The statistical mechanics of particles obeying discrete spatial quantum theory

Stéphane Ouvry, Alexios P. Polychronakos

We formulate and study the microscopic statistical mechanics of systems of particles with exclusion statistics in a discrete one-body spectrum. The statistical mechanics of these systems can be expressed in terms of effective single-level grand partition functions obeying a generalization of the standard thermodynamic exclusion statistics equation of state. We derive explicit expressions for the thermodynamic potential in terms of microscopic cluster coefficients and show that the mean occupation numbers of levels satisfy a nesting relation involving a number of adjacent levels determined by the exclusion parameter. We apply the formalism to the harmonic Calogero model and point out a relation with the Ramanujan continued fraction identity and appropriate generalizations.

N. N. Bogolyubov, A. M. Kurbatov, A. S. Shumovskiǐ

Edward G. Harris

Won-Young Hwang, Jeong‐Young Ji, Jongbae Hong

The concept of wavefunction reduction should be introduced to standard quantum mechanics in any physical processes where effective reduction of wavefunction occurs, as well as in the measurement processes. When the overlap is negligible, each particle obey Maxwell-Boltzmann statistics even if the particles are in principle described by totally symmetrized wavefunction [P.R.Holland, The Quantum Theory of Motion, Cambridge Unversity Press, 1993, p293]. We generalize the conjecture. That is, particles obey some generalized statistics that contains the quantum and classical statistics as special cases, where the degree of overlapping determines the statistics that particles should obey among continuous generalized statistics. We present an example consistent with the conjecture.

Mishra, A. K., G. Rajasekaran

Orthofermi statistics is characterized by an exclusion principle which is more ``exclusive'' than Pauli's exclusion principle: an orbital state shall not contain more than one particle, no matter what the spin direction is. The wavefunction is antisymmetric in spatial indices alone with arbitrary symmetry in the spin indices. Orthobose statistics is corresponding Bose analog: the wavefunction is symmetric in spatial indices, with arbitrary symmetry in spin indices. We construct the quantum field theory of particles obeying these new kinds of quantum statistics. Non-relativistic as well as relativistic quantum field theories with interactions are considered.

Wesley E. Brittin, Asım Orhan Barut