TY - JOUR
T1 - Lindbladian operators, von Neumann entropy and energy conservation in time-dependent quantum open systems
AU - Ou, Congjie
AU - Chamberlin, Ralph
AU - Abe, Sumiyoshi
N1 - Publisher Copyright:
© 2016 Elsevier B.V.
PY - 2017/1/15
Y1 - 2017/1/15
N2 - 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.
AB - 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.
KW - Conservation of internal energy
KW - Lindblad equation
KW - Quantum dissipative systems
KW - von Neumann entropy
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U2 - 10.1016/j.physa.2016.09.016
DO - 10.1016/j.physa.2016.09.016
M3 - Article
AN - SCOPUS:84991258764
SN - 0378-4371
VL - 466
SP - 450
EP - 454
JO - Physica A: Statistical Mechanics and its Applications
JF - Physica A: Statistical Mechanics and its Applications
ER -