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 - Funding Information:
The work of CO was supported by the grants from Fujian Province (Nos. 2015J01016 , JA12001 , 2014FJ-NCET-ZR04 ) and from Huaqiao University (No. ZQN-PY114 ). He also thanks Toka-Donghua Educational and Cultural Exchange Foundation for providing him with the scholarship and Mie University for the hospitality extended to him. SA would like to thank the High-End Foreign Expert Program of China for support and the warm hospitality of Huaqiao University. His work was also supported in part by a Grant-in-Aid for Scientific Research from the Japan Society for the Promotion of Science (No. 26400391 ) and by the Program of Competitive Growth of Kazan Federal University from the Ministry of Education and Science of the Russian Federation .

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

VL - 466

SP - 450

EP - 454

JO - Physica A: Statistical Mechanics and its Applications

JF - Physica A: Statistical Mechanics and its Applications

SN - 0378-4371

ER -