Quantum Markovian Kinetic Equation for Harmonic Oscillator

TL;DR

This paper introduces a quantum Markovian kinetic equation for the harmonic oscillator, enabling analysis of nonequilibrium states and their equilibrium solutions within the Lindblad framework.

Contribution

It presents a new kinetic equation for quantum harmonic oscillators and derives equilibrium statistical matrices and mean value equations.

Findings

Derived specific nonequilibrium states using the Lindblad equation

Obtained equilibrium statistical matrices for the system

Formulated mean value equations and their solutions

Abstract

Specific nonequilibrium states of the quantum harmonic oscillator described by the Lindblad equation have been hereby suggested. This equation makes it possible to determine time-varying effects produced by statistical operator or statistical matrix. Thus, respective representation-varied equilibrium statistical matrixes have been found. Specific mean value equations have been found and their equilibrium solutions have been obtained.