Entropy production from chaoticity in Yang-Mills field theory with use of the Husimi function
Entropy production from chaoticity in Yang-Mills field theory with use of the Husimi function
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DOI：
10.1103/physrevd.94.091502
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发表时间：
2016-03
影响因子：
5
通讯作者：
Hidekazu Tsukiji;H. Iida;T. Kunihiro;A. Ohnishi;Toru T. Takahashi
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作者：
Hidekazu Tsukiji;H. Iida;T. Kunihiro;A. Ohnishi;Toru T. Takahashi
利用Wigner函数的粗粒化和非负维格纳函数给出的量子分布函数Husimi函数fH(a，E,t)，研究了杨-米尔斯（YM）场论中可能产生的熵。我们计算了Husimi-Wehrl （HW）熵SHW(t) = TrfH log fH，定义为相空间上的积分，并结合蒙特卡罗方法对测试粒子法进行了两种改进。我们利用半经典近似得到了已知在经典极限下呈现混沌行为的YM场分布函数的时间演化。我们还通过对Husimi函数进行积分析来简化多维相空间积分，发现对于具有几个自由度的量子系统，该函数给出了10- 20%的HW熵高估。我们证明了量子YM理论确实表现出熵的产生，并且熵的产生速率与正Lyapunov指数或Kolmogorov-Sinai熵的和一致，这表明经典YM场的混沌性导致了量子YM理论中的熵的产生。PACS数字：11.15。我,12.38。Gc, 11.10。天气,25.75.Nq
We investigate possible entropy production in Yang-Mills (YM) field theory by using a quantum distribution function called Husimi function fH(A,E,t) for YM field, which is given by a coarse graining of Wigner function and non-negative. We calculate the Husimi-Wehrl (HW) entropy SHW(t) = TrfH log fH defined as an integral over the phase-space, for which two adaptations of the test-particle method are used combined with Monte-Carlo method. We utilize the semiclassical approximation to obtain the time evolution of the distribution functions of the YM field, which is known to show a chaotic beha vior in the classical limit. We also make a simplification of the multi-dimensional phase-space inte grals by making a product ansatz for the Husimi function, which is found to give a 10-20 per cent over estimate of the HW entropy for a quantum system with a few degrees of freedom. We show that the quantum YM theory does exhibit the entropy production, and that the entropy production rate agrees with the sum of positive Lyapunov exponents or the Kolmogorov-Sinai entropy, suggesting that the chaoticity of the classical YM field caus es the entropy production in the quantum YM theory. PACS numbers: 11.15.Me, 12.38.Gc, 11.10.Wx, 25.75.Nq