Duality and Hidden Symmetries in Interacting Particle Systems
By C. Giardinà, Jorge Kurchan, Frank Redig, K. Vafayi. 2008
187 citations recorded by the source corpus.
In the context of Markov processes, both in discrete and continuous setting, we show a general relation between duality functions and symmetries of the generator. If the generator can be written in the form of a Hamiltonian of a quantum spin system, then the “hidden” symmetries are easily derived. We illustrate our approach in processes of symmetric exclusion type, in which the symmetry is of SU(2) type, as well as for the Kipnis-Marchioro-Presutti (KMP) model for which we unveil its SU(1,1) symmetry. The KMP model is in turn an instantaneous thermalization limit of the energy process associated to a large family of models of interacting diffusions, which we call Brownian energy process (BEP) and which all possess the SU(1,1) symmetry. We treat in details the case where the system is in contact with reservoirs and the dual process becomes absorbing.
Subfields: Condensed Matter Physics, Mathematical Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/5457f50e605b0a924b942f0fde24dfc325467502
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In Condensed Matter Physics
In Mathematical Physics
In Statistical and Nonlinear Physics
Citations in the corpus
- On the notion(s) of duality for Markov processes (2012, methodology): “tions into birth and death of particles; for example, in Eq. (42), the hopping of a particle from site kto site k+ 1 is written as death at site kfollowed by birth at site k+1. We refer the reader to [GKRV09] for a systematic treatment of the method for finding dualities; the remainder of this sectio”