Related papers: The virial expansion of a classical interacting sy…
A version of the continuum Widom-Rowlinson model is introduced and studied. It is a two-component gas of point particles placed in $\mathbf{R}^d$ in which like particles do not interact and unlike particles contained in a given vessel of…
Richardson equations can be mapped on the classical electrostatic problem in two dimensions. We have recently suggested a new analytical approach to these equations in the thermodynamical limit, which is based on the `probability' of the…
We consider the long time behavior of heterogeneously interacting diffusive particle systems and their large population limit. The interaction is of mean field type with weights characterized by an underlying graphon. The limit is given by…
Quantum effects in statistical mechanics are important when the thermal wavelength is of the order of, or greater than, the mean interatomic spacing. This is examined at depth taking the example of a hard-sphere Boltzmann gas. Using the…
We use the virial expansion to investigate the behavior of the two-component, attractive Fermi gas in the high-temperature limit, where the system smoothly evolves from weakly attractive fermions to weakly repulsive bosonic dimers as the…
In this paper we consider an interacting Bose gas at zero temperature, constrained to a finite box and in the mean field limiting regime. The N gas particles interact through a pair potential of positive type and with an ultraviolet…
We study a class of one-dimensional classical fluids with penetrable particles interacting through positive, purely repulsive, pair-potentials. Starting from some lower bounds to the total potential energy, we draw results on the…
We study the expansion of a dilute ultracold sample of fermions initially trapped in a anisotropic harmonic trap. The expansion of the cloud provides valuable information about the state of the system and the role of interactions. In…
By generalizing our automated algebra approach from homogeneous space to harmonically trapped systems, we have calculated the fourth- and fifth-order virial coefficients of universal spin-1/2 fermions in the unitary limit, confined in an…
We evaluate the small-amplitude excitations of a spin-polarized vapour of Fermi atoms confined inside a harmonic trap. The dispersion law $\omega=\omega_{f}[l+4n(n+l+2)/3]^{1/2}$ is obtained for the vapour in the collisional regime inside a…
Classical relativistic system of point particles coupled with an electromagnetic field is considered in the three-dimensional representation. The gauge freedom connected with the chronometrical invariance of the four-dimensional description…
We study simple nonequilibrium distributions describing a classical gas of particles interacting via a pair potential ${\phi}(x/{\epsilon})$, in the Boltzmann-Grad scaling ${\epsilon} \rightarrow 0$. We establish bounds for truncated…
We prove the existence of solutions of a cross-diffusion parabolic population problem. The system of partial differential equations is deduced as the limit equations satisfied by the densities corresponding to an interacting particles…
We study a one dimensional gas of $N$ noninteracting diffusing particles in a harmonic trap, whose stiffness switches between two values $\mu_1$ and $\mu_2$ with constant rates $r_1$ and $r_2$ respectively. Despite the absence of direct…
We emphasize the fact the evolution of quantum states in the inverted oscillator (IO) is reduced to classical equations of motion, stressing that the corresponding tunnelling and reflexion coefficients addressed in the literature are…
In a general class of one dimensional random differential equation the convergence of the distribution function of the solution to stationary state distribution is studied. In particular it is proved the boundedness respectively the…
A two-component four-fermion system with equal masses, interspecies s-wave scattering length a and vanishing intraspecies interactions under external spherically symmetric harmonic confinement is considered. Using a correlated Gaussian…
Consider the overdamped limit for a system of interacting particles in the presence of hydrodynamic interactions. For two-body hydrodynamic interactions and one- and two-body potentials, a Smoluchowski-type evolution equation is rigorously…
It has been conjectured that the Pauli exclusion principle alone may be responsible for a particular geometric arrangement of confined systems of identical fermions even when there is no interaction between them. These geometric structures,…
It is shown that in equilibrium a canonical ensemble of particles with two-particle interaction the Gibbs distribution function may be expressed uniquely through a pair distribution function. It means, that for given values of the particle…