Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Straße 38, 01187 Dresden, Germany.
Technische Universität Dresden, Institut für Theoretische Physik and Center for Dynamics, 01062 Dresden, Germany.
Phys Rev E. 2018 Mar;97(3-1):032136. doi: 10.1103/PhysRevE.97.032136.
In an ideal Bose gas that is driven into a steady state far from thermal equilibrium, a generalized form of Bose condensation can occur. Namely, the single-particle states unambiguously separate into two groups: the group of Bose-selected states, whose occupations increase linearly with the total particle number, and the group of all other states whose occupations saturate [Phys. Rev. Lett. 111, 240405 (2013)PRLTAO0031-900710.1103/PhysRevLett.111.240405]. However, so far very little is known about how the number of Bose-selected states depends on the properties of the system and its coupling to the environment. The answer to this question is crucial since systems hosting a single, a few, or an extensive number of Bose-selected states will show rather different behavior. While in the former two scenarios each selected mode acquires a macroscopic occupation, corresponding to (fragmented) Bose condensation, the latter case rather bears resemblance to a high-temperature state of matter. In this paper, we systematically investigate the number of Bose-selected states, considering different classes of the rate matrices that characterize the driven-dissipative ideal Bose gases in the limit of weak system-bath coupling. These include rate matrices with continuum limit, rate matrices of chaotic driven systems, random rate matrices, and rate matrices resulting from thermal baths that couple to a few observables only.
在远离热平衡的稳态下被驱动的理想玻色气体中，可以发生广义的玻色凝聚。也就是说，单粒子态可以明确地分为两组：一组是玻色选择态，其占据数随总粒子数线性增加；另一组是所有其他态，其占据数达到饱和[Phys. Rev. Lett. 111, 240405 (2013)PRLTAO0031-900710.1103/PhysRevLett.111.240405]。然而，到目前为止，人们对玻色选择态的数量如何取决于系统的性质及其与环境的耦合知之甚少。这个问题的答案是至关重要的，因为承载单个、少数或大量玻色选择态的系统将表现出相当不同的行为。虽然在前两种情况下，每个选择模式都会获得宏观占据数，对应于（碎片化）玻色凝聚，而后一种情况更类似于高温物质状态。在本文中，我们系统地研究了玻色选择态的数量，考虑了不同类别的速率矩阵，这些矩阵描述了在弱系统-浴耦合极限下驱动耗散理想玻色气体的性质。这些矩阵包括具有连续极限的速率矩阵、混沌驱动系统的速率矩阵、随机速率矩阵以及仅与少数可观测量耦合的热浴产生的速率矩阵。
