On Completely Positive Non-Markovian Evolution of a d-Level System

Kossakowski, Andrzej; Rebolledo, Rolando

doi:10.1142/s1230161208000122

Cited by 25 publications

(17 citation statements)

References 31 publications

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“…For this case a general consistent theoretical framework has not yet been found, and partial results have been obtained as a result of intense efforts (see, e.g., Refs. [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21]). An important step in the development of a general theory consists in the construction of a suitable measure that quantifies the degree of non-Markovianity for a given dynamical evolution [22,23].…”

Section: Introductionmentioning

confidence: 99%

Exact master equations for the non-Markovian decay of a qubit

2010

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Exact master equations describing the decay of a two-state system into a structured reservoir are constructed. Employing the exact solution for the model we determine analytical expressions for the memory kernel of the Nakajima-Zwanzig master equation and for the generator of the corresponding time-convolutionless master equation. This approach allows a detailed investigation and comparison of the convergence behavior of the corresponding perturbation expansions. Moreover, we find that the structure of widely used phenomenological master equations with memory kernel may be incompatible with a non-perturbative treatment of the underlying microscopic model. We discuss several physical implications of our results on the microscopic analysis and the phenomenological modelling of non-Markovian quantum dynamics of open systems.

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Section: Introductionmentioning

confidence: 99%

Exact master equations for the non-Markovian decay of a qubit

2010

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“…which clearly satisfies conditions (3)- (5). The mean values of the operators M (k) (t) can then be approximated [24] using techniques from Random Matrix Theory and a second order self-consistent Born approximation [27,28].…”

Section: Self-consistent Born Approximationmentioning

confidence: 99%

“…Non-Markovian generalizations of the well known Kossakowski-Lindblad master equation [1] have been a focus of many recent studies [2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18] in quantum open systems theory [19]. Such structures can preserve complete positivity [2,3,4,5,6,7] or positivity [8,9,10].…”

Section: Introductionmentioning

confidence: 99%

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Optimally chosen Nakajima–Zwanzig master equation for mean field approximation

Wilkie¹,

Wong²

2012

Physics Letters A

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Abstract.We define an ensemble of projection operators, each of which has an exact associated Nakajima-Zwanzig master equation for quantum open system evolution. A mean field approximation for the memory kernels is introduced that yields, for an optimally chosen projection operator, a completely determined inhomogeneous master equation. Previous proofs of positivity and equilibration are extended to these new inhomogeneous non-Markovian master equations. We study a nitrogen vacancy center in diamond interacting with 13 C impurities to illustrate the method.

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“…In particular it may protect the system against the sudden death of entanglement [10]. Non-Markovian dynamics was recently studied in [11][12][13][14][15][16][17][18][19][20][21][22][23]. Interestingly, several measures of non-Markovianity were proposed during last year [24][25][26][27].…”

Section: Introductionmentioning

confidence: 99%