Thermal Equilibrium of a Macroscopic Quantum System in a Pure State.
Thermal Equilibrium of a Macroscopic Quantum System in a Pure State.
复制标题
纯态宏观量子系统的热平衡。
DOI：
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发表时间：
2015
影响因子：
8.6
通讯作者：
R. Tumulka
中科院分区：
文献类型：
--
作者：
S. Goldstein;D. Huse;J. Lebowitz;R. Tumulka
我们考虑了单个封闭宏观量子系统在纯态下的热平衡概念，即用波函数来描述。由波函数决定的体系的热平衡宏观性质必须与热力学性质相同，例如温度和化学势的空间均匀性。当这是真的时，我们说系统处于宏观热平衡(Mate)。然而，这样的系统可能不处于微观热平衡(MITE)。后者要求小子系统的约化密度矩阵与整个系统的微正则系综约化密度矩阵相近，等价于正则系综。Mate和Mate之间的区别对于具有多体局部化的系统特别相关，对于多体局部化系统，其能量本征函数不在Mite中，而它们中的大多数(但不是全部)在Mate中。然而，我们注意到，对于一般的宏观系统，包括那些具有MBL的系统，能量壳层中的大多数波函数都是Mate和Mite的。对于一个经典的宏观系统，Mate对能面上的大多数相点都成立，而Mite对任何相点都不成立。
We consider the notion of thermal equilibrium for an individual closed macroscopic quantum system in a pure state, i.e., described by a wave function. The macroscopic properties in thermal equilibrium of such a system, determined by its wave function, must be the same as those obtained from thermodynamics, e.g., spatial uniformity of temperature and chemical potential. When this is true we say that the system is in macroscopic thermal equilibrium (MATE). Such a system may, however, not be in microscopic thermal equilibrium (MITE). The latter requires that the reduced density matrices of small subsystems be close to those obtained from the microcanonical, equivalently the canonical, ensemble for the whole system. The distinction between MITE and MATE is particularly relevant for systems with many-body localization for which the energy eigenfuctions fail to be in MITE while necessarily most of them, but not all, are in MATE. We note, however, that for generic macroscopic systems, including those with MBL, most wave functions in an energy shell are in both MATE and MITE. For a classical macroscopic system, MATE holds for most phase points on the energy surface, but MITE fails to hold for any phase point.
影响因子：
3.3
作者：
Reimann, Peter
通讯作者：
Reimann, Peter