Related papers: Generalized partition functions, interpolating sta…
A generalization of symmetrized density matrices in combination with the technique of generating functions allows to calculate the partition function of identical particles in a parabolic confining well. Harmonic two-body interactions…
We consider a fractional generalization of Hamiltonian and gradient systems. We use differential forms and exterior derivatives of fractional orders. We derive fractional generalization of Helmholtz conditions for phase space. Examples of…
The method of separation of variables is significant, it has been applied to physics, engineering , chemistry and other fields. It allows to reduce the diffculity of problems by separating the variables from partial differential equation…
We pose the question of what is the best generalization of the factorial and the binomial coefficient. We give several examples, derive their combinatorial properties, and demonstrate their interrelationships. On cherche ici \`a…
We consider dilute gases of dipolar bosons or fermions in the high-temperature limit in a spherically symmetric harmonic trapping potential. We examine the system using a virial expansion up to second order in the fugacity. Using the Born…
This research introduces a new method for the transition from partial to ordinary differential equations that is based on the Kolmogorov superposition theorem. In this paper, we discuss the numerical implementation of the Kolmogorov theorem…
We present an interpolation between the bosonic and fermionic relations. This interpolation is given by an object which we call `generalized Brownian motion' and which is characterized by a generalization of the pairing rule for the…
We study two generalizations of fractional variational problems by considering higher-order derivatives and a state time delay. We prove a higher-order integration by parts formula involving a Caputo fractional derivative of variable order…
The problem of the calculation of equilibrium thermodynamic properties and the establishment of statistical-thermodynamically-consistent finite bound-state partition functions in nonideal multi-component plasma systems is revised within the…
A convenient way to calculate $N$-particle quantum partition functions is by confining the particles in a weak harmonic potential instead of using a finite box or periodic boundary conditions. There is, however, a slightly different…
This article develops a periodic version of a time varying parameter fractional process in the stationary region. It is a partial extension of Hosking (1981)'s article which dealt with the case where the coefficients are invariant in time.…
George and Wilson [Acta. Cryst. D 50, 361 (1994)] looked at the distribution of values of the second virial coefficient of globular proteins, under the conditions at which they crystallise. They found the values to lie within a fairly…
We compute the continuum limit of the spectra for the XX-model with arbitrary complex boundary fields. In the case of hermitian boundary terms one obtains the partition functions of the free compactified boson field on a cylinder with…
We consider a recently proposed approach to bosonization in which the original fermionic partition function is expressed as a product of a $G/G$-coset model and a bosonic piece that contains the dynamics. In particular we show how the…
Using a description of the Levin-Wen model excitations in terms of Wilson lines, we compute the degeneracy of the energy levels for any input anyon theory and for any trivalent graph embedded on any (orientable) compact surface. This result…
It is shown that the potential of Keesom which depends on temperature cannot be used for calculate the second virial coefficient of polar molecules and the formulae for second virial coefficient of [2] have no molecular statistical…
Evaluating the propagator by the usual time-sliced manner, we use it to compute the second virial coefficient of an anyon gas interacting through the repulsive potential of the form $g/r^2 (g > 0)$. All the cusps for the unpolarized…
We show that the particles in the Calogero-Sutherland Model obey fractional exclusion statistics as defined by Haldane. We construct anyon number densities and derive the energy distribution function. We show that the partition function…
Quadratic irrationals posses a periodic continued fraction expansion. Much less is known about cubic irrationals. We do not even know if the partial quotients are bounded, even though extensive computations suggest they might follow…
We give a prescription for calculating the high-temperature expansion of the thermal sunset integral to arbitrary order. We derive all terms odd in $T$, and rederive previous results up to $\mathcal{O}(T^0) $ for both bosonic and fermionic…