On Time-Local Generators of Quantum Evolution

Chruściński, Dariusz

doi:10.1142/s1230161214400046

Cited by 28 publications

(30 citation statements)

References 29 publications

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“…the corresponding task is to envisage conditions on the operator kernel K(t) warranting preservation of positivity and trace of the solutions of the integrodifferential equation. In both cases the most general solution to the problem is not known, even not heuristically, while partial results have been recently obtained [29,30,31,32,33,34,35,34,36]. In particular we will consider how to obtain well-defined quantum memory kernels K(t).…”

Section: Non-markovian Evolution Equationsmentioning

confidence: 99%

Frontiers of Open Quantum System Dynamics

Vacchini

2019

Quantum Physics and Geometry

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We briefly examine recent developments in the field of open quantum system theory, devoted to the introduction of a satisfactory notion of memory for a quantum dynamics. In particular, we will consider a possible formalization of the notion of non-Markovian dynamics, as well as the construction of quantum evolution equations featuring a memory kernel. Connections will be draw to the corresponding notions in the framework of classical stochastic processes, thus pointing to the key differences between a quantum and classical formalization of the notion of memory effects.

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Section: Non-markovian Evolution Equationsmentioning

confidence: 99%

Frontiers of Open Quantum System Dynamics

Vacchini

2019

Quantum Physics and Geometry

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“…In this section we generalize the IFE states defined for unitary evolution to the evolution corresponding to quantum Markovian semigroup [19,20,21,22,23] (see also recent review [24]). A general quantum evolution of a system living in the Hilbert space H is described by a dynamical map, that is, a family of completely positive trace-preserving maps (CPTP) Λ t : B(H) → B(H) such that Λ 0 = 1l (an identity map).…”

Section: Markovian Semigroup and Decoherence Free Statesmentioning

confidence: 99%

Interaction free and decoherence free states

Chruściński¹,

Napoli²,

Guccione³

et al. 2015

Phys. Scr.

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An interaction free evolving state of a closed bipartite system composed of two interacting subsystems is a generally mixed state evolving as if the interaction were a c-number. In this paper we find the characteristic equation of states possessing similar properties for a bipartite systems governed by a linear dynamical equation whose generator is sum of a free term and an interaction term. In particular in the case of a small system coupled to its environment, we deduce the characteristic equation of decoherence free states namely mixed states evolving as if the interaction term were effectively inactive. Several examples illustrate the applicability of our theory in different physical contexts.Dedicated to Margarita and Volodia Man'ko for their 150th birthday

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“…Firstly, we have a much larger freedom due to the lack of knowledge about the total system and, most importantly, necessary and sufficient conditions on the superoperator L t of eq. (1) to be physically legitimate are generally not known [12]. Nevertheless, special classes of valid generators can be identified and their mathematical structure reflect important properties of the environment [13].…”

Section: Introductionmentioning

confidence: 99%

A Possible Time-Dependent Generalization of the Bipartite Quantum Marginal Problem

2018

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In this work we study an inverse dynamical problem for a bipartite quantum system governed by the time local master equation: to find the class of generators which give rise to a certain time evolution with the constraint of fixed reduced states (marginals). The compatibility of such choice with a global unitary evolution is considered. For the non unitary case we propose a systematic method to reconstruct examples of master equations and address them to different physical scenarios.

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On Time-Local Generators of Quantum Evolution

Cited by 28 publications

References 29 publications

Frontiers of Open Quantum System Dynamics

Frontiers of Open Quantum System Dynamics

Interaction free and decoherence free states

A Possible Time-Dependent Generalization of the Bipartite Quantum Marginal Problem

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