Misbeliefs and misunderstandings about the non-Markovian dynamics of a damped harmonic oscillator

Maniscalco, Sabrina; Intravaia, Francesco; Piilo, Jyrki; Messina, A.

doi:10.1088/1464-4266/6/3/016

Cited by 39 publications

(40 citation statements)

References 30 publications

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“…to an 'interaction' picture); (iii) the decoherence rates can be negative, corresponding to interactions between the environment and the system in such a way that the system may recohere, reversing earlier decay processes [19,31,32,39]; and (iv) the decoherence operators L k (t) are restricted to correspond to a set of 'orthogonal' decoherence channels, as per Eq. (5).…”

Section: Canonical Form For Master Equationmentioning

confidence: 99%

Canonical form of master equations and characterization of non-Markovianity

et al. 2014

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Master equations govern the time evolution of a quantum system interacting with an environment, and may be written in a variety of forms. Time-independent or memoryless master equations, in particular, can be cast in the well-known Lindblad form. Any time-local master equation, Markovian or non-Markovian, may in fact also be written in a Lindblad-like form. A diagonalisation procedure results in a unique, and in this sense canonical, representation of the equation, which may be used to fully characterize the non-Markovianity of the time evolution. Recently, several different measures of non-Markovianity have been presented which reflect, to varying degrees, the appearance of negative decoherence rates in the Lindblad-like form of the master equation. We therefore propose using the negative decoherence rates themselves, as they appear in the canonical form of the master equation, to completely characterize non-Markovianity. The advantages of this are especially apparent when more than one decoherence channel is present. We show that a measure proposed by Rivas et al. is a surprisingly simple function of the canonical decoherence rates, and give an example of a master equation that is non-Markovian for all times t > 0, but to which nearly all proposed measures are blind. We also give necessary and sufficient conditions for trace distance and volume measures to witness non-Markovianity, in terms of the Bloch damping matrix.

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Section: Canonical Form For Master Equationmentioning

confidence: 99%

Canonical form of master equations and characterization of non-Markovianity

et al. 2014

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“…To understand how initial-slips work [16,17,18,26,23,19,24,20,21,25], it helpful to neglect the matrix structure of the master equation. Then one has (d/dt)ρ(t) = −F (t) ρ(t),…”

Section: Appendix B a Simple Picture Of Initial-slipsmentioning

confidence: 99%

Staying positive: going beyond Lindblad with perturbative master equations

Whitney¹

2008

J. Phys. A: Math. Theor.

133

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Abstract. The perturbative master equation (Bloch-Redfield) is extensively used to study dissipative quantum mechanics -particularly for qubitsdespite the 25 year old criticism that it violates positivity (generating negative probabilities). We take an arbitrary system coupled to an environment containing many degrees-of-freedom, and cast its perturbative master equation (derived from a perturbative treatment of Nakajima-Zwanzig or Schoeller-Schön equations) in the form of a Lindblad master equation. We find that the equation's parameters are time-dependent. This time-dependence is rarely accounted for, and invalidates Lindblad's dynamical semigroup analysis. We analyze one such Bloch-Redfield master equation (for a two-level system coupled to an environment with a short but non-vanishing memory time), which apparently violates positivity. We show analytically that, once the time-dependence of the parameters is accounted for, positivity is preserved.

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“…The QBM model is one of the few models of open quantum systems amenable to an analytical solution [1,2,[8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24].…”

Section: Introductionmentioning

confidence: 99%

Environment-dependent dissipation in quantum Brownian motion

et al. 2009

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The dissipative dynamics of a quantum Brownian particle is studied for different types of environment. We derive analytic results for the time evolution of the mean energy of the system for Ohmic, sub-Ohmic and super-Ohmic environments, without performing the Markovian approximation. Our results allow to establish a direct link between the form of the environmental spectrum and the thermalization dynamics. This in turn leads to a natural explanation of the microscopic physical processes ruling the system time evolution both in the short-time non-Markovian region and in the long-time Markovian one. Our comparative study of thermalization for different environments sheds light on the physical contexts in which non-Markovian dissipation effects are dominant.

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Misbeliefs and misunderstandings about the non-Markovian dynamics of a damped harmonic oscillator

Cited by 39 publications

References 30 publications

Canonical form of master equations and characterization of non-Markovianity

Canonical form of master equations and characterization of non-Markovianity

Staying positive: going beyond Lindblad with perturbative master equations

Environment-dependent dissipation in quantum Brownian motion

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