标题： 具有线性耦合到浴中的时间依赖二次系统的量子行为 显示英文标题

标题： The quantum behavior of general time dependent quadratic systems linearly coupled to a bath

摘要： 本文我们求解了一般含时的二次位置和动量耦合系统的量子传播子，该系统线性耦合到无限多个谐振子组成的浴中。 我们在量子光学主方程成立的范围内工作。 我们将这个主方程映射到超希尔伯特空间上的薛定谔方程，并利用李代数技术求解此空间中的动力学。 然后我们回到原来的希尔伯特空间以获得量子动力学的解。 所用的李代数技术优于标准的魏-诺方法，因为在该方法中只需求解一组一阶常微分方程组和纯代数方程。 我们研究了两个例子。 显示英文摘要

摘要： In this paper we solve for the quantum propagator of a general time dependent system quadratic in both position and momentum, linearly coupled to an infinite bath of harmonic oscillators. We work in the regime where the quantum optical master equation is valid. We map this master equation to a Schroedinger equation on Super-Hilbert space and utilize Lie Algebraic techniques to solve for the dynamics in this space. We then map back to the original Hilbert space to obtain the solution of the quantum dynamics. The Lie Algebraic techniques used are preferable to the standard Wei-Norman methods in that only coupled systems of first order ordinary differential equations and purely algebraic equations need only be solved. We look at two examples.