Scaling approach to existence of long cycles in Casimir boxes

Mathieu Beau (1, 2)

1 CPT - Centre de Physique Théorique - UMR 6207
2 CPT - Centre de Physique Théorique - UMR 7332

We analyse the concept of generalized Bose-Einstein condensation (g-BEC) known since 1982 for the perfect Bose gas (PBG) in Casimir boxes (anisotropic boxes) via the relation between concepts of long cycles and Off-Diagonal-Long-Range-Order (ODLRO) usually considered as an adequate way to describe the standard BEC on the ground state for the cubic box. First we show that these three criterions are equivalent in this case. Then we revise definitions of these concepts which are based on a scaling approach to prove that the classification of the g-BEC (in three types I,II,III) implies a hierarchy of long cycles (depending on their size) and a hierarchy of ODLRO (depending on the coherence length of the condensate).

Mots clés: Scaling; Generalized Bose-Einstein condensation; (Long) Cycles; Off-Diagonal-Long-Range-Order (ODLRO); perfect Bose gas; Casimir boxes; Scaling.

Domaines: Physique mathématique [math-ph]; Physique mathématique [math-ph]

Mathieu Beau. Scaling approach to existence of long cycles in Casimir boxes. 2009. ⟨hal-00332745v2⟩