Abstract
A new form of Quantum Statistics is deduced from a general model of interactions between particles based on Probability Theory and by the minimization of energy of quantum states. As a result of the theory a new definition of entropy is obtained, together with a generalization of the Pauli’s exclusion principle valid for fermions and bosons. The new statistics obtained for these two kinds of matter, is expressed as function of the number of occupied quantum states ω(ε) at energy level ε, and it is an alternative and complementary form of the classical statistics of Bose–Einstein and Fermi–Dirac. New informations are deduced about the “condensation” of matter into single states of quantum coherence and a unified description of BEC phenomena is drawn for bosons and fermions.
Similar content being viewed by others
References
Anderson, M.H., Ensher, J.R., Matthews, M.R., Wieman, C.E., Cornell, E.A.: Observation of Bose–Einstein condensation in a dilute atomic vapor. Science 269, 198 (1995)
Barbarani, V.: Design and Management of Complexity in Software Systems: a model based on Probability Theory. AQuIS’96 3rd International Conference on Achieving Quality in Software, Florence (unpublished) (1996)
Bardeen, J., Cooper, L.N., Schrieffer, J.R.: Phys. Rev. Lett. 108, 1175 (1957)
Boltzmann, L.: Uber die Beziehung zwischen dem zweiten Hauptsatz der mechanischen Warmetheorie und der Wahrscheinlichkeitsrechnung respektive den Satzen uber des Warmegleichgewicht. Wien. Ber. 76, 373–435 (1877)
Born, M.: Atomic Physics. Blackie, Glasgow (1969)
Bose, S.N.: Z. Phys. 26, 178 (1924)
Cohen, E.G.D.: Boltzmann and statistical mechanics. In: Accademia Nazionale dei Lincei International Meeting “Boltzmann’s Legacy—150 Years after his Birth”, Rome, May 1994
Cornell, E.A., Ensher, J.R., Wieman, C.E.: Experiments in dilute atomic Bose–Einstein condensation. In: Inguscio, M., Stringari, S., Wieman, C.E. (eds.) Bose–Einstein Condensation in Atomic Gases, Proceedings of the International School of Physics Enrico Fermi Course CXL. Italian Physical Society (1999)
Davis, K.B., Mewes, M.O., Andrews, M.R., van Druten, N.J., Durfee, D.S., Kurn, D.M., Ketterle, W.: Bose–Einstein condensation in a gas of sodium atoms. Phys. Rev. Lett. 75, 3969 (1995)
Einstein, A.: Sitzber. Kgl. Preuss. Akad. Wiss. XVIII–XXV, 3 (1925)
Fermi, E.: Sulla quantizzazione del gas perfetto monoatomico. Rend. Lincei 3, 145–149 (1926)
Fermi, E.: Zur Quantelung des idealen einatomigen Gases. Z. Phys. 36, 902–912 (1926)
Ketterle, W.: (2001). When atoms behave as waves: Bose–Einstein condensation and the atom laser. In: Nobel Lecture, 8 December 2001
Kompaneyets, A.S.: Theoretical Physics. Peace, Moscow (1961)
Laborit, H.: Dieu ne joue pas aux des. Grasset & Fasquelle, Paris (1987)
Landau, L.D., Lifshic, E.M.: Meccanica Quantistica—Teoria non relativistica. Boringhieri, Torino (1969)
Osheroff, D.D., Richardson, R.C., Lee, D.M.: Evidence for a new phase of solid He-3. Phys. Rev. Lett. 28, 885 (1972)
Sinai, Y.G.: Probability Theory—An Introductory Course. Springer, Berlin (1992)
Wiener, N.: Cybernetics or Control and Communication in the Animal and the Machine. Wiley, New York (1953)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Barbarani, V. New Quantum Statistics and the Theory of Bose–Einstein Condensation. Int J Theor Phys 46, 2401–2428 (2007). https://doi.org/10.1007/s10773-007-9358-6
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10773-007-9358-6