标题： 熵与压缩量子开放系统的不确定性 显示英文标题

标题： Entropy and Uncertainty of Squeezed Quantum Open Systems

摘要： 我们定义与热浴相互作用的压缩系统的熵和不确定性函数，并通过在影响泛函形式中跟踪约化密度矩阵的演化来研究它们随时间的变化。 作为例子，我们计算了两个精确可解的压缩系统的熵：一个倒置谐波振子和一个在暴胀宇宙中演化的标量场模。 对于与热浴弱耦合的倒置振子，在高温和低温下，$S\to r $，其中 r 是压缩参数。 在德西特情况下，在高温下，$S\to (1-c)r$，其中$c = \gamma_0/H$，$\gamma_0$是与热浴的耦合，H 是哈勃常数。 这三个情况确认了基于更随意的熵计算方法的先前结果。 但在低温下，德西特熵$S\to (1/2-c)r$明显不同。 这一结果来自于更严格的方法，表明通常被传统方法忽略的因素，即环境的性质以及系统与环境之间的耦合强度，是重要的。 显示英文摘要

摘要： We define the entropy S and uncertainty function of a squeezed system interacting with a thermal bath, and study how they change in time by following the evolution of the reduced density matrix in the influence functional formalism. As examples, we calculate the entropy of two exactly solvable squeezed systems: an inverted harmonic oscillator and a scalar field mode evolving in an inflationary universe. For the inverted oscillator with weak coupling to the bath, at both high and low temperatures, $S\to r $, where r is the squeeze parameter. In the de Sitter case, at high temperatures, $S\to (1-c)r$ where $c = \gamma_0/H$, $\gamma_0$ being the coupling to the bath and H the Hubble constant. These three cases confirm previous results based on more ad hoc prescriptions for calculating entropy. But at low temperatures, the de Sitter entropy $S\to (1/2-c)r$ is noticeably different. This result, obtained from a more rigorous approach, shows that factors usually ignored by the conventional approaches, i.e., the nature of the environment and the coupling strength betwen the system and the environment, are important.