Hsiang Jen-Tsung, Hu Bei-Lok
Center for High Energy and High Field Physics, National Central University, Taoyuan 32001, Taiwan.
Maryland Center for Fundamental Physics and Joint Quantum Institute, University of Maryland, College Park, MD 20742, USA.
Entropy (Basel). 2021 Nov 20;23(11):1544. doi: 10.3390/e23111544.
Density contrasts in the universe are governed by scalar cosmological perturbations which, when expressed in terms of gauge-invariant variables, contain a classical component from scalar metric perturbations and a quantum component from inflaton field fluctuations. It has long been known that the effect of cosmological expansion on a quantum field amounts to squeezing. Thus, the entropy of cosmological perturbations can be studied by treating them in the framework of squeezed quantum systems. Entropy of a free quantum field is a seemingly simple yet subtle issue. In this paper, different from previous treatments, we tackle this issue with a fully developed nonequilibrium quantum field theory formalism for such systems. We compute the covariance matrix elements of the parametric quantum field and solve for the evolution of the density matrix elements and the Wigner functions, and, from them, derive the von Neumann entropy. We then show explicitly why the entropy for the squeezed yet closed system is zero, but is proportional to the particle number produced upon coarse-graining out the correlation between the particle pairs. We also construct the bridge between our quantum field-theoretic results and those using the probability distribution of classical stochastic fields by earlier authors, preserving some important quantum properties, such as entanglement and coherence, of the quantum field.
宇宙中的密度反差由标量宇宙学微扰所支配，当用规范不变变量表示时，这些微扰包含来自标量度规微扰的经典分量和来自暴胀场涨落的量子分量。长期以来，人们都知道宇宙膨胀对量子场的影响相当于压缩。因此，可以通过在压缩量子系统的框架内处理宇宙学微扰来研究其熵。自由量子场的熵看似简单实则微妙。在本文中，与以往的处理方法不同，我们用一种针对此类系统的完全发展的非平衡量子场论形式来解决这个问题。我们计算参数化量子场的协方差矩阵元，并求解密度矩阵元和维格纳函数的演化，进而从中推导出冯·诺依曼熵。然后我们明确展示了为何压缩但封闭系统的熵为零，但与在粗粒化掉粒子对之间的相关性后产生的粒子数成正比。我们还在我们的量子场论结果与早期作者使用经典随机场概率分布得到的结果之间搭建了桥梁，同时保留了量子场的一些重要量子特性，如纠缠和相干性。
