Related papers: A Statistical Analysis of Anharmonic Gases
A classical (non-quantum-mechanical) relativistic ideal gas in thermodynamic equilibrium in a uniformly accelerated frame of reference is studied using Gibbs's microcanonical and grand canonical formulations of statistical mechanics. Using…
We determine the quantitative effect, in the maximum number of particles and other static observables, due to small anharmonic terms added to the confining potential of an atomic condensed system with negative two-body interaction. As an…
A new kind of quantum statistics which interpolates between Bose and Fermi statistics is proposed beginning with the assumption that the quantum state of a many-particle system is a functional on the internal space of the particles. The…
The partition function for a system of non-interacting $N-$particles can be found by summing over all the states of the system. The classical partition function for an ideal gas differs from Bosonic or Fermionic partition function in the…
We investigate symmetric oscillators, and in particular their quantization, by employing semiclassical and quantum phase functions introduced in the context of Liouville-Green transformations of the Schr\"{o}dinger equation. For anharmonic…
A classical linear oscillator is treated in the small amplitude limit so that it will be approximately relativistic. The oscillator involves a charge particle in a linear potential in classical zero-point radiation. It is found that the…
In this paper, we investigate the stability of the configurations of harmonic oscillator potential that are directly proportional to the square of the displacement. We derive expressions for fluctuations in partition function due to…
We establish an analytical criterion for dynamical thermalization within harmonic systems, applicable to both classical and quantum models. Specifically, we prove that thermalization of various observables, such as particle energies in…
In our previous paper I (del Valle--Turbiner, Int. J. Mod. Phys. A34, 1950143, 2019) it was developed the formalism to study the general $D$-dimensional radial anharmonic oscillator with potential $V(r)= \frac{1}{g^2}\,\hat{V}(gr)$. It was…
In this work we address the problem of the quantization of a simple harmonic oscillator that is perturbed by a time dependent force. The approach consists of removing the perturbation by a canonical change of coordinates. Since the…
We consider an analytic way to make the interacting N-body problem tractable by using harmonic oscillators in place of the relevant two-body interactions. The two body terms of the N-body Hamiltonian are approximated by considering the…
We reveal a new face of the old clich\'ed system: a dissipative quantum harmonic oscillator. We formulate and study a quantum counterpart of the energy equipartition theorem satisfied for classical systems.Both mean kinetic energy $E_k$ and…
The most important recent results in the theory of phase transitions and quantum effects in quantum anharmonic crystals are presented and discussed. In particular, necessary and sufficient conditions for a phase transition to occur at some…
We consider the dynamics of a charged particle interacting with background electromagnetic field under the influence of linearized gravitational waves in the long wave-length and low-velocity limit. Following the prescription in…
Relations between Hamiltonian mechanics and quantum mechanics are studied. It is stressed that classical mechanics possesses all the specific features of quantum theory: operators, complex variables, probabilities (in case of ergodic…
We study a heavy piston of mass $M$ that separates finitely many ideal, unit mass gas particles moving in two or three dimensions. Neishtadt and Sinai previously determined a method for finding this system's averaged equation and showed…
We introduce a functional perturbative method for treating weakly nonlinear systems coupled with a quantum field bath. We demonstrate using this method to obtain the covariance matrix elements and the correlation functions of a quantum…
A new simple method to measure the spatial distribution of the electric field in the plasma sheath is proposed. The method is based on the experimental investigation of vertical oscillations of a single particle in the sheath of a…
The asymptotic partition function for quantized Abelian Higgs vortices at high temperature $T$ is found to leading and subleading order, and from this the equation of state of the vortex gas is derived, including the first quantum…
In this paper we discuss mechanical systems with inequality constraints. We demonstrate how such constraints can be taken into account by proper modification of the action which describes the original unconstrained dynamics. To illustrate…