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 a concept of generalized Bose-Einstein condensation (g-BEC) for the perfect Bose gas (PBG) in Casimir boxes via relation between concepts of long cycles and Off-Diagonal-Long- Range-Order (ODLRO) usually considered as an adequate way to describe the standard BEC in the fundamental state of the cubic box. We revise definitions of theses concepts, called scaled Bose- Einstein condensation (s-BEC), scaled short/long cycles (s-short/long cycles) and scaled ODLRO (s-ODLRO) which are based on some scaling arguments. The principle result is that the classification of the g-BEC in three types (I,II,III) implies a hierarchy of long cycles (depending of their size) and a hierarchy of ODLRO (depending of the size of spatial delocalization of the condensate).

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

Domaines: Physique mathématique [math-ph]

Mathieu Beau. Scaling approach to existence of long cycles in Casimir boxes. 2008. ⟨hal-00332745v1⟩