Dubey Shawn, Silvestri Luciano, Finn Justin, Vinjanampathy Sai, Jacobs Kurt
Department of Physics, University of Massachusetts at Boston, 100 Morrissey Boulevard, Boston, Massachusetts 02125, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Jan;85(1 Pt 1):011141. doi: 10.1103/PhysRevE.85.011141. Epub 2012 Jan 25.
The recent discovery that for large Hilbert spaces, almost all (that is, typical) Hamiltonians have eigenstates that place small subsystems in thermal equilibrium, has shed much light on the origins of irreversibility and thermalization. Here we give numerical evidence that many-body lattice systems generically approach typicality as the number of subsystems is increased, and thus provide further support for the eigenstate thermalization hypothesis. Our results indicate that the deviation of many-body systems from typicality decreases exponentially with the number of systems. Further, by averaging over a number of randomly selected nearest-neighbor interactions, we obtain a powerlaw for the atypicality as a function of the Hilbert space dimension, distinct from the power law possessed by random Hamiltonians.
最近发现，对于大型希尔伯特空间，几乎所有（即典型的）哈密顿量都具有能使小子系统处于热平衡的本征态，这为不可逆性和热化的起源提供了很多启示。在此我们给出数值证据，表明随着子系统数量的增加，多体晶格系统一般会趋近于典型性，从而为量子热化假说提供进一步支持。我们的结果表明，多体系统与典型性的偏差会随着系统数量呈指数下降。此外，通过对多个随机选择的最近邻相互作用进行平均，我们得到了一个作为希尔伯特空间维度函数的非典型性幂律，这与随机哈密顿量所具有的幂律不同。
