scholarly journals Olbert’s Kappa Fermi and Bose Distributions

2021 ◽  
Vol 9 ◽  
Author(s):  
R. A. Treumann ◽  
Wolfgang Baumjohann
Keyword(s):  
Partition Function ◽  
Condensed Matter ◽  
Kappa Distribution ◽  
Microscopic Scale ◽  
Quantum Plasmas ◽  
Astrophysical Objects ◽  
Quantum Version ◽  
Statistical Mechanical ◽  
Energy And Momentum ◽  
Very Low Temperature

The quantum version of Olbert’s kappa distribution applicable to fermions is obtained. Its construction is straightforward but requires recognition of the differences in the nature of states separated by Fermi momenta. Its complement, the bosonic version of the kappa distribution is also given, as is the procedure of how to construct a hypothetical kappa-anyon distribution. At very low temperature the degenerate kappa Fermi distribution yields a kappa-modified version of the ordinary degenerate Fermi energy and momentum. We provide the Olbert-generalized expressions of the Olbert-Fermi partition function and entropy which may serve determining all relevant statistical mechanical quantities. Possible applications are envisaged to condensed matter physics, possibly quantum plasmas, and dense astrophysical objects like the interior state of terrestrial planets, neutron stars, magnetars where quantum effects come into play and dominate the microscopic scale but may have macroscopic consequences.

THE EXACT SOLUTION OF SOME LATTICE STATISTICS MODELS WITH FOUR STATES PER SITE

1964 ◽  
Vol 42 (8) ◽  
pp. 1564-1572 ◽  
Author(s):  
D. D. Betts
Keyword(s):  
Partition Function ◽  
Nearest Neighbor ◽  
Quaternary Alloy ◽  
Interesting Property ◽  
Two Dimensions ◽  
Lattice Statistics ◽  
Critical Temperatures ◽  
Different Types ◽  
Interacting Systems ◽  
Statistical Mechanical

Statistical mechanical ensembles of interacting systems localized at the sites of a regular lattice and each having four possible states are considered. A set of lattice functions is introduced which permits a considerable simplification of the partition function for general nearest-neighbor interactions. The particular case of the Potts four-state ferromagnet model is solved exactly in two dimensions. The order–disorder problem for a certain quaternary alloy model is also solved exactly on a square net. The quaternary alloy model has the interesting property that it has two critical temperatures and exhibits two different types of long-range order. The partition function for the spin-3/2 Ising model on a square net is expressed in terms of graphs without odd vertices, but has not been solved exactly.

scholarly journals Structural, Optical and Dynamic Properties of Thin Smectic Films

Crystals ◽  
2020 ◽  
Vol 10 (4) ◽  
pp. 321 ◽  
Author(s):  
Izabela Śliwa ◽  
A. V. Zakharov
Keyword(s):  
Optical Properties ◽  
Liquid Crystal ◽  
Transition Temperature ◽  
Solid Surface ◽  
Dynamic Properties ◽  
Condensed Matter ◽  
Theoretical Description ◽  
Structural And Optical Properties ◽  
Statistical Mechanical ◽  
Crystal Phases

The problem of predicting structural and dynamic behavior associated with thin smectic films, both deposited on a solid surface or stretched over an opening, when the temperature is slowly increased above the bulk transition temperature towards either the nematic or isotropic phases, remains an interesting one in the physics of condensed matter. A useful route in studies of structural and optical properties of thin smectic films is provided by a combination of statistical–mechanical theories, hydrodynamics of liquid crystal phases, and optical and calorimetric techniques. We believe that this review shows some useful routes not only for the further examining of the validity of a theoretical description of thin smectic films, both deposited on a solid surface or stretched over an opening, but also for analyzing their structural, optical, and dynamic properties.

THERMODYNAMICS OF q-MODIFIED BOSONS

1996 ◽  
Vol 10 (06) ◽  
pp. 683-699 ◽  
Author(s):  
P. NARAYANA SWAMY
Keyword(s):  
Mechanical Properties ◽  
Phase Transition ◽  
Equation Of State ◽  
Partition Function ◽  
Statistical Mechanics ◽  
Specific Heat ◽  
Thermodynamic Functions ◽  
Bose Condensation ◽  
Grand Partition Function ◽  
Statistical Mechanical

Based on a recent study of the statistical mechanical properties of the q-modified boson oscillators, we develop the statistical mechanics of the q-modified boson gas, in particular the Grand Partition Function. We derive the various thermodynamic functions for the q-boson gas including the entropy, pressure and specific heat. We demonstrate that the gas exhibits a phase transition analogous to ordinary bose condensation. We derive the equation of state and develop the virial expansion for the equation of state. Several interesting properties of the q-boson gas are derived and compared with those of the ordinary boson which may point to the physical relevance of such systems.

scholarly journals Annihilating random walks and perfect matchings of planar graphs

2003 ◽  
Vol DMTCS Proceedings vol. AC,... (Proceedings) ◽  
Author(s):  
Massimiliano Mattera
Keyword(s):  
Partition Function ◽  
Random Walks ◽  
Mechanical Model ◽  
Planar Graphs ◽  
Perfect Matchings ◽  
Statistical Mechanical Model ◽  
International Audience ◽  
Statistical Mechanical ◽  
Annihilating Random Walks

International audience We study annihilating random walks on $\mathbb{Z}$ using techniques of P.W. Kasteleyn and $R$. Kenyonon perfect matchings of planar graphs. We obtain the asymptotic of the density of remaining particles and the partition function of the underlying statistical mechanical model.

scholarly journals Extreme boundary conditions and random tilings

2021 ◽  
Author(s):  
Jean-Marie Stéphan
Keyword(s):  
Boundary Conditions ◽  
Quantum Particle ◽  
Condensed Matter ◽  
Two Dimensions ◽  
Basic Knowledge ◽  
Dimer Model ◽  
Long Range Correlations ◽  
Statistical Mechanical ◽  
Local Densities ◽  
Random Tilings

Standard statistical mechanical or condensed matter arguments tell us that bulk properties of a physical system do not depend too much on boundary conditions. Random tilings of large regions provide counterexamples to such intuition, as illustrated by the famous 'arctic circle theorem' for dimer coverings in two dimensions. In these notes, I discuss such examples in the context of critical phenomena, and their relation to 1+1d quantum particle models. All those turn out to share a common feature: they are inhomogeneous, in the sense that local densities now depend on position in the bulk. I explain how such problems may be understood using variational (or hydrodynamic) arguments, how to treat long range correlations, and how non trivial edge behavior can occur. While all this is done on the example of the dimer model, the results presented here have much greater generality. In that sense the dimer model serves as an opportunity to discuss broader methods and results. [These notes require only a basic knowledge of statistical mechanics.]

scholarly journals Amplification of Waves Reflected from Kerr Black Holes

1974 ◽  
Vol 64 ◽  
pp. 94-94 ◽  
Author(s):  
A. A. Starobinsky
Keyword(s):  
Black Hole ◽  
Gravitational Waves ◽  
Quantum Effect ◽  
Kerr Black Hole ◽  
Kerr Metric ◽  
Black Hole Mass ◽  
Quantum Version ◽  
Penrose Process ◽  
The One ◽  
Energy And Momentum

The effect of amplification of electromagnetic and gravitational waves reflected from a rotating black hole (‘superradiance scattering’) is investigated. This effect was proposed by Zel'dovich (1971). It leads, as well as the Penrose process, to the energy extraction from a Kerr black hole at the expense of its rotational energy and momentum decrease. The coefficient of wave reflection R>1 if ω<nω, where ω is the wave frequency, n - its angular momentum and ω is the black hole angular velocity. The value of this effect is not small in the case of gravitational waves, for example, if l=n = 2, ω →nω and a = M, then R≈2.38.There also exists a quantum version of the effect, namely, the one of spontaneous pair creation in the Kerr metric, but this quantum effect is exceedingly small in real astrophysical conditions, because its characteristic time is of the order G2M3/hc4, where M is the black hole mass.

Isotope effect on the thermodynamic quantities of gaseous uranium hexafluoride

1976 ◽  
Vol 54 (1) ◽  
pp. 160-165 ◽  
Author(s):  
Jan Bron
Keyword(s):  
Partition Function ◽  
Quantum Correction ◽  
Isotope Effects ◽  
Uranium Atom ◽  
Uranium Hexafluoride ◽  
Thermodynamic Quantities ◽  
Heavy Isotope ◽  
Statistical Mechanical ◽  
Lower Temperature ◽  
The Masses

For gaseous UF6 changes in the thermodynamic quantifies ΔG (= ΔA), ΔH (= ΔU), ΔCp (= ΔCv), and ΔS upon isotopic substitution can be determined by using the spectroscopically determined geometry and force field. The differences ΔG etc. are defined as (G238 – Gx), where 238 and x (x = 235, 234, 233, and 232) are the masses of the central uranium atom. The changes in the thermodynamic quantities are related to the logarithm of the partition function ratio of the UF6 species compared. The logarithm of the partition function ratio can be conveniently expressed as a series in temperature and hence, by using statistical mechanical relationships, the changes in thermodynamic quantities can be expressed as a series in temperature.Since these changes form examples of heavy isotope effects the validity and utility of the first quantum correction can be investigated. Uncertainties and trends in the magnitudes of the differences in the thermodynamic quantities due to uncertainties or changes in spectroscopic parameters are discussed by means of the first quantum correction. It has been found that the first quantum correction has little quantitative value in the lower temperature region, but it can be used in that range to explain some observed trends in the isotope effects. Some of the conclusions can also be applied to kinetic and equilibrium heavy isotope effects.

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