### 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) |
---|---|

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

### Cite this

**Lindbladian operators, von Neumann entropy and energy conservation in time-dependent quantum open systems.** / Ou, Congjie; Chamberlin, Ralph; Abe, Sumiyoshi.

Research output: Contribution to journal › Article

}

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

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

UR - http://www.scopus.com/inward/record.url?scp=84991258764&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84991258764&partnerID=8YFLogxK

U2 - 10.1016/j.physa.2016.09.016

DO - 10.1016/j.physa.2016.09.016

M3 - Article

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 -