Nonideal Bose Gases: Correlation Inequalities and Bose Condensation

We consider two simple model systems describing effective repulsion in a nonideal Bose gas. The interaction Hamiltonians in these systems can be analytically represented as functions of the occupation number operators for modes with nonzero momenta (p0). One of these models contains an interaction term corresponding to repulsion of bosons with the mode p=0 and ensuring the thermodynamic superstability of the system; the other model does not contain such a term. We use the Bogoliubov–Dirac–Ginibre approximation and the method of correlation inequalities to prove that a Bose condensate can exist in these model systems. Because of the character of interaction, the condensate can be formed in the superstable case for any values of the spatial dimensions, temperature, and positive chemical potentials.     

Huang-Yang-Luttinger model: Gaussian dominance and Bose condensation

We prove the Gaussian dominance condition for the Huang-Yang-Luttinger model in the case with an arbitrary chemical potential. Using this condition in the framework of the method of correlation inequalities, we obtain two-sided bounds on the corresponding two-point thermodynamic means. Based on these bounds, we prove the existence of Bose condensation in this model. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 121, No. 2, pp. 347–352, November, 1999.     

The infrared bounds method in the study of boson systems

This is a study of the equilibrium thermodynamics of a lattice boson gas with on-site repulsion and nearest-neighbor site attraction. For this system, the existence of a Bose condensate is proved and an equation for the lower estimate of the critical temperature is obtained. Moreover, the upper and lower bounds for the structure factor are derived. Finally, in the framework of the infrared bounds method, a Huang-Davies-type Bose system is studied.Republished from Teoreticheskaya i Matematicheskaya Fizika, Vol. 108, No. 3, pp. 421–430, September, 1996.     

Local Gaussian Dominance: An Anharmonic Excitation of Free Bosons

We prove the local Gaussian dominance condition for a Bose system whose Hamiltonian is diagonal with respect to the particle number operators. The proof is based on obtaining an upper bound estimate for the Bogoliubov inner product of the Bose creation and annihilation operators.     

Two-Sided Estimates for the Internal Energy of Thermal Photons

The upper- and lower-bound estimates for the thermodynamic averages of the occupation number operators are obtained for the case of a nonlinear photon system in thermal equilibrium with the thermostat. Two-sided inequalities for the internal energy of such a system are constructed from the obtained estimates.     

Bogolyubov approximation for diagonal model of an interacting Bose gas

We study, using the Bogolyubov approximation, the thermodynamic behavior of a superstable Bose system whose energy operator in the second-quantized form contains a nonlinear expression in the occupation numbers operators. We prove that for all values of the chemical potential satisfying μ>λ(0)$\mu >\lambda (0)$, where λ(0)?0$\lambda (0)?0$ is the lowest energy value, the system undergoes Bose–Einstein condensation.