Duality, supersymmetry and non-conservative random walks

Autor(es)

Belitsky, V ; Schuetz, G. M.

• Tipo de documento: Artigo Científico
• Fonte: JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT; v. N/A, p. 17-pg., 2019-05-01.

Resumo

We derive a probabilistic interpretation of the observation that the quantum XY chain is supersymmetric in the sense that the Hamiltonian commutes with the generators of a subalgebra of the universal enveloping algebra of the Lie superalgebra sl(1 vertical bar 1) and its deformations. The XY chain is shown to be the generator of a Markov process that describes classical vicious random walkers that annihilate immediately when they arrive on the same site, while new random walkers are created at neighbouring sites. The supersymmetry leads to a probabilistic self-duality relation and a duality between the random walk model with an even and odd number of particles, respectively. (AU)

• Processo FAPESP: 17/20696-0 - De sistemas de partículas interagentes a análise topológica de dados
• Beneficiário: Vladimir Belitsky
• Modalidade de apoio: Auxílio à Pesquisa - Pesquisador Visitante - Internacional
• Processo FAPESP: 17/10555-0 - Modelagem estocástica de sistemas interagentes
• Beneficiário: Fabio Prates Machado
• Modalidade de apoio: Auxílio à Pesquisa - Temático