Exact eigenspectrum of the symmetric simple exclusion process on the complete, complete bipartite, and related graphs

Abstract

We show that the infinitesimal generator of the symmetric simple exclusion process, recast as a quantum spin-1/2 ferromagnetic Heisenberg model, can be solved by elementary techniques on the complete, complete bipartite, and related multipartite graphs. Some of the resulting infinitesimal generators are formally identical to homogeneous as well as mixed higher spins models. The degeneracies of the eigenspectra are described in detail, and the Clebsch-Gordan machinery needed to deal with arbitrary spin-s representations of the SU(2) is briefly developed. We mention in passing how our results fit within the related questions of a ferromagnetic ordering of energy levels and a conjecture according to which the spectral gaps of the random walk and the interchange process on finite simple graphs must be equal.

Final version as published, 19 pages, 4 figures, 40 references given in full format

References in corpus (12)

• Non equilibrium steady states: fluctuations and large deviations of the density and of the current
• Nonequilibrium Steady States of Matrix Product Form: A Solver's Guide
• Mapping out of equilibrium into equilibrium in one-dimensional transport models
• The totally asymmetric simple exclusion process on networks
• Fastest mixing Markov chain on graphs with symmetries
• Nonequivalence of ensembles for long-range quantum spin systems in optical lattices
• A multi-lane TASEP model for crossing pedestrian traffic flows
• A Ferromagnetic Lieb-Mattis Theorem
• Nonequivalence of ensembles in the Curie-Weiss anisotropic quantum Heisenberg model
• Balance network of asymmetric simple exclusion process
• Asymmetric Simple Exclusion Process on a Cayley Tree
• Equilibrium Properties of Quantum Spin Systems with Non-additive Long-Range Interactions

Cited by in corpus (6)

• Noisy Coupled Qubits: Operator Spreading and the Fredrickson-Andersen Model
• Spin Multiplicities
• Composition of many spins, random walks and statistics
• Composing arbitrarily many $SU(N)$ fundamentals
• The spectrum and convergence rates of exclusion and interchange processes on the complete graph
• Domain-wall melting in all-to-all QSSEP from random-matrix theory