非平衡BEC黑洞霍金辐射及热力学的研究

Considering the energy dissipation, the project intends to investigate Hawking radiation and the thermodynamic property of BEC black holes by use of the dynamical theory of the non-equilibrium systems. The research method of theoretical derivation and calculation，the discussion after comparing with results obtained are adopted. Firstly, viewing a BEC black hole as the quantum condensates at a critical point of N particles, and considering the effects of dissipation and noise, stochastic equations of scalar field are derived; Secondly, puts the non-equilibrium fluctuations theory into stochastic equations of scalar field, the second law of thermodynamics of a BEC black hole is derived; Finally, Hawking radiation flows of BEC black holes are calculated, and then the heat capacity, black hole entropy etc. The thermal properties of BEC black holes will be discussed from the viewpoint of the fact that a BEC black hole is a quantum phase transition point of condensed system.. The significance of this project are: on the one hand, research on Hawking radiation and thermodynamic properties of BEC black holes can provide reference for detecting the universe black holes, which has important practical significance; On the other hand, it can promote the development of both non-equilibrium statistical theory and black holes physics meanwhile to investigate the Hawking radiation and thermodynamic properties of BEC black holes from the viewpoint of the non-equilibrium theory .

本项目拟考虑能量耗散，利用非平衡系统中的动力学理论研究BEC黑洞的霍金辐射及其热性质。研究采用理论推导和计算，并将结果对比讨论的方法。首先，将BEC黑洞视作N粒子的量子态，考虑耗散项和噪声项，推导标量场的随机方程；其次，将非平衡涨落定理应用于BEC黑洞的标量场随机方程，推导热力学第二定律；最后，计算BEC黑洞的霍金辐射流，进而得到BEC黑洞的热容量、黑洞熵等物理量，从BEC黑洞作为多体凝聚态的相变点角度深入讨论BEC黑洞的热性质。. 本项目的意义在于：一方面，BEC黑洞的霍金辐射及热性质的研究为物理工作者进行宇宙黑洞的探测提供了借鉴，具有重要的现实意义。另一方面，从非平衡角度研究BEC黑洞的霍金辐射及热力学可以同时促进非平衡统计理论和黑洞物理的发展。

由于黑洞的热效应极其微弱，当前难以实际观测。实验室中声学黑洞的实现及其霍金辐射的探测为研究真实黑洞提供了借鉴。本项目通过将弯曲时空中的量子场的运动规律与实验室中流体中声波的动力学方程的类比,来研究类比声学黑洞的霍金辐射及其热性质。进行了如下三方面的研究：首先，研究了两种有代表性的声学黑洞的霍金辐射，求解出声学黑洞视界上的波动方程的精确解，计算出声学黑洞的霍金辐射谱的表达式，得到了霍金温度。其次，探讨了广义测不准原理对声学黑洞霍金辐射的修正，求解出带量子修正项的声学黑洞霍金辐射谱，进而讨论量子效应对声学黑洞霍金辐射及其热力学的影响。最后，探讨了如何提高黑洞的能量提取率的问题，分别从彭若斯过程和黑洞并合过程这两种途径计算黑洞能量提取率的极限，进而给出了两种理论上可行的提高黑洞能量提取率的方案。本研究的意义在于：一方面，类比声学黑洞的霍金辐射及热性质的研究为物理工作者进行宇宙黑洞的探测提供了借鉴，可以使人类更深入地理解引力的本质；另一方面，本研究能促进量子场论、流体力学、统计力学、凝聚态物理等其它相关领域理论的发展。