Reduced dynamics of two oscillators collectively coupled to a thermal bath

Tay, B.A.

doi:10.1103/physreve.87.052117

Cited by 3 publications

(8 citation statements)

References 48 publications

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“…The reduced dynamics of a pair of excitons in a thermal bath of phonons interacting through the trilinear boson model has the Kossakowski-Lindblad's form in the weak coupling limit, and can be solved analytically [15]. The exciton subsystem density matrix, ρ, evolves according to the equation ∂ρ/∂t = −Kρ, where [15]…”

Section: Solution Of the Markovian Master Equationmentioning

confidence: 99%

“…(B1)-(B4), that we will ignore in our discussion since they do not affect our results. We have also dropped a many-body term in K 0 [15] since it does not contribute to the reduced dynamics in the one excitation subspace we consider. We further assume that the phonon bath has the Bose-Einstein distribution…”

Section: Solution Of the Markovian Master Equationmentioning

confidence: 99%

“…In the reduced dynamics of K (30), the total excitation quantum number is a constant of motion. The underlying Liouville space therefore separates into disconnected subspaces according to this quantum number [15]. Each subspace evolves independently of each other and behaves like a finite-level system.…”

Section: Solution Of the Markovian Master Equationmentioning

confidence: 99%

“…In the weak coupling and rotating-wave approximation [11], the transformed system then reduces to the trilinear boson model [12][13][14]. The quantum Markovian master equation of this model can be solved analytically [15]. The reduced dynamics of the dimer subsystem permits a set of metastable states, and possesses a longer relaxation lifetime than the dephasing time of the individual oscillator coupled to the field in a similar way.…”

Section: Introductionmentioning

confidence: 99%

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Attenuation of excitation decay rate due to collective effect

2014

Phys. Rev. E

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We study a series of N oscillators, each coupled to its nearest neighbors, and linearly to a phonon field through the oscillator's number operator. We show that the Hamiltonian of a pair of adjacent oscillators, or a dimer, within the series of oscillators can be transformed into a form in which they are collectively coupled to the phonon field as a composite unit. In the weak coupling and rotating-wave approximation, the system behaves effectively as the trilinear boson model in the one excitation subspace of the dimer subsystem. The reduced dynamics of the one excitation subspace of the dimer subsystem coupled weakly to a phonon bath is similar to that of a two-level system, with a metastable state against the vacuum. The decay constant of the subsystem is proportional to the dephasing rate of the individual oscillator in a phonon bath, attenuated by a factor that depends on site asymmetry, intersite coupling, and the resonance frequency between the transformed oscillator modes, or excitons. As a result of the collective effect, the excitation relaxation lifetime is prolonged over the dephasing lifetime of an individual oscillator coupled to the same bath.

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Section: Solution Of the Markovian Master Equationmentioning

confidence: 99%

Section: Solution Of the Markovian Master Equationmentioning

confidence: 99%

Section: Solution Of the Markovian Master Equationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Attenuation of excitation decay rate due to collective effect

2014

Phys. Rev. E

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“…We have omitted a renormalization to the frequency of the exciton modes [29,33]. The transition rate between two exciton levels can be written in the form…”

Section: Reduced Dynamics Of Molecular Chainmentioning

confidence: 99%

Excitation relaxation in molecular chain and energy transfer at steady state

Tay

2021

Preprint

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We consider the reduced dynamics of a molecular chain weakly coupled to a phonon bath. With a small and constant inhomogeneity in the coupling, the excitation relaxation rates are obtained in closed form. They are dominated by transitions between exciton modes lying next to each other in the energy spectrum. The rates are quadratic in the number of sites in a long chain. Consequently, the evolution of site occupation numbers exhibits longer coherence lifetime for short chains only. When external source and sink are added, the rate equations of exciton occupation numbers are similar to those obtained earlier by Fröhlich to explain energy storage and energy transfer in biological systems. There is a clear separation of time scale into a faster one pertaining to internal influence of the chain and phonon bath, and a slower one determined by external influence, such as the pumping rate of the source, the absorption rate of the sink and the rate of radiation loss. The energy transfer efficiency at steady state depends strongly on these external parameters, and is robust against a change in the internal parameters, such as temperature and inhomogeneity. Excitations are predicted to concentrate to the lowest energy mode when the source power is sufficiently high. In the site basis, this implies that when sustained by a high power source, a sink positioned at the center of the chain is more efficient in trapping energy than a sink placed at its end. Analytic expressions of energy transfer efficiency are obtained in the high power and low power source limit. Parameters of a photosynthetic system are used as examples to illustrate the results.

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Excitation relaxation in a molecular chain and energy transfer at steady state

Tay

2021

Phys. Rev. E

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Reduced dynamics of two oscillators collectively coupled to a thermal bath

Cited by 3 publications

References 48 publications

Attenuation of excitation decay rate due to collective effect

Attenuation of excitation decay rate due to collective effect

Excitation relaxation in molecular chain and energy transfer at steady state

Excitation relaxation in a molecular chain and energy transfer at steady state

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