受力耗散谐振子主方程的解析解

An Analytical Solution to the Master Equation for the Dissipative Harmonic Oscillator Driven by an External Field

基于受力耗散谐振子的主方程中的密度算符的左右空间代数结构,首先将主方程改写成具有类似薛定谔方程的形式,再利用三次规范变换求出了主方程在粒子数表象中的精确解.最后,讨论了当演化时间趋于无限大时的方程的定态解.

By using the algebraic structure of the dual space of the density operator in the master equation for the driven dissipative harmonic oscillator, we first rewrite the master equation as a Schrdinger-like equation. Then we use three gauge transformations to obtaine an exact solution to the master equation in the particle number representation. Finally, we discuss the steady-state solution when the evolving time tends to infinity.