能量的量子统计涨落及其新的赝规范依赖
Quantum statistical fluctuation of energy and its novel pseudo-gauge dependence
摘要：
本文讨论了热相对论气体子系统中自旋为零和自旋为半的粒子的量子统计能量涨落。我们明确地显示了系统的大小依赖的量子统计涨落的能量。我们的研究结果表明，随着系统尺寸的减小，量子统计涨落大大增加。作为框架的一致性，我们还指出，如果子系统的尺寸足够大，量子统计涨落会导致正则系综中能量的统计涨落的已知结果。对于自旋半粒子，量子涨落表现出一些有趣的新特征。我们表明，在一个小的子系统的自旋半粒子的量子统计涨落的能量依赖于各种赝规范的选择的能量动量张量。有趣的是，对于足够大的子系统的量子涨落得到不同的伪规范的选择收敛，我们恢复的正则系综公式已知的统计波动的能量。我们的计算非常通用，可以应用于物理学的任何分支，只要涉及热系统。作为一个实际应用，我们认为，我们的研究结果可以用来确定一个粗粒化的尺度，引入经典的能量密度或流体元素的概念，强相互作用的物质，特别是小系统产生的重离子碰撞。
英文摘要：
We discuss the quantum statistical fluctuations of energy in subsystems of hot relativistic gas for both spin-zero and spin half particles. We explicitly show the system size dependence of the quantum statistical fluctuation of energy. Our results show that with decreasing system size quantum statistical fluctuations increase substantially. As the consistency of the framework, we also argue that the quantum statistical fluctuations give rise to the known result for statistical fluctuation of energy in the canonical ensemble if we consider the size of the subsystem to be sufficiently large. For a spin-half particle quantum fluctuations show some interesting novel features. We show that within a small sub-system quantum statistical fluctuation of energy for spin half particles depends on the various pseudo-gauge choices of the energy-momentum tensor. Interestingly, for sufficiently large subsystems quantum fluctuations obtained for different pseudo-gauge choices converge and we recover the canonical-ensemble formula known for statistical fluctuations of energy. Our calculation is very general and can be applied to any branch of physics whenever one deals with a thermal system. As a practical application, we argue that our results can be used to determine a coarse-graining scale to introduce the concept of classical energy density or fluid element relevant for the strongly interacting matter, in particular for small systems produced in heavy-ion collisions.
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