Memory effects in the relaxation of quantum open systems

Suárez, Alberto; Silbey, R.; Oppenheim, Irwin

doi:10.1063/1.463831

Cited by 246 publications

(291 citation statements)

References 18 publications

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“…In view of possible fast relaxation processes and the build-up of system-bath correlations [23,24,26] after the interaction has been switched on, this inverse propagator will not be defined on the total set of possible density matrices [32]. Still, it is a linear operator and thus the blow-up map (32) also is linear.…”

Section: Discussion Implications and Conclusionmentioning

confidence: 99%

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Is the dynamics of open quantum systems always linear?

2004

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We study the influence of the preparation of an open quantum system on its reduced time evolution. In contrast to the frequently considered case of an initial preparation where the total density matrix factorizes into a product of a system density matrix and a bath density matrix the time evolution generally is no longer governed by a linear map nor is this map affine. Put differently, the evolution is truly nonlinear and cannot be cast into the form of a linear map plus a term that is independent of the initial density matrix of the open quantum system. As a consequence, the inhomogeneity that emerges in formally exact generalized master equations is in fact a nonlinear term that vanishes for a factorizing initial state. The general results are elucidated with the example of two interacting spins prepared at thermal equilibrium with one spin subjected to an external field. The second spin represents the environment. The field allows the preparation of mixed density matrices of the first spin that can be represented as a convex combination of two limiting pure states, i.e. the preparable reduced density matrices make up a convex set. Moreover, the map from these reduced density matrices onto the corresponding density matrices of the total system is affine only for vanishing coupling between the spins. In general, the set of the accessible total density matrices is nonconvex.

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Section: Discussion Implications and Conclusionmentioning

confidence: 99%

“…in several works [19,20,21,22,23,24,25,26,27]. In an experiment this initial state is imposed by a preparation procedure.…”

mentioning

confidence: 99%

Is the dynamics of open quantum systems always linear?

2004

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“…This is also the standard result in other formalisms, obtained theoretically, e.g., in [25], and by numerical calculations [27].…”

Section: Probabilities For a Two-state System Coupled To A Bosonic Rementioning

confidence: 53%

“…(For a historical remark, singularities of the solutions in the density matrix at t = 0 were noted early on, in section 4 of [24]. The fast "slippage" or initially irregular behavior of solutions was recognized in [25]. ) We now assume that all solutions of the rate equations for the γ's correspond to a physical system in the ensemble.…”

Section: Initial Conditionsmentioning

confidence: 99%

A “square-root” method for the density matrix and its applications to Lindblad operators

Yahalom

Englman

2006

Physica A: Statistical Mechanics and its Applications

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The evolution of open systems, subject to both Hamiltonian and dissipative forces, is studied by writing the nm element of the time (t) dependent density matrix in the formThe so called "square root factors", the γ(t)'s, are non-square matrices and are averaged over A systems (α) of the ensemble. This square-root description is exact. Evolution equations are then postulated for the γ(t) factors, such as to reduce to the Lindblad-type evolution equations for the diagonal terms in the density matrix. For the off-diagonal terms they differ from the Lindblad-equations. The "square root factors" γ(t) are not unique and the equations for the γ(t)'s depend on the specific representation chosen. Two criteria can be suggested for fixing the choice of γ(t)'s one is simplicity of the resulting equations and the other has to do with the reduction of the difference between the γ(t) formalism and the Lindblad-equations. When the method is tested on cases which have been previously treated by other methods, our results agree with them. Examples chosen are (i) molecular systems, such that are either periodically driven 1 near level degeneracies, for which we calculate the decoherence occurring in multiple Landau-Zener transition, or else when undergoing descent around conical intersections in the potential surfaces, (ii) formal dissipative systems with Lindblad-type operators representing either a non-Markovian process or a two-state system coupled to bosons.Attractive features of the present factorization method are complete positivity, the no higher than linear increase of the implementation effort with the number of states involved and the introduction of randomness only at the start of the process.

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“…In particular, it has been shown that this deficiency has a physical origin, as most of the MEs are only compatible with certain class of initial states, or are only applicable in some parameter range. [82][83][84] An alternative approach is the restriction of the equations of motion to satisfy some minimal requirements such as positivity and trace preservation. The KL equation is an example of the latter approach, 85,86 but non-Markovian analogues also exist.…”

Section: E Deficiencies Of Arbitrary Master Equation Approachesmentioning

confidence: 99%

Remarks on time-dependent [current]-density functional theory for open quantum systems

Yuen-Zhou

Aspuru‐Guzik

2013

Phys. Chem. Chem. Phys.

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Time-dependent [current]-density functional theory for open quantum systems (OQS) has emerged as a formalism that can incorporate dissipative effects in the dynamics of many-body quantum systems.Here, we review and clarify some formal aspects of these theories that have been recently questioned in the literature. In particular, we provide theoretical support for the following conclusions: (1) contrary to what we and others had stated before, within the master equation framework, there is in fact a one-to-one mapping between vector potentials and current densities for fixed initial state, particleparticle interaction, and memory kernel; (2) regardless of the first conclusion, all of our recently suggested Kohn-Sham (KS) schemes to reproduce the current and particle densities of the original OQS, and in particular, the use of a KS closed driven system, remains formally valid; (3) the Lindblad master equation maintains the positivity of the density matrix regardless of the time-dependence of the Hamiltonian or the dissipation operators; (4) within the stochastic Schrödinger equation picture, a one-to-one mapping from stochastic vector potential to stochastic current density for individual trajectories has not been proven so far, except in the case where the vector potential is the same for every member of the ensemble, in which case, it reduces to the Lindblad master equation picture; (5) master equations may violate certain desired properties of the density matrix, such as positivity, but they remain as one of the most useful constructs to study OQS when the environment is not easily incorporated explicitly in the calculation. The conclusions support our previous work as formally rigorous, offer new insights into it, and provide a common ground to discuss related theories.

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Memory effects in the relaxation of quantum open systems

Cited by 246 publications

References 18 publications

Is the dynamics of open quantum systems always linear?

Is the dynamics of open quantum systems always linear?

A “square-root” method for the density matrix and its applications to Lindblad operators

Remarks on time-dependent [current]-density functional theory for open quantum systems

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