Effects of a small deviation from fermi statistics

By considering a generalized statistics with occupation numbers between Bose-Einstein and Fermi-Dirac statistics we study the resultant distribution when the states differ by a small factor from a Fermi-Dirac distribution. Both the Fermi energy and any level crossing phenomena are sensitive to such statistics; in particular, the electrical conductivity and the free electron heat capacity of fermions at low temperatures receive corrections due to alterations of Fermi-Dirac statistics.     

On the interaction of a black-body radiation field with a photoconductor

In this article we consider the problem of how to reconcile the Bose-Einstein statistics of the incident radiation field with the Fermi-Dirac statistics of the electron population in a photoconductor which is in equilibrium with the radiation field. A Langevin approach is followed, based on Einstein's rate equations. Results for the noise sources associated with absorption, stimulated emission, and spontaneous emission, are derived. These results are shown to be consistent with the Fermi-Dirac statistics of the electron processes; also, the various sources are shown to reconstitute the black-body radiation field.     

The lifetime of the dimuon atom

Summary The weak decay of a muon in the ground state of a dimuon atom is analysed. Although the two muons are correlated by Fermi-Dirac statistics, it is shown that, in marked contrast to the seemingly analogous case of neutron beta-decay in³H, statistics have no effect on the muon decay rate. The distinction between the two cases is discussed. To speed up publication, the author of this paper has agreed to not receive the proofs for correction.     

Unified statistical distribution of quantum particles and Symmetry

In this paper we propose a unified statistics of Bose-Einstein and Fermi-Dirac statistics by suggesting that every particle can be associated with matter or fundamental forces with certain probability. The main Justification for this proposal is the possibility of extension of the spin-statistics theory to include a hypothetical quantum particles have fractional spin. The concept of Supersymmetry can be related to this unified statistics.     

黑体辐射中两类粒子的辐射规律

考虑到相对论效应,采用量子统计的方法,得到了满足Bose-Einstein统计分布和Fermi-Dirac统计分布的两类粒子的黑体辐射公式（包括Planck黑体辐射公式）．发现辐射谱不仅与黑体的辐射温度有关,还与辐射粒子的能量、化学势和种类有关．辐射强度与辐射粒子的能量、静质量、简并因子有关。     

Statistical mechanics of a confinement electron gas in a uniform electromagnetic field

In this paper we study an ideal electron gas in the presence of a uniform electromagnetic field and confinement by a three-dimensional harmonic potential. We find the partition function of this system and in the sequel we examine the Boltzmann statistics and Fermi-Dirac statistics applying the grand canonical ensemble method.     

Intermediate statistics as a consequence of deformed algebra

We present a formulation of deformed oscillator algebra which leads to intermediate statistics as a continuous interpolation between Bose-Einstein and Fermi-Dirac statistics. It is deduced that a generalized permutation or exchange symmetry leads to the introduction of the basic number and it is then established that this in turn leads to the deformed algebra of oscillators. We obtain the mean occupation number describing the particles obeying intermediate statistics which thus establishes the interpolating statistics and describe boson-like and fermion-like particles obeying intermediate statistics. We also obtain an expression for the mean occupation number in terms of an infinite continued fraction, thus clarifying successive approximations.     

Toda solitons as Fermi-quasiparticles

The Bethe ansatz leads to Yang-Yang integral equations. The particle-hole structure of the zero-temperature excitations is generalized to finite temperatures, which leads to the definition of soliton- and phonon-quasiparticles. The solitons approximately follow the Fermi-Dirac statistics and have a chemical potential with an unusual temperature dependence, because the number of solitons is not constant.     

Generalized statistical mechanics for the N-body quantum problem — ideal gases

Within Tsallis generalized thermostatistics, the grand canonical ensemble is derived for quantum systems. In particular, the generalized Fermi-Dirac, Bose-Einstein and Maxwell-Boltzmann statistics are defined. The behavior of the chemical potential is depicted as a function of the temperature. Some thermodynamic quantities at high and low temperature are studied as well.     

Generalized Fock spaces,new forms of quantum statistics and their algebras

We formulate a theory of generalized Fock spaces which underlies the different forms of quantum statistics such as ‘infinite’, Bose-Einstein and Fermi-Dirac statistics. Single-indexed systems as well as multi-indexed systems that cannot be mapped into single-indexed systems are studied. Our theory is based on a three-tiered structure consisting of Fock space, statistics and algebra. This general formalism not only unifies the various forms of statistics and algebras, but also allows us to construct many new forms of quantum statistics as well as many algebras of creation and destruction operators. Some of these are: new algebras for infinite statistics,q-statistics and its many avatars, a consistent algebra for fractional statistics, null statistics or statistics of frozen order, ‘doubly-infinite’ statistics, many representations of orthostatistics, Hubbard statistics and its variations.     

Renormalization of boundary conditions for distribution functions of quasiparticles obeying quantum statistics at interfaces between crystalline grains

Boundary conditions for distribution functions of quasiparticles scattered by an interface between two crystalline grains are presented. In contradistinction to former formulations where the Maxwell-Boltzmann statistics was considered, the present boundary conditions take into account the quantum (Fermi-Dirac or Bose-Einstein) statistics of the quasiparticles. Provided that small deviations from the thermodynamical equilibrium only are present, the boundary conditions are linearized, and then their “renormalization” is investigated in case of the elastic scattering. The final results of the renormalization, which are obtained for a simplified model of an interface, suggest that the portion of the Fermi (Bose)-quasiparticles reflected or transmitted specularly is decreased (increased) in comparison with the case of quasiparticles obeying the Maxwell-Boltzmann statistics.     

H-theorem and generalized semi-detailed balance condition for lattice gas systems

For lattice gas systems obeying Fermi-Dirac statistics, an H-theorem can be proved with a more general condition that the semi-detailed balance condition. This new condition allows more flexible transition rates among states, so that it has broader applicability for various lattice gas models, including those which have multiple phase properties.     

金属中自由电子气体的非广延统计研究

采用分解近似的方法讨论了在Tsallis量子统计物理框架中，金属中自由电子气体的非广延参数q的热力学统计处理，计算出了总粒子数、总能量、自由能、热容量等热力学量，得出结论：在低温区域，q→1时，所有结果都可以回到传统的Fermi-Dirac分布，非广延参数q控制着系统的非广延程度.最后，详细讨论了q与热容量之间的关系，并与以前的结果作了比较. 关键词： Tsallis广义统计 非广延参数q 自由电子气体 Fermi-Dirac分布     

Non-equilibrium electron and phonon dynamics in metals under femtosecond laser pulses

Different models for relaxation dynamics of electrons and phonons in a thin metal film heated by femto-pico second laser pulses have been discussed. The traditional two-temperature approach reveals to be inaccurate due to deviations of electrons and phonons from Fermi-Dirac and Bose-Einstein distributions, respectively. Coupled Boltzmann kinetic equations have been adapted for the quantum statistics to study the energy distribution of electrons and phonons in metals. Theoretical details have been discussed and a new solution method has been proposed overcoming numerical problems and improving stability, allowing the study of the dynamics until the complete relaxation. Numerical results have been compared with photoemission spectroscopy experimental data.     

Hypercomplex number approach to Schwinger's quantum source theory

The hypercomplex numbers associated with the Dirac-Clifford algebra, are applied to the spin–0, –1/2, and –1 structures for Schwinger's source theory of quantum electrodynamics. The generalizations to 5-vectors and 5-space relativity are introduced. The anticommuting numbers, associated with Fermi-Dirac statistics, are examined in some detail. The hyper-complex number formulation is suitable for curved space quantum computations.     

Exchange monte carlo for molecular simulations with monoelectronic hamiltonians

We introduce a general Monte Carlo scheme for achieving atomistic simulations with monoelectronic Hamiltonians including the thermalization of both nuclear and electronic degrees of freedom. The kinetic Monte Carlo algorithm is used to obtain the exact occupation numbers of the electronic levels at canonical equilibrium, and comparison is made with Fermi-Dirac statistics in infinite and finite systems. The effects of a nonzero electronic temperature on the thermodynamic properties of liquid silver and sodium clusters are presented.     

Über die statistische Begründung des Nernstschen Wärmetheorems

It is shownNernst's theorem holds when the number of energy levels per energy interval of the system as a whole satisfies certain conditions asymptotically when the number of particles in the system tends toward infinity. These conditions are found to be satisfied for all realistic physical models that have so far been studied. The case of Fermi-Dirac statistics is a limiting case; this may be related with the phenomenon of superconductivity.     

The thermodynamics of hydrogen-vacancy interactions in aluminum

The thermodynamic properties of Al-H solid solutions containing lattice vacancies have been discussed using an approach in which the grand canonical ensemble is used to elucidate the behavior of the Al-VAC-H system in Fermi-Dirac statistics. Calculations have been presented and compared for specific models in which H-atoms act both as a simple interstitial species and forms either decorated vacancies or substitutional defects.Vacancy concentrations concomitant to different levels of hydrogenization are calculated and approximate penetration curves for the ingress of vacancies from the metal surface are presented.