Proper condensates

In this article a novel characterization of Bose-Einstein condensates is proposed. Instead relying on occupation numbers few dominant modes, which become macroscopic in the limit infinite particle numbers, it focuses regular excitations whose stay bounded limit. manner, subspaces global, respectively local wave functions are identified. Their orthogonal complements determine particles forming proper (infinite) contrast to concept does not sharply fix states, notion unambiguously defined. It outlined, how can be used analysis models. The method illustrated by example trapped non-interacting ground states and their multifarious thermodynamic limits, differing structure accompanying Fock vacuum. also compared with Onsager-Penrose criterion, based eigenvalues one-particle density matrices. shown that useful there as well for identification condensates.