Two-time correlation functions in an exactly solvable spin-boson model

Morozov, V. G.; Roepke, G.

doi:10.1007/s11232-011-0104-0

Cited by 8 publications

(7 citation statements)

References 8 publications

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“…We consider a simple version of the spin-boson model describing a two-state system (S) coupled to a bath (B) of harmonic oscillators [25,27]. In the spin representation for a qubit, the total Hamiltonian of the model is written as (in our units = 1)…”

Section: The Model Hamiltonianmentioning

confidence: 99%

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Master equation for open quantum systems: Zwanzig-Nakajima projection technique and the intrinsic bath dynamics

Ignatyuk,

Morozov

2019

Preprint

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The non-Markovian master equation for open quantum systems is obtained by generalization of the ordinary Zwanzig-Nakajima (ZN) projection technique. To this end, a coupled chain of equations for the reduced density matrices of the bath ̺ B (t) and the system ̺ S (t) are written down. A formal solution of the equation for ̺ B (t), having been inserted in the equation for the reduced density matrix of the system, in the 2-nd approximation in interaction yields a very specific extra term in the generalized master equation. This term, being nonlinear in ̺ S (t), is related to the intrinsic bath dynamics and vanishes in the Markovian limit. To verify the consistence and robustness of our approach, we applied the generalized ZN projection scheme to a simple dephasing model. It is shown that consideration of the lowest order in interaction is insufficient to describe time evolution of the system coherence adequately. We explain this fact by analyzing the exact and approximate forms of ̺ B (t) and give some hints how to take the dynamic correlations (which originate from the spin-bath coupling) into account.

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Section: The Model Hamiltonianmentioning

confidence: 99%

“…On the other hand, transformation rules the for creation/annihilation operators look as follows [27]:…”

Section: Appendix Bmentioning

confidence: 99%

Master equation for open quantum systems: Zwanzig-Nakajima projection technique and the intrinsic bath dynamics

Ignatyuk,

Morozov

2019

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…We consider a simple version of the spin-boson model describing the two-state system (S) coupled to the bath (B) of harmonic oscillators [24,29]. In the spin representation for a qubit, the total Hamiltonian of the model is written as…”

Section: Non-markovian Quantum Kinetic Equation For the Dephasing Modelmentioning

confidence: 99%

Decoherence in open quantum systems: influence of the intrinsic bath dynamics

Ignatyuk,

Morozov

2021

Preprint

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The non-Markovian master equation for open quantum systems is obtained by generalization of the standard Zwanzig-Nakajima (ZN) projection technique. To this end, a coupled chain of equations for the reduced density matrices of the bath ̺ B (t) and of the system ̺ S (t) are written. Formal solution of the equation for ̺ B (t) in the 2-nd approximation in interaction yields a specific extra term, related to the intrinsic bath dynamics. This term is nonlinear in the reduced density matrix ̺ S (t), and vanishes in the Markovian limit. To verify the consistence and robustness of our approach, we apply the generalized ZN projection scheme to a simple dephasing model. We study the obtained kinetic equation both in the Markovian approximation and beyond it (for the term related to the intrinsic bath dynamics) and compare the results with the exact ones.

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“…However, the choice of an initial product state has to be put under scrutiny, like all other assumptions used to treat open quantum systems, whenever one wants to associate a given description with concrete physical systems. While the absence of initial system-environment correlations is naturally expected if the interaction between the open system and the environment starts at a specific instant of time and it can be rigorously proven to be justified in the weak-coupling regime [4,5], it is by now clear that initial correlations can have instead a significant impact in many situations, including the interaction of a two-level system with bosonic modes [6][7][8][9], the damped harmonic oscillator [10][11][12][13], spin systems [14], and even many-body [15,16] and transport-related [17][18][19][20] open systems. In addition, a full understanding of the role of the correlations, and possibly of their quantum or classical nature, in the evolution of open quantum systems should indeed include the analysis of those correlations that are present between the system and the environment at the initial time, thus complementing the related studies on the correlations built up by the dynamics [21][22][23][24][25].…”

Section: Introductionmentioning

confidence: 99%

Adapted projection operator technique for the treatment of initial correlations

et al. 2021

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Standard theoretical descriptions of the dynamics of open quantum systems rely on the assumption that the correlations with the environment can be neglected at some reference (initial) time. While being reasonable in specific instances, such as when the coupling between the system and the environment is weak or when the interaction starts at a distinguished time, the use of initially uncorrelated states is questionable if one wants to deal with general models, taking into account the mutual influence that the open-system and environmental evolutions perform on each other. Here we introduce a perturbative method that can be applied to any microscopic modeling of the system-environment interaction, including fully general initial correlations. Extending the standard technique based on projection operators that single out the relevant part of the global dynamics, we define a family of projections adapted to a convenient decomposition of the initial state, which involves a convex mixture of product operators with proper environmental states. This leads us to characterize the open-system dynamics via an uncoupled system of differential equations, which are homogeneous and whose number is limited by the dimensionality of the open system, for any kind of initial correlations. Our method is further illustrated by means of two case studies, for which it reproduces the expected dynamical behavior in the long-time regime more consistently than the standard projection technique.

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Two-time correlation functions in an exactly solvable spin-boson model

Cited by 8 publications

References 8 publications

Master equation for open quantum systems: Zwanzig-Nakajima projection technique and the intrinsic bath dynamics

Master equation for open quantum systems: Zwanzig-Nakajima projection technique and the intrinsic bath dynamics

Decoherence in open quantum systems: influence of the intrinsic bath dynamics

Adapted projection operator technique for the treatment of initial correlations

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