Information transport in classical statistical systems
Abstract
For "static memory materials" the bulk properties depend on boundary conditions. Such materials can be realized by classical statistical systems which admit no unique equilibrium state. We describe the propagation of information from the boundary to the bulk by classical wave functions. The dependence of wave functions on the location of hypersurfaces in the bulk is governed by a linear evolution equation that can be viewed as a generalized Schrödinger equation. Classical wave functions obey the superposition principle, with local probabilities realized as bilinears of wave functions. For static memory materials the evolution within a subsector is unitary, as characteristic for the time evolution in quantum mechanics. The spacedependence 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 on a Euclidean twodimensional lattice represents the time evolution of free relativistic fermions in twodimensional Minkowski space.
 Publication:

arXiv eprints
 Pub Date:
 November 2016
 arXiv:
 arXiv:1611.04820
 Bibcode:
 2016arXiv161104820W
 Keywords:

 Condensed Matter  Statistical Mechanics;
 Condensed Matter  Quantum Gases;
 High Energy Physics  Lattice;
 Quantum Physics
 EPrint:
 additional material and references, 38 pages