Indexed on: 15 Nov '16Published on: 15 Nov '16Published in: arXiv - Physics - Statistical Mechanics
In many materials or equilibrium statistical systems the information of boundary conditions is lost inside the bulk of the material. In contrast, we describe here static classical statistical probability distributions for which bulk properties depend on boundary conditions. Such "static memory materials" can be realized if no unique equilibrium state exists. The propagation of information from the boundary to the bulk is described by a classical wave function or a density matrix, which obey generalized Schr\"odinger or von Neumann equations. For static memory materials the evolution within a subsector is unitary, as characteristic for the time evolution in quantum mechanics. The space-dependence in static memory materials can be used as an analogue representation of the time evolution in quantum mechanics - such materials are "quantum simulators". For example, an asymmetric Ising model represents the time evolution of relativistic fermions in two-dimensional Minkowski space.