An asymptotic formula for the logarithm of generalized partition functions

2019 ◽  
Vol 49 (1) ◽  
pp. 39-53
Author(s):  
Seiken Saito
Keyword(s):  
Asymptotic Formula ◽  
Partition Functions ◽  
Generalized Partition

scholarly journals GENERALIZED PARTITION FUNCTIONS AND INTERPOLATING STATISTICS

1998 ◽  
Vol 13 (11) ◽  
pp. 843-852 ◽  
Author(s):  
P. F. BORGES ◽  
H. BOSCHI-FILHO ◽  
C. FARINA
Keyword(s):  
High Temperature ◽  
Low Temperature ◽  
Virial Coefficient ◽  
Second Virial Coefficient ◽  
Temperature Limit ◽  
Partition Functions ◽  
High Temperature Limit ◽  
Full Temperature ◽  
Generalized Partition ◽  
Relativistic Particles

We show that the assumption of quasiperiodic boundary conditions (those that interpolate continuously periodic and antiperiodic conditions) in order to compute partition functions of relativistic particles in 2+1 space–time can be related with anyonic physics. In particular, in the low temperature limit, our result leads to the well-known second virial coefficient for anyons. Besides, we also obtain the high temperature limit as well as the full temperature dependence of this coefficient.

Generalized partition functions and subgroup growth of free products of nilpotent groups

Analysis ◽  
2005 ◽  
Vol 25 (4) ◽  
Author(s):  
Thomas W. Müller ◽  
Jan-Christoph Schlage-Puchta
Keyword(s):  
Nilpotent Group ◽  
Nilpotent Groups ◽  
Partition Functions ◽  
Free Products ◽  
Subgroup Growth ◽  
Free Nilpotent Group ◽  
Generalized Partition ◽  
Torsion Free

SummaryWe estimate the growth of homomorphism numbers of a torsion-free nilpotent group

scholarly journals On the parity of generalized partition functions, III

2010 ◽  
Vol 22 (1) ◽  
pp. 51-78 ◽  
Author(s):  
Fethi Ben Saïd ◽  
Jean-Louis Nicolas ◽  
Ahlem Zekraoui
Keyword(s):  
Partition Functions ◽  
Generalized Partition

scholarly journals NON-EXTENSIVE STUDY OF RIGID AND NON-RIGID ROTATORS

2004 ◽  
Vol 18 (11) ◽  
pp. 467-477 ◽  
Author(s):  
GŎKHAN B. BAĞCI ◽  
RAMAZAN SEVER ◽  
CEVDET TEZCAN
Keyword(s):  
Low Temperature ◽  
Temperature Regime ◽  
Scale Parameter ◽  
Extensive Study ◽  
Heat Capacities ◽  
Partition Functions ◽  
Rigid Rotator ◽  
Tsallis Statistics ◽  
Rotator Model ◽  
Generalized Partition

The isotropic rigid and non-rigid rotators in the framework of Tsallis statistics are studied in the high and low temperature limits. The generalized partition functions, internal energies and heat capacities are calculated. Classical results of the Boltzmann–Gibbs statistics have been recovered as non-extensivity parameter approaches to 1. It has also been observed that non-extensivity parameter q behaves like a scale parameter in the low temperature regime of the rigid rotator model.

scholarly journals GENERALIZED PARTITION FUNCTIONS, INTERPOLATING STATISTICS AND HIGHER VIRIAL COEFFICIENTS

1999 ◽  
Vol 14 (18) ◽  
pp. 1217-1226 ◽  
Author(s):  
P. F. BORGES ◽  
H. BOSCHI-FILHO ◽  
C. FARINA
Keyword(s):  
Boundary Condition ◽  
Finite Temperature ◽  
Virial Coefficient ◽  
Second Virial Coefficient ◽  
Virial Coefficients ◽  
Partition Functions ◽  
Generalized Partition

Starting from determinants at finite temperature obeying an intermediate boundary condition between the periodic (bosonic) and antiperiodic (fermionic) cases, we find results which can be mapped onto those obtained from anyons for the second virial coefficient. Using this approach, we calculate the corresponding higher virial coefficients and compare them with the results in the literature.

Heavy Tails of Discounted Aggregate Claims in the Continuous-Time Renewal Model

2007 ◽  
Vol 44 (02) ◽  
pp. 285-294 ◽  
Author(s):  
Qihe Tang
Keyword(s):  
Asymptotic Formula ◽  
Continuous Time ◽  
Heavy Tails ◽  
Tail Behavior ◽  
Renewal Model ◽  
Discounted Aggregate Claims ◽  
Aggregate Claims ◽  
Tail Asymptotic

We study the tail behavior of discounted aggregate claims in a continuous-time renewal model. For the case of Pareto-type claims, we establish a tail asymptotic formula, which holds uniformly in time.

Approximation properties of Szász type operators involving Charlier polynomials

Filomat ◽  
2017 ◽  
Vol 31 (2) ◽  
pp. 479-487
Author(s):  
Didem Arı
Keyword(s):  
Asymptotic Formula ◽  
Weighted Space ◽  
Approximation Properties ◽  
Charlier Polynomials

In this paper, we give some approximation properties of Sz?sz type operators involving Charlier polynomials in the polynomial weighted space and we give the quantitative Voronovskaya-type asymptotic formula.

Bimolecular Reactions, Transition-State Theory

2018 ◽  
Author(s):  
Niels Engholm Henriksen ◽  
Flemming Yssing Hansen
Keyword(s):  
Transition State ◽  
Saddle Point ◽  
Transition State Theory ◽  
Classical Mechanics ◽  
Small Degree ◽  
State Theory ◽  
Reaction Coordinate ◽  
Partition Functions ◽  
Bimolecular Reactions ◽  
Activated Complex

This chapter discusses an approximate approach—transition-state theory—to the calculation of rate constants for bimolecular reactions. A reaction coordinate is identified from a normal-mode coordinate analysis of the activated complex, that is, the supermolecule on the saddle-point of the potential energy surface. Motion along this coordinate is treated by classical mechanics and recrossings of the saddle point from the product to the reactant side are neglected, leading to the result of conventional transition-state theory expressed in terms of relevant partition functions. Various alternative derivations are presented. Corrections that incorporate quantum mechanical tunnelling along the reaction coordinate are described. Tunnelling through an Eckart barrier is discussed and the approximate Wigner tunnelling correction factor is derived in the limit of a small degree of tunnelling. It concludes with applications of transition-state theory to, for example, the F + H2 reaction, and comparisons with results based on quasi-classical mechanics as well as exact quantum mechanics.

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