Nakajima-Zwanzig versus time-convolutionless master equation for the non-Markovian dynamics of a two-level system

Journal Article · Sun Aug 15 00:00:00 EDT 2010 · Physical Review. A

DOI:https://doi.org/10.1103/PHYSREVA.82.022110· OSTI ID:21448437

Smirne, Andrea; Vacchini, Bassano ^[1]

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1. Dipartimento di Fisica, Universita degli Studi di Milano, Via Celoria 16, I-20133 Milano (Italy)

We consider the exact reduced dynamics of a two-level system coupled to a bosonic reservoir, further obtaining the exact time-convolutionless and Nakajima-Zwanzig non-Markovian equations of motion. The system considered includes the damped and undamped Jaynes-Cummings model. The result is obtained by exploiting an expression of quantum maps in terms of matrices and a simple relation between the time evolution map and the time-convolutionless generator as well as the Nakajima-Zwanzig memory kernel. This nonperturbative treatment shows that each operator contribution in Lindblad form appearing in the exact time-convolutionless master equation is multiplied by a different time-dependent function. Similarly, in the Nakajima-Zwanzig master equation each such contribution is convoluted with a different memory kernel. It appears that, depending on the state of the environment, the operator structures of the two sets of equations of motion can exhibit important differences.

• OSTI ID: 21448437
• Journal Information: Physical Review. A, Vol. 82, Issue 2; Other Information: DOI: 10.1103/PhysRevA.82.022110; (c) 2010 The American Physical Society; ISSN 1050-2947
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
74 ATOMIC AND MOLECULAR PHYSICS
BOSONS
ENERGY LEVELS
EQUATIONS OF MOTION
KERNELS
MARKOV PROCESS
MATRICES
QUANTUM MECHANICS
QUANTUM OPERATORS
QUANTUM STATES
TIME DEPENDENCE
DIFFERENTIAL EQUATIONS
EQUATIONS
MATHEMATICAL OPERATORS
MECHANICS
PARTIAL DIFFERENTIAL EQUATIONS
STOCHASTIC PROCESSES