Related papers: Some applications of the Lambert W function to cla…
Statistical functions such as the moment-generating function, characteristic function, cumulant-generating function, and second characteristic function are cornerstone tools in classical statistics and probability theory. They provide a…
We study the emergence of Boltzmann's law for the "single particle energy distribution" in a closed system of interacting classical spins. It is shown that for a large number of particles Boltzmann's law may occur, even if the interaction…
We develop a classical density functional for water which combines the White Bear fundamental-measure theory (FMT) functional for the hard sphere fluid with attractive interactions based on the Statistical Associating Fluid Theory…
Lattice molecule models are proposed in order to study statistical mechanics of glass transition in finite dimensions. Molecules in the models are represented by hard Wang tiles and their density is controlled by a chemical potential. An…
In order to improve the teaching of the course of statistical physics in universities, in this article we introduce nonextensive statistics, a new statistical theory about complex systems. We study the two modification coefficients a and b…
In the framework of higher transcendental functions the Wright functions of the second kind have increased their relevance resulting from their applications in probability theory and, in particular, in fractional diffusion processes. Here,…
We present the analytical solution in closed form for the semiclassical limit of the quantum mechanical Coulomb Green function in position space in n dimensions. We utilize a projection method which has its roots in Lambert's theorem and…
Ladder functions in classical mechanics are defined in a similar way as ladder operators in the context of quantum mechanics. In the present paper, we develop a new method for obtaining ladder functions of one dimensional systems by means…
The methods of statistical mechanics are applied to two-dimensional foams under macroscopic agitation. A new variable -- the total cell curvature -- is introduced, which plays the role of energy in conventional statistical thermodynamics.…
Classical dynamical density functional theory (DDFT) is one of the cornerstones of modern statistical mechanics. It is an extension of the highly successful method of classical density functional theory (DFT) to nonequilibrium systems.…
The concept of the Wigner function is used to construct a semi-classical kinetic theory describing the evolution of the axial-current phase-space density of spin-1/2 particles in the relaxation time approximation. The resulting approach can…
In this paper we complete our understanding of the role played by the limiting (or residue) function in the context of mod-Gaussian convergence. The question about the probabilistic interpretation of such functions was initially raised by…
We find a class of exact solutions to the Lighthill Whitham Richards Payne (LWRP) traffic flow equations. Using two consecutive lagrangian transformations, a linearization is achieved. Next, depending on the initial density, we either apply…
We present a brief review of the classical density functional theory of atomic and molecular fluids. We focus on the application of the theory to the determination of the solvation properties of arbitrary molecular solutes in arbitrary…
The lattice field theory approach to the statistical mechanics of a classical Coulomb gas [R. Coalson and A. Duncan, J. Chem. Phys. 97,5653(1992)] is generalized to include charged polymer chains. Saddle-point analysis is done on the…
We review how antiparticles may be introduced in classical relativistic mechanics, and emphasize that many of their paradoxical properties can be more transparently understood in the classical than in the quantum domain.
In this paper we revise two classical examples of Relativistic Hydrodynamics in order to illustrate in detail the numerical methods commonly used in fluid dynamics, specifically those designed to deal with shocks, which are based on a…
We present a formulation of classical statistical mechanics based on a Lagrangian description on the tangent bundle. In this approach, a Wick rotation from real time to imaginary time is employed as a technical device that facilitates the…
The relationship between classical and quantum mechanics is explored in an intuitive manner by the exercise of constructing a wave in association with a classical particle. Using special relativity, the time coordinate in the frame of…
We present a new description of the known large deviation function of the classical symmetric simple exclusion process by exploiting its connection with the quantum symmetric simple exclusion processes and using tools from free probability.…