Se p 20 09 7616 : Critical number of ideal Bose gas confined in a cubic box
نویسنده
چکیده
We conduct a rigorous investigation into the thermodynamic instability of ideal Bose gas confined in a cubic box. Based on the exact expression of canonical partition function, we perform numerical computations up to the number of particles one million. We report that if the number of particles is equal to or greater than 7616, the ideal Bose gas subject to Dirichlet boundary condition reveals a thermodynamic instability and consequently undergoes a first-order phase transition. This paper demonstrates for the first time that canonical ensembles with finite number of physical degrees can exhibit a discontinuous phase transition featuring a genuine mathematical singularity, provided we keep not volume but pressure constant. Besides, we show for a generic canonical ensemble that if the ground state energy is volume independent, the system becomes thermodynamically unstable at low temperature near absolute zero. PACS : 05.70.Fh, 12.40.Ee, 51.30.+i
منابع مشابه
Condensation of ideal Bose gas confined in a box within a canonical ensemble
We set up recursion relations for the partition function and the ground-state occupancy for a fixed number of noninteracting bosons confined in a square box potential and determine the temperature dependence of the specific heat and the particle number in the ground state. A proper semiclassical treatment is set up which yields the correct small-T behavior in contrast to an earlier theory in Fe...
متن کاملOn the Magnetization of a Charged Bose Gas in the Canonical Ensemble
Consider a charged Bose gas without self-interactions, confined in a three dimensional cubic box of side L ≥ 1 and subjected to a constant magnetic field B 6= 0. If the bulk density of particles ρ and the temperature T are fixed, then define the canonical magnetization as the partial derivative with respect to B of the reduced free energy. Our main result is that it admits thermodynamic limit f...
متن کاملInfluence of boundary conditions on statistical properties of ideal Bose-Einstein condensates.
We investigate the probability distribution that governs the number of ground-state particles in a partially condensed ideal Bose gas confined to a cubic volume within the canonical ensemble. Imposing either periodic or Dirichlet boundary conditions, we derive asymptotic expressions for all its cumulants. Whereas the condensation temperature becomes independent of the boundary conditions in the...
متن کاملOrder via Nonlinearity in Randomly Confined Bose gases
A Hartree-Fock mean-field theory of a weakly interacting Bose-gas in a quenched white noise disorder potential is presented. A direct continuous transition from the normal gas to a localized Bose-glass phase is found which has localized short-lived excitations with a gapless density of states and vanishing superfluid density. The critical temperature of this transition is as for an ideal gas un...
متن کاملSimple theoretical tools for low dimension Bose gases
We first consider an exactly solvable classical field model to understand the coherence properties and the density fluctuations of a one-dimensional (1D) weakly interacting degenerate Bose gas with repulsive interactions at temperatures larger than the chemical potential. In a second part, using a lattice model for the quantum field, we explain how to carefully generalize the usual Bogoliubov a...
متن کامل