Equivalence of ensembles, condensation and glassy dynamics in the Bose-Hubbard Hamiltonian
Huveneers, François; Theil, Elias (2019), Equivalence of ensembles, condensation and glassy dynamics in the Bose-Hubbard Hamiltonian, Journal of Statistical Physics, 177, 5, p. 917–935. 10.1007/s10955-019-02396-z
TypeArticle accepté pour publication ou publié
Journal nameJournal of Statistical Physics
MetadataShow full item record
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Abstract (EN)We study mathematically the equilibrium properties of the Bose–Hubbard Hamiltonian in the limit of a vanishing hopping amplitude. This system conserves the energy and the number of particles. We establish the equivalence between the microcanonical and the grand-canonical ensembles for all allowed values of the density of particles ρ and density of energy ε . Moreover, given ρ , we show that the system undergoes a transition as ε increases, from a usual positive temperature state to the infinite temperature state where a macroscopic excess of energy condensates on a single site. Analogous results have been obtained by Chatterjee  for a closely related model. We introduce here a different method to tackle this problem, hoping that it reflects more directly the basic understanding stemming from statistical mechanics. We discuss also how, and in which sense, the condensation of energy leads to a glassy dynamics.
Subjects / KeywordsStatistical physics; Statistical ensemble; Condensation; Glass
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Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems Huveneers, François; Abanin, Dmitry A.; De Roeck, Wojciech; Wen-Wei, Ho (2017) Article accepté pour publication ou publié