Exploring complete positivity in hierarchy equations of motion

Witt, Björn; Rudnicki, Łukasz; Tanimura, Yoshitaka; Mintert, Florian

doi:10.1088/1367-2630/19/1/013007

Cited by 12 publications

(9 citation statements)

References 36 publications

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“…In simulations shown below in this work we truncate after 5 -15 levels, depending on the specific system. We note that depending on the system parameters, truncation of the HEOM can occasionally cause loss of positivity [43][44][45] and it is important to check that this is not the case in any specific calculation.…”

Section: Chromophore Interaction With Phonon Bathmentioning

confidence: 99%

Single-photon absorption by single photosynthetic light-harvesting complexes

Chan

Gamel

Fleming

et al. 2018

J. Phys. B: At. Mol. Opt. Phys.

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We provide a unified theoretical approach to the quantum dynamics of absorption of single photons and subsequent excitonic energy transfer in photosynthetic light-harvesting complexes. Our analysis combines a continuous mode n -photon quantum optical master equation for the chromophoric system with the hierarchy of equations of motion describing excitonic dynamics in presence of non-Markovian coupling to vibrations of the chromophores and surrounding protein. We apply the approach to simulation of absorption of single-photon coherent states by pigment-protein complexes containing between one and seven chromophores, and compare with results obtained by excitation using a thermal radiation field. We show that the values of excitation probability obtained under single-photon absorption conditions can be consistently related to bulk absorption cross-sections. Analysis of the timescale and efficiency of single-photon absorption by light-harvesting systems within this full quantum description of pigment-protein dynamics coupled to a quantum radiation field reveals a non-trivial dependence of the excitation probability and the excited state dynamics induced by exciton-phonon coupling during and subsequent to the pulse, on the bandwidth of the incident photon pulse. For bandwidths equal to the spectral bandwidth of Chlorophyll a, our results yield an estimation of an average time of ∼0.09 s for a single chlorophyll chromophore to absorb the energy equivalent of one (single-polarization) photon under irradiation by single-photon states at the intensity of sunlight.

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Section: Chromophore Interaction With Phonon Bathmentioning

confidence: 99%

Single-photon absorption by single photosynthetic light-harvesting complexes

Chan

Gamel

Fleming

et al. 2018

J. Phys. B: At. Mol. Opt. Phys.

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“…for any pair X, Y . The set of equations ( 27) is a special case of hierarchical master equations of motion (HEOM) considered in [49]…”

Section: Hierarchy Of Master Equationsmentioning

confidence: 99%

“…In our case n = 2 and L ij are in general time-dependent. In [48,49] one can find a characterization of the matrix super-operator L ij giving rise to legitimate evolution of the system. One solves the hierarchy (27) (cf Appendix) and finds for the system's density operator [27]…”

Section: Hierarchy Of Master Equationsmentioning

confidence: 99%

Eternally non-Markovian dynamics of a qubit interacting with a single-photon wavepacket

Dąbrowska,

Chruściński,

Chakraborty

et al. 2020

Preprint

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An evolution of a two-level system (qubit) interacting with a single-photon wave packet is analyzed. It is shown that a hierarchy of master equations gives rise to phase covariant qubit evolution. The temporal correlations in the input field induce nontrivial memory effects for the evolution of a qubit. It is shown that in the resonant case whenever time-local generator is regular (does not display singularities) the qubit evolution never displays information backflow. However, in general the generator might be highly singular leading to intricate non-Markovian effects. A detailed analysis of the exponential profile is provided which allows to illustrate all characteristic feature of the qubit evolution.

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“…Only in some limited cases definite statements in this respect have been obtained, see e.g. [9,14,[36][37][38][39][40][41][42][43][44][45].…”

Section: Structure Of the Master Equationsmentioning

confidence: 99%

The interplay between local and non-local master equations: exact and approximated dynamics

Megier,

Smirne,

Vacchini

2020

Preprint

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Master equations are a useful tool to describe the evolution of open quantum systems. In order to characterize the mathematical features and the physical origin of the dynamics, it is often useful to consider different kinds of master equations for the same system. Here, we derive an exact connection between the time-local and the integro-differential descriptions, focusing on the class of commutative dynamics. The use of the damping-basis formalism allows us to devise a general procedure to go from one master equation to the other and vice-versa, by working with functions of time and their Laplace transforms only. We further analyze the Lindbladian form of the time-local and the integro-differential master equations, where we account for the appearance of different sets of Lindbladian operators. In addition, we investigate a Redfield-like approximation, that transforms the exact integro-differential equation into a time-local one by means of a coarse graining in time. Besides relating the structure of the resulting master equation to those associated with the exact dynamics, we study the effects of the approximation on Markovianity. In particular, we show that, against expectation, the coarse graining in time can possibly introduce memory effects, leading to a violation of a divisibility property of the dynamics.

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Exploring complete positivity in hierarchy equations of motion

Cited by 12 publications

References 36 publications

Single-photon absorption by single photosynthetic light-harvesting complexes

Single-photon absorption by single photosynthetic light-harvesting complexes

Eternally non-Markovian dynamics of a qubit interacting with a single-photon wavepacket

The interplay between local and non-local master equations: exact and approximated dynamics

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