Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:hep-th/9508055 · Physics Letters B

Simple criterion for the occurrence of Bose-Einstein condensation

Klaus Kirsten, David J. Toms

Published Jan 1, 1996• 22 citations
arXivHTMLPDF
DOI
10.1016/0370-2693(95)01505-1

Related papers

Necessary and sufficient condition for the occurrence of Bose-Einstein condensation in ideal gases

G.S. Rosa

•Jan 1, 1975•0 citations

On the generalized Bose-Einstein condensation

Sergio Curilef

Physics Letters A•Jul 1, 1996•25 citations

Simple criterion for the occurrence of Bose-Einstein condensation and the Meissner-Ochsenfeld effect

Klaus Kirsten, David J. Toms

We examine the occurrence of Bose-Einstein condensation in both nonrelativistic and relativistic systems with no self-interactions in a general setting. A simple condition for the occurrence of Bose-Einstein condensation is given. We show that condensation can occur only if $q>~3$, where $q$ is the dimension associated with the continuous part of the eigenvalue spectrum of the Hamiltonian for nonrelativistic systems or the spatial part of the Klein-Gordon operator for relativistic systems. Furthermore we show that the criterion for the appearance of the Meissner-Ochsenfeld effect is closely connected with that for the appearance of Bose-Einstein condensation.

arXiv:cond-mat/9703161•Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields•Jun 15, 1997•10 citations

Note on the Bose-Einstein Condensation

Takeo Nagamiya

Proceedings of the Physico-Mathematical Society of Japan. 3rd Series•Jan 1, 1939•1 citation

Simple criterion for the occurrence of Bose-Einstein condensation

Klaus Kirsten, David J. Toms

We examine the occurrence of Bose-Einstein condensation in both nonrelativistic and relativistic systems with no self-interactions in a general setting. A simple condition for the occurrence of Bose-Einstein condensation can be given if we adopt generalized \\zeta-functions to define the quantum theory. We show that the crucial feature governing Bose-Einstein condensation is the dimension q associated with the continuous part of the eigenvalue spectrum of the Hamiltonian for nonrelativistic systems or the spatial part of the Klein-Gordon operator for relativistic systems. In either case Bose-Einstein condensation can only occur if q\\ge3.

•Aug 13, 1995•10 citations

Bose-Einstein Condensation under External Conditions

Klaus Kirsten

We examine the occurrence of Bose-Einstein condensation in both nonrelativistic and relativistic systems with no self-interactions in a general setting. A simple condition for the occurrence of Bose-Einstein condensation can be given if we adopt generalized ζ-functions to define the quantum theory. We show that the crucial feature governing Bose-Einstein condensation is the dimension q associated with the continuous part of the eigenvalue spectrum of the Hamiltonian for nonrelativistic systems or the spatial part of the Klein-Gordon operator for relativistic systems. In either case Bose-Einstein condensation can only occur if q ≥ 3 [1]. Several examples, some of them not completely solved before, may be treated very easily using our simple criterion [2]. These examples are charged free gases confined in finite volumes as torus, boxes, spheres, cylinders (see also [3, 4, 5, 6]) and in the presence of general constant external magnetic fields ([7, 8, 9, 10]).

Teubner-Texte zur Physik•Jan 1, 1996•4 citations
We examine the occurrence of Bose-Einstein condensation in both nonrelativistic and relativistic systems with no self-interactions in a general setting. A simple condition for the occurrence of Bose-Einstein condensation is given. We show that condensation can occur only if q> 3q>~3q> 3, where qqq is the dimension associated with the continuous part of the eigenvalue spectrum of the Hamiltonian for nonrelativistic systems or the spatial part of the Klein-Gordon operator for relativistic systems. Furthermore we show that the criterion for the appearance of the Meissner-Ochsenfeld effect is closely connected with that for the appearance of Bose-Einstein condensation.
We examine the occurrence of Bose-Einstein condensation in both nonrelativistic and relativistic systems with no self-interactions in a general setting. A simple condition for the occurrence of Bose-Einstein condensation can be given if we adopt generalized \\zeta-functions to define the quantum theory. We show that the crucial feature governing Bose-Einstein condensation is the dimension q associated with the continuous part of the eigenvalue spectrum of the Hamiltonian for nonrelativistic systems or the spatial part of the Klein-Gordon operator for relativistic systems. In either case Bose-Einstein condensation can only occur if q\\ge3.
We examine the occurrence of Bose-Einstein condensation in both nonrelativistic and relativistic systems with no self-interactions in a general setting. A simple condition for the occurrence of Bose-Einstein condensation can be given if we adopt generalized ζ-functions to define the quantum theory. We show that the crucial feature governing Bose-Einstein condensation is the dimension q associated with the continuous part of the eigenvalue spectrum of the Hamiltonian for nonrelativistic systems or the spatial part of the Klein-Gordon operator for relativistic systems. In either case Bose-Einstein condensation can only occur if q ≥ 3 [1]. Several examples, some of them not completely solved before, may be treated very easily using our simple criterion [2]. These examples are charged free gases confined in finite volumes as torus, boxes, spheres, cylinders (see also [3, 4, 5, 6]) and in the presence of general constant external magnetic fields ([7, 8, 9, 10]).