Related papers: Analytic expressions for Debye functions and the h…
Thermal vibrations alter the external potential. Allen (Phys. Rev. B 18 (1978) 5217) proved that at finite temperatures the pseudopotential form factors are corrected by a Debye-Waller Factor (DWF). We generalize this result to the crystal…
An asymptotic expansions for the grand partition function of ideal Bose gas in the canonical ensemble with arbitrary number of particles is obtained. It is shown that the expressions found are valid in the whole temperature region, the…
The N-particle partition function of a one-dimensional $\delta$-function bose gas is calculated explicitly using only the periodic boundary condition (the Bethe ansatz equation). The N-particles cluster integrals are shown to be the same as…
In a recent paper (Phys. Rev. E {\bf 104}, 014103 (2021) ) M. Baggioli and A. Zaccone formulate a theoretical description of the specific heat of liquids by using Debye's expression for the specific heat of solids and inserting a density of…
We develop exact, simple closed form expressions for partition functions associated with relativistic bosons and fermions in odd spatial dimensions. These expressions, valid at high temperature, include the effects of a non-trivial Polyakov…
This review presents the effective temperature notion as defined from the deviations from the equilibrium fluctuation-dissipation theorem in out of equilibrium systems with slow dynamics. The thermodynamic meaning of this quantity is…
The density of accessible levels in the ($^3$He,$\alpha \gamma$) reaction has been extracted for the $^{162}$Dy, $^{166}$Er and $^{172}$Yb nuclei. The nuclear temperature is measured as a function of excitation energy in the region of 0 --…
A generalized physical model is introduced to describe the impulsive stimulated scattering (ISS) response of relaxing systems to photothermal excitation in a periodical grating geometry. The proposed approach starts from Debye and…
This is the second paper in a series studying the global asymptotics of discrete $N$-particle systems with inverse temperature parameter $\theta$ in the high temperature regime. In the first paper, we established necessary and sufficient…
The high temperature asymptotics of thermodynamic functions of electromagnetic field subjected to boundary conditions with spherical and cylindrical symmetries are constructed by making use of a general expansion in terms of heat kernel…
The nonequilibrium thermodynamics feature of a Brownian motor operating between two different heat baths is explored as a function of time $t$. Using the Gibbs entropy and Schnakenberg microscopic stochastic approach, we find exact closed…
Active matter and driven systems exhibit statistical fluctuations in density and particle positions, providing an indirect indicator of dissipation across multiple length and time scales. Here, we quantitatively relate these measurable…
One-dimensional repulsive delta-function bose system is studied. By only using the Bethe ansatz equation, n-particle partition functions are exactly calculated. From this expression for the n-particle partition function, the n-particle…
We investigate the three-dimensional SU(3) gauge theory at finite temperature in the framework of dimensional reduction. The large scale properties of this theory are expected to be conceptually more complicated than in four dimensions. The…
For an elliptic differential operator $D$ of order $h$ in $n$ dimensions, the spectral $\zeta$-function $\zeta_D(s)$ for $\Re s > \frac{n}{h}$ can be evaluated as an integral over the heat kernel $e^{-t D}$. Here, alternative expressions…
Self-consistent approach for interacting phonons description in lattice, which generalized Debye model, is proposed. Notion of "self-consistent" phonons is introduced, speed of which depends on temperature and is determined from non-linear…
We present closed analytical expressions for the particle and kinetic energy spatial densities at finite temperatures for a system of noninteracting fermions (bosons) trapped in a d-dimensional harmonic oscillator potential. For d=2 and 3,…
Development generating diffraction-related valuable expressions and formulas capable of initiating new era for diffraction and for scientific domains that use it provided. The main expression, among these, gives diffracted intensity as…
Sequences of experimental ground-state energies for both odd and even $A$ are mapped onto concave patterns cured from convexities due to pairing and/or shell effects. The same patterns, completed by a list of excitation energies, give…
We study the behavior of the pressure function for H\"{o}lder continuous potentials on mixing subshifts of finite type. The classical theory of thermodynamic formalism shows that such pressure functions are convex, analytic and have slant…