A scaling approach to the existence of long cycles in Casimir boxes

摘要

We analyze the concept of generalized Bose_Einstein condensation (g-BEC), known since 1982 for the perfect Bose gas (PBG) in Casimir (or anisotropic) boxes. Our aim is to establish a relation between this phenomenon and two concepts: the concept of long cycles and the off-diagonal-long_range-order (ODLRO), which are usually considered as an adequate way to describe standard BEC on the ground state for cubic boxes. First, we show that these three criteria are equivalent in this latter case. Then, based on a scaling approach, we revise the formulation of these concepts to prove that the classification of g-BEC into three types I, II, III, implies a hierarchy of long cycles (depending on their size scale) as well as a hierarchy of ODLRO which depends on the coherence length of the condensate.