### 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.

Original language | English (US) |
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Pages (from-to) | 450-454 |

Number of pages | 5 |

Journal | Physica A: Statistical Mechanics and its Applications |

Volume | 466 |

DOIs | |

State | Published - Jan 15 2017 |

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### Keywords

- Conservation of internal energy
- Lindblad equation
- Quantum dissipative systems
- von Neumann entropy

### ASJC Scopus subject areas

- Statistics and Probability
- Condensed Matter Physics