2009
DOI: 10.1142/s1230161209000190
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On the Structure of Generators for Non-Markovian Master Equations

Abstract: Complete characterization of complete positivity preserving non-Markovian master equations is presented.

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Cited by 37 publications
(41 citation statements)
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References 38 publications
(35 reference statements)
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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%
“…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%
“…It turns out that the popular Markovian approximation which does not take into account memory effects is not sufficient for modern applications and todays technology calls for truly nonMarkovian approach. Non-Markovian dynamics was recently studied in [3][4][5][6][7][8][9][10][11][12][13][14][15]. Interestingly, several measures of non-Markovianity were proposed during last year [16][17][18][19].…”
mentioning
confidence: 99%
“…Let us observe that this problem may be reformulated as follows [19]: any completely positive solution Λ t of Eq. (3) may be represented by…”
Section: Preliminary Ideas a Non-markovian Dynamicsmentioning
confidence: 99%
“…where B is a quantum channel (i.e., a trace preserving CP map) [12,18,19]. L t generates a completely positive trace preserving dynamics Λ t if the Laplace transform κ(s) satisfies…”
Section: B Quantum Channelmentioning
confidence: 99%