The Bogoliubov inequality and the nature of Bose-Einstein condensates for interacting atoms in spatial dimensions $D \le 2$ The Bogoliubov inequality and the nature of Bose-Einstein condensates for interacting atoms in spatial dimensions $D \le 2$

Moorad Alexanian

We consider the restriction placed by the Bogoliubov inequality on the nature of the Bose-Einstein condensates (BECs) for interacting atoms in a spatial dimension D - 2 and in the presence of an external arbitrary potential, which may be a confining "box", a periodic, or a disordered potential. The atom-atom interaction gives rise to a (gauge invariance) symmetry-breaking term that places further restrictions on BECs in the form of a consistency proviso. The necessary condition for the existence of a BEC in D - 2 in all cases is macroscopic occupation of many single-particle momenta states with the origin a limit point (or accumulation point) of condensates. It is shown that the nature of BECs for noninteracting atoms in a disordered potential is precisely the same as that of BECs for interacting atoms in the absence of an external potential.We consider the restriction placed by the Bogoliubov inequality on the nature of the Bose-Einstein condensates (BECs) for interacting atoms in a spatial dimension D - 2 and in the presence of an external arbitrary potential, which may be a confining "box", a periodic, or a disordered potential. The atom-atom interaction gives rise to a (gauge invariance) symmetry-breaking term that places further restrictions on BECs in the form of a consistency proviso. The necessary condition for the existence of a BEC in D - 2 in all cases is macroscopic occupation of many single-particle momenta states with the origin a limit point (or accumulation point) of condensates. It is shown that the nature of BECs for noninteracting atoms in a disordered potential is precisely the same as that of BECs for interacting atoms in the absence of an external potential.

arXiv:1009.3302Sep 17, 20101 citation

Experimental studies of Bose–Einstein condensates in disorder

Yong P. Chen, J. M. Hitchcock, D. Dries +5 more

Physica D Nonlinear PhenomenaFeb 18, 20098 citations

Superfluidity versus Bose-Einstein condensation in a Bose gas with disorder

G. E. Astrakharchik, Jordi Boronat, J. Casulleras +1 more

We investigate the phenomenon of Bose-Einstein condensation and superfluidity in a Bose gas at zero temperature with disorder. By using the diffusion Monte Carlo method, we calculate the superfluid and the condensate fraction of the system as a function of density and strength of disorder. In the regime of weak disorder we find agreement with the analytical results obtained within the Bogoliubov model. For strong disorder the system enters an unusual regime where the superfluid fraction is smaller than the condensate fraction.We investigate the phenomenon of Bose-Einstein condensation and superfluidity in a Bose gas at zero temperature with disorder. By using the diffusion Monte Carlo method, we calculate the superfluid and the condensate fraction of the system as a function of density and strength of disorder. In the regime of weak disorder we find agreement with the analytical results obtained within the Bogoliubov model. For strong disorder the system enters an unusual regime where the superfluid fraction is smaller than the condensate fraction.

arXiv:cond-mat/0111165Physical Review AAug 9, 200291 citations

GROUND STATE ENERGY OF BOSE-EINSTEIN CONDENSATION IN A DISORDERED SYSTEM

Virulh Sa‐Yakanit, Wattana Lim

Dec 1, 20080 citations

Bose-Einstein condensation in quantum magnets

Vivien S. Zapf, Marcelo Jaime, Cristian D. Batista

This article reviews experimental and theoretical work on Bose-Einstein condensation in quantum magnets. These magnets are natural realizations of gases of interacting bosons whose relevant parameters such as dimensionality, lattice geometry, amount of disorder, nature of the interactions, and particle concentration can vary widely between different compounds. The particle concentration can be easily tuned by applying an external magnetic field which plays the role of a chemical potential. This rich spectrum of realizations offers a unique possibility for studying the different physical behaviors that emerge in interacting Bose gases from the interplay between their relevant parameters. The plethora of other bosonic phases that can emerge in quantum magnets, of which the Bose-Einstein condensate is the most basic ground state, is reviewed. The compounds discussed in this review have been intensively studied in the last two decades and have led to important contributions in the area of quantum magnetism. In spite of their apparent simplicity, these systems often exhibit surprising behaviors. The possibility of using controlled theoretical approaches has triggered the discovery of unusual effects induced by frustration, dimensionality, or disorder.This article reviews experimental and theoretical work on Bose-Einstein condensation in quantum magnets. These magnets are natural realizations of gases of interacting bosons whose relevant parameters such as dimensionality, lattice geometry, amount of disorder, nature of the interactions, and particle concentration can vary widely between different compounds. The particle concentration can be easily tuned by applying an external magnetic field which plays the role of a chemical potential. This rich spectrum of realizations offers a unique possibility for studying the different physical behaviors that emerge in interacting Bose gases from the interplay between their relevant parameters. The plethora of other bosonic phases that can emerge in quantum magnets, of which the Bose-Einstein condensate is the most basic ground state, is reviewed. The compounds discussed in this review have been intensively studied in the last two decades and have led to important contributions in the area of quantum magnetism. In spite of their apparent simplicity, these systems often exhibit surprising behaviors. The possibility of using controlled theoretical approaches has triggered the discovery of unusual effects induced by frustration, dimensionality, or disorder.

Reviews of Modern PhysicsMay 15, 2014382 citations

The Bogoliubov inequality and the nature of Bose-Einstein condensates for interacting atoms in spatial dimensions

D \le 2