Lindbladian operators, von Neumann entropy and energy conservation in time-dependent quantum open systems

Congjie Ou, Ralph V. Chamberlin and Sumiyoshi Abe

Physica A: Statistical Mechanics and its Applications, 2017, vol. 466, issue C, 450-454

Abstract: The Lindblad equation is widely employed in studies of Markovian quantum open systems. Here, the following question is posed: in a quantum open system with a time-dependent Hamiltonian such as a subsystem in contact with the heat bath, what is the corresponding Lindblad equation for the quantum state that keeps the internal energy of the subsystem constant in time? This issue is of importance in realizing quasi-stationary states of open systems such as quantum circuits and batteries. As an illustrative example, the time-dependent harmonic oscillator is analyzed. It is shown that the Lindbladian operator is uniquely determined with the help of a Lie-algebraic structure, and the time derivative of the von Neumann entropy is shown to be nonnegative if the curvature of the harmonic potential monotonically decreases in time.

Keywords: Quantum dissipative systems; Lindblad equation; Conservation of internal energy; von Neumann entropy (search for similar items in EconPapers)
Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:466:y:2017:i:c:p:450-454

DOI: 10.1016/j.physa.2016.09.016

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