common in textbooks and papers on quantum mechanics and superposition of basis states is a fundamental tool in quantum mechanics. Paul Dirac described the superposition principle as follows: The non-classical nature of the superposition process is brought out clearly if we consider the superposition of two states, A and B , such that there exists an observation which, when made on

594-534: The Born rule ). Before the measurement occurs the qubit is in a superposition of both states. The interference fringes in the double-slit experiment provide another example of the superposition principle. The theory of quantum mechanics postulates that a wave equation completely determines the state of a quantum system at all times. Furthermore, this differential equation is restricted to be linear and homogeneous . These conditions mean that for any two solutions of

627-763: The FMO complex exhibits remarkably long quantum coherence , but after about a decade of debate, it was shown that this quantum coherence has no significance to the functioning of the complex. Furthermore, it was shown that the reported long lived oscillations observed in the spectra are solely due to groundstate vibrational dynamics and do not reflect any energy transfer dynamics. Light harvesting in photosynthesis employs both classical and quantum mechanical processes with an energy efficiency of almost 100 percent. For light to produce energy in classical processes, photons must reach reaction sites before their energy dissipates in less than one nanosecond. In photosynthetic processes, this

660-516: The FMO complex relative to the RC are possible. The orientation with BChl 3 and 4 close to the RC and BChl 1 and 6 (following Fenna and Matthews' original numbering) oriented towards the chlorosomes is useful for efficient energy transfer. The complex is the simplest PPC appearing in nature and therefore a suitable test object for the development of methods that can be transferred to more complex systems like photosystem I. Engel and co-workers observed that

693-574: The classical 0 bit , and | 1 ⟩ {\displaystyle |1\rangle } to the classical 1 bit. The probabilities of measuring the system in the | 0 ⟩ {\displaystyle |0\rangle } or | 1 ⟩ {\displaystyle |1\rangle } state are given by | c 0 | 2 {\displaystyle |c_{0}|^{2}} and | c 1 | 2 {\displaystyle |c_{1}|^{2}} respectively (see

SECTION 20

#1732775399053

726-500: The coefficients of the superposition, suppressing the details of the superposed functions. This leads to quantum systems expressed in the Dirac bra-ket notation : | v ⟩ = d 1 | 1 ⟩ + d 2 | 2 ⟩ {\displaystyle |v\rangle =d_{1}|1\rangle +d_{2}|2\rangle } This approach is especially effect for systems like quantum spin with no classical coordinate analog. Such shorthand notation

759-465: The environment changes the wave-like nature of the quantum state just enough to prevent Anderson localisation, while the quantum zeno effect extends the quantum state's lifetime, allowing it to reach the reaction centre. The proposed long lifetime of quantum coherence in the FMO influenced many scientists to investigate quantum coherence in the system, with Engel's 2007 paper being cited over 1500 times within 5 years of its publication. The proposal of Engel

792-450: The magnitudes of the complex coefficients give the probability of finding the electron in either definite spin state: where the probability of finding the particle with either spin up or down is normalized to 1. Notice that c 1 {\displaystyle c_{1}} and c 2 {\displaystyle c_{2}} are complex numbers, so that is an example of an allowed state. We now get If we consider

825-434: The original states. Anton Zeilinger , referring to the prototypical example of the double-slit experiment , has elaborated regarding the creation and destruction of quantum superposition: "[T]he superposition of amplitudes ... is only valid if there is no way to know, even in principle, which path the particle took. It is important to realize that this does not imply that an observer actually takes note of what happens. It

858-448: The same term [REDACTED] This disambiguation page lists articles associated with the title FMO . 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=FMO&oldid=1147217953 " Category : Disambiguation pages Hidden categories: Articles containing Dutch-language text Short description

891-518: The set of eigenstates of the Hamiltonian with energy eigenvalues E n , {\displaystyle E_{n},} we see immediately that where is a solution of the Schrödinger equation but is not generally an eigenstate because E n {\displaystyle E_{n}} and E n ′ {\displaystyle E_{n'}} are not generally equal. We say that | Ψ ⟩ {\displaystyle |\Psi \rangle }

924-450: The spread of quantum states in random media. Because the state acts like a wave, it is vulnerable to disruptive interference effects. Another issue is the quantum zeno effect , in which an unstable state never changes if it is continuously measured/watched, because watching constantly nudges the state, preventing it from collapsing. Interactions between quantum states and the environment act like measurements. The classical interaction with

957-451: The superposition of momentum functions are also solutions: Φ ( p → ) = d 1 Φ 1 ( p → ) + d 2 Φ 2 ( p → ) {\displaystyle \Phi ({\vec {p}})=d_{1}\Phi _{1}({\vec {p}})+d_{2}\Phi _{2}({\vec {p}})} The position and momentum solutions are related by

990-426: The superposition process. It will never be different from both a and b [i.e., either a or b ]. The intermediate character of the state formed by superposition thus expresses itself through the probability of a particular result for an observation being intermediate between the corresponding probabilities for the original states, not through the result itself being intermediate between the corresponding results for

1023-419: The system in state A , is certain to lead to one particular result, a say, and when made on the system in state B is certain to lead to some different result, b say. What will be the result of the observation when made on the system in the superposed state? The answer is that the result will be sometimes a and sometimes b , according to a probability law depending on the relative weights of A and B in

FMO - Misplaced Pages Continue

1056-449: The wave equation has more than two solutions, combinations of all such solutions are again valid solutions. The quantum wave equation can be solved using functions of position, Ψ ( r → ) {\displaystyle \Psi ({\vec {r}})} , or using functions of momentum, Φ ( p → ) {\displaystyle \Phi ({\vec {p}})} and consequently

1089-599: The wave equation, Ψ 1 {\displaystyle \Psi _{1}} and Ψ 2 {\displaystyle \Psi _{2}} , a linear combination of those solutions also solve the wave equation: Ψ = c 1 Ψ 1 + c 2 Ψ 2 {\displaystyle \Psi =c_{1}\Psi _{1}+c_{2}\Psi _{2}} for arbitrary complex coefficients c 1 {\displaystyle c_{1}} and c 2 {\displaystyle c_{2}} . If

#52947