Properties of quantum Markovian master equations. [Semigroup law, detailed balance]

Gorini, Vittorio; Frigerio, A.; Verri, Maurizio; Kossakowski, Andrzej; Sudarshan, E. C. G.

doi:10.2172/7329564

Cited by 226 publications

(349 citation statements)

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“…is a generator of a completely positive dynamical semigroup [44,45]. The approximation of omitting the R b terms is called secular approximation (SA) or rotating wave approximation [1].…”

Section: Decomposition Of Qmementioning

confidence: 99%

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A Perturbative Method for Nonequilibrium Steady State of Open Quantum Systems

Yuge

Sugita

2015

J. Phys. Soc. Jpn.

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We develop a method of calculating the nonequilibrium steady state (NESS) of an open quantum system that is weakly coupled to reservoirs in different equilibrium states. We describe the system using a Redfield-type quantum master equation (QME). We decompose the Redfield QME into a Lindblad-type QME and the remaining part R. Regarding the steady state of the Lindblad QME as the unperturbed solution, we perform a perturbative calculation with respect to R to obtain the NESS of the Redfield QME. The NESS thus determined is exact up to the first order in the system-reservoir coupling strength (pump/loss rate), which is the same as the order of validity of the QME. An advantage of the proposed method in numerical computation is its applicability to systems larger than those in methods of directly solving the original Redfield QME. We apply the method to a noninteracting fermion system to obtain an analytical expression of the NESS density matrix. We also numerically demonstrate the method in a nonequilibrium quantum spin chain.

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“…is a generator of a completely positive dynamical semigroup [44,45]. The approximation of omitting the R b terms is called secular approximation (SA) or rotating wave approximation [1].…”

Section: Decomposition Of Qmementioning

confidence: 99%

“…Therefore, the SA-QME is not appropriate for analyzing the steady state itself (however, note Ref. [46]), and one often uses any of the original Redfield QME, alternatively approximated Lindblad QME [9], or axiomatic Lindblad QME [44,45] for nonequilibrium situations.…”

Section: Decomposition Of Qmementioning

confidence: 99%

A Perturbative Method for Nonequilibrium Steady State of Open Quantum Systems

Yuge

Sugita

2015

J. Phys. Soc. Jpn.

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“…84 There are several approaches to describing the dynamics of Markovian open quantum systems, most notably, Redfield theory 85,86 and the semigroup formalism developed by Lindblad 87 and Gorini, Kossakowski and Sudarshan. 88 The Redfield equations were derived for the matrix elements of the density operator in the energy representation: 89 with perturbation theory, 29 thus limiting the applicability of his approach to the weak coupling regime. Outside the applicability limits of perturbation theory, as well as on timescales smaller than the correlation time of the environment, Redfield theory does not retain the density operator completely non-negative.…”

Section: This Journal Is C the Owner Societies 2010mentioning

confidence: 99%

“…An alternative approach is not to use one of the more formal relaxation theories, 87,88,[97][98][99][100][101] but to incorporate the system-environment coupling in a phenomenological way. In this case the density operator r s of the system is propagated with the von Neumann equation, eqn (10), with additional relaxation terms.…”

Section: This Journal Is C the Owner Societies 2010mentioning

confidence: 99%

Single molecule charge transport: from a quantum mechanical to a classical description

Kocherzhenko

Grozema

Siebbeles

2011

Phys. Chem. Chem. Phys.

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This paper explores charge transport at the single molecule level. The conductive properties of both small organic molecules and conjugated polymers (molecular wires) are considered. In particular, the reasons for the transition from fully coherent to incoherent charge transport and the approaches that can be taken to describe this transition are addressed in some detail. The effects of molecular orbital symmetry, quantum interference, static disorder and molecular vibrations on charge transport are discussed. All of these effects must be taken into account (and may be used in a functional way) in the design of molecular electronic devices. An overview of the theoretical models employed when studying charge transport in small organic molecules and molecular wires is presented.

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“…The standard approach to the dynamics of open quantum systems, which employs the concept of a quantum Markov process, was developed already in the seventies [14,15] and has been successfully applied in modeling many quantum systems [16,17]. For a quantum Markov process the dynamics is given by a semigroup of completely positive dynamical maps and the corresponding master equation describing the dynamics is in the Lindblad form.…”

Section: Introductionmentioning

confidence: 99%

Local-in-time master equations with memory effects: applicability and interpretation

Laine¹,

Luoma²,

Piilo³

2012

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

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Abstract. Non-Markovian local in time master equations give a relatively simple way to describe the dynamics of open quantum systems with memory effects. Despite their simple form, there are still many misunderstandings related to the physical applicability and interpretation of these equations. Here we clarify these issues both in the case of quantum and classical master equations. We further introduce the concept of a classical non-Markov chain signified through negative jump rates in the chain configuration.

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Properties of quantum Markovian master equations. [Semigroup law, detailed balance]

Cited by 226 publications

References 0 publications

A Perturbative Method for Nonequilibrium Steady State of Open Quantum Systems

A Perturbative Method for Nonequilibrium Steady State of Open Quantum Systems

Single molecule charge transport: from a quantum mechanical to a classical description

Local-in-time master equations with memory effects: applicability and interpretation

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