Soluble model of Bose-atoms with two level internal structure: non-conventional Bose-Einstein condensation

Abstract

For a Bose atom system whose energy operator is diagonal in the so-called number operators and its ground state has an internal two-level structure with negative energies, exact expressions for the limit free canonical energy and pressure are obtained. The existence of non-conventional Bose-Einstein condensation has been also proved.

New scenario for the emergence of non-conventional Bose-Einstein condensation. Beyond the notion of energy gap

“…Proof. The demonstration of this theorem is a simple variation of an approach based on the use of the canonical ensemble, already applied by other authors with similar purposes (see for example [16] and references therein). Let f per ℓ (β, ̺), f id ℓ (β, ̺) be the free canonical energies at finite volume V ℓ , inverse temperature β and density ̺ ℓ , corresponding to the perturbed system and the free Bose gas, respectively.…”

Model of Interacting Spin One Bosons

“…In the next sections we shall study a system of bosonic atoms with internal degrees of freedom whose energy operator contains cross-scattering and self-scattering terms and in absence of spin mixing. The case of atoms in two different hyperfine states (spin-1/2), confined in a hypercube was analyzed in three early works [5,6,7] in the framework of the approximating Hamiltonian methods and large deviations methods.…”

“…However, under attractive boundary conditions or by introducing a spectrum gap in the excitation spectrum of the free energy operator the above situation changes dramatically since an independent on temperature macroscopic occupation of the ground state takes place. In this sense, we are in presence of a different kind of condensation -non-conventional BEC (see, for example, works [5,6,7,17,18,19,20] for further details).…”

“…In earlier papers we take different approaches such as large deviations [7] and approximating Hamiltonian [5,6] strategies for obtaining the limit pressures in the case of Bose-atom systems with internal two level (spin-1/2) an one level (spin-0) structures. This enabled us to prove interesting results related to nonconventional or independent on temperature BEC in the case of Bose systems whose ground states are associated to negative values of energies.…”