Speaker: Valentin Zagrebnov (Institut de Mathématiques de Marseille, France)

Title: Permanental Random Point Process and BEC

Abstract: This is lecture a short review of applications of the Permanental Random Point Processes (PRPP) method to description of the Bose-Einstein Condensation (BEC) in quantum Bose-gas (will be explained/defined). After recall of the Determinantal/Permanental Random Point Processes formalism a link with the quantum Bose-gas and BEC of the non-interacting PRPP is outlined. The next level of discussion is BEC of interacting PRPP in the Mean-Field approximation. This result is combined with the BEC of PRPP in weak harmonic traps. Then limit theorems, including the Large Deviation Principle, are presented for non-interacting PRPP in the infinite size limit of weak harmonic traps to describe the position distribution of bosons in BEC. Position distributions of constituent particles of the PRPP trapped in exponentially (and polynomially) anisotropic traps is a subject of discussion for BEC and for normal phases. For exponentially anisotropic case one observes a generalised BEC and qualitatively different PRPP particle density distributions.