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arXiv:cond-mat/9612069 · Physical Review Letters

Properties of Particles Obeying Ambiguous Statistics

Mikhail V. Medvedev

Published Jun 2, 1997• 24 citations
arXivHTMLPDF

Abstract

A new class of identical particles which may exhibit both Bose and Fermi statistics with respective probabilities ${p}_{b}$ and ${p}_{f}$ is introduced. Such an uncertainty may be either an intrinsic property of a particle or can be viewed as an ``experimental uncertainty.'' Statistical equivalence of such particles and particles obeying parastatistics of infinite order is shown. Generalized statistical distributions are derived, and statistical and thermodynamical properties of an ideal gas of the particles are investigated. The physical nature of such particles and the implications of this investigation for the statistics of extremal black holes are discussed.

DOI
10.1103/physrevlett.78.4147

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A new class of identical particles which may exhibit both Bose and Fermi statistics with respective probabilities pb{p}_{b}pb​ and pf{p}_{f}pf​ is introduced. Such an uncertainty may be either an intrinsic property of a particle or can be viewed as an ``experimental uncertainty.'' Statistical equivalence of such particles and particles obeying parastatistics of infinite order is shown. Generalized statistical distributions are derived, and statistical and thermodynamical properties of an ideal gas of the particles are investigated. The physical nature of such particles and the implications of this investigation for the statistics of extremal black holes are discussed.
A new kind of quantum statistics which interpolates between Bose and Fermi statistics is proposed beginning with the assumption that the quantum state of a many-particle system is a functional on the internal space of the particles. The quantum commutation relations for such particle creation and annihilation operators are derived, and statistical partition function and thermodynamical properties of an ideal gas of the particles are investigated. The application of this quantum statistics for the ensemble of extremal black holes are discussed.
A hypothetical gas of identical spinless particles obeying r-parastatistics is dealt with. The method allows a unified treatment of both the Fermi and the Bose gases. The partition function, the equation of state, and the thermodynamic functions are simple generalizations of those for the physical quantum gases, which are included as special cases. All paragases have a Fermi energy and a Bose-Einstein condensation. A quantitative criterion of degeneracy for the physical quantum gases is proposed. The fluctuations of occupation numbers and density are also discussed. Expansions for high and low temperatures are given to third order.
ABSTRACT The Feynman probability amplitudes for interactions between spin ½ fields and fields of integral spin quantized according to the generalized method of Green are investigated. It is shown that the scattering amplitudes are independent of the method of quantization though the amplitudes of the vacuum fluctuations are not. The question of distinguishing particles satisfying the generalized statistics, if they exist in nature, from Fermi or Bose particles is considered. It is shown that the statistical thermodynamics of the particles depends on the statistics, but as this requires a large number of particles in thermodynamical equilibrium, it offers no means of distinction for particles with short lifetimes. In practice, an examination of particles in bound states would identify particles obeying generalized statistics.
Abstract Chapter 11 presents a statistical mechanical treatment of the quantum ideal gases, i.e., the ideal Boltzmann, fermion, and boson gases. The discussion begins with the microscopic description and the solution of the eigenvalue problem for a quantum ideal gas. It is argued that calculating the partition function is most readily accomplished in the grand canonical ensemble using a second-quantized formulation. When the particles are distinguishable, the equation of state is identical to that of a classical ideal gas. For fermions and bosons, however, the problem of computing thermodynamic properties is significantly more complex and can only be solved exactly in certain limits. Away from these limits approximations are needed and are discussed in detail. The relevant distributions - the Fermi-Dirac and Bose-Einstein distributions are derived. The local density approximation of density functional theory is derived for the ideal electron gas. For the ideal boson gas, the phenomenon of Bose-Einstein condensation is discussed
We derive some physical properties of ideal assemblies of identical particles obeying generalized exclusion statistics. We discuss fluctuations and in this connection point out a fundamental contrast to conventional quantum statistics. We demonstrate a duality relating the distribution of particles at statistics ggg to the distribution of holes at statistics 1g\frac{1}{g}g1​. We suggest an application to Mott insulators.