Non-Gibbs states on a Bose-Hubbard lattice

Abstract

We study the equilibrium properties of the repulsive quantum Bose-Hubbard model at high temperatures in arbitrary dimensions, with and without disorder. In its microcanonical setting the model conserves energy and particle number. The microcanonical dynamics is characterized by a pair of two densities: energy density $\epsilon$ and particle number density $n$. The macrocanonical Gibbs distribution also depends on two parameters: the inverse nonnegative temperature $\beta$ and the chemical potential $\mu$. We prove the existence of non-Gibbs states, that is, pairs $(\epsilon ,n)$ which cannot be mapped onto $(\beta ,\mu )$. The separation line in the density control parameter space between Gibbs and non-Gibbs states $\epsilon \sim n^2$ corresponds to infinite temperature $\beta =0$. The non-Gibbs phase cannot be cured into a Gibbs one within the standard Gibbs formalism using negative temperatures.

8 pages, 1 figure, misprints corrected

References in corpus (4)

• Many-Body Physics with Ultracold Gases
• Weakly nonergodic dynamics in the Gross--Pitaevskii lattice
• Statistical Mechanics of a Discrete Schrödinger Equation with Saturable Nonlinearity
• Spreading, Nonergodicity, and Selftrapping: a puzzle of interacting disordered lattice waves

Cited by in corpus (11)

• Statistical Mechanics of Systems with Negative Temperature
• Dynamical freezing of relaxation to equilibrium
• Localization transition in the Discrete Non-Linear Schrödinger Equation: ensembles inequivalence and negative temperatures
• Condensation transition and ensemble inequivalence in the Discrete Nonlinear Schrödinger Equation
• Fragile Many Body Ergodicity
• Density Resolved Wave Packet Spreading in Disordered Gross-Pitaevskii Lattices
• Localization in the Discrete Non-Linear Schrödinger Equation and geometric properties of the microcanonical surface
• Equivalence of ensembles, condensation and glassy dynamics in the Bose-Hubbard Hamiltonian
• Quench dynamics in disordered two-dimensional Gross-Pitaevskii Lattices
• Thermal lifetime of breathers
• Transient ordering in the Gross-Pitaevskii lattice subject to an energy quench within the disordered phase