Related papers: Infinite volume limit for the dipole gas
We consider impulsive semiflows defined on compact metric spaces and give sufficient conditions, both on the semiflows and the potentials, for the existence and uniqueness of equilibrium states. We also generalize the classical notion of…
In this paper, we consider an anharmonic perturbation to the harmonic oscillator in the classical and the quantum regimes. We analyse a relativistic particle subjected to such a potential and then proceed to study a gas of such particles.…
In this paper it is proven that the volume entropy of a riemannian metric evolving by the Ricci flow, if does not collapse, nondecreases. Therefore, it provides a sufficient condition for a solution to collapse. Then, for the limit…
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 prove an upper bound on the free energy of a two-dimensional homogeneous Bose gas in the thermodynamic limit. We show that for $a^2 \rho \ll 1$ and $\beta \rho \gtrsim 1$ the free energy per unit volume differs from the one of the…
We introduce the volume entropy semi-norm in real homology and show that it satisfies functorial properties similar to the ones of the simplicial volume. Answering a question of M. Gromov, we prove that the volume entropy semi-norm is…
We study the energy flow of dissipative dynamics on infinite lattices, allowing the total energy to be infinite and considering formally gradient dynamics. We show that in spatial dimensions 1,2, the flow is for almost all times arbitrarily…
Among the normalized metrics on a graph, we show the existence and the uniqueness of an entropy-minimizing metric, and give explicit formulas for the minimal volume entropy and the metric realizing it.
We consider two-dimensional dipolar bosonic gas with dipoles oriented perpendicularly to the plane in a weak random potential. We investigate analytically and numerically the condensate depletion, the one-body density-matrix, the ground…
The number of droplets which may be formed with a supersaturated vapor in presence of a gas cannot exceed a number proportional to (pv-pvo)4 where pv and pvo denote at the same temperature the pressure of the supersaturated vapor-gas…
It is proven that the volume of an infinitesimally flexible polyhedron in $R^3$ is a multiple root of its volume polynomial.
We focus on the thermodynamic behavior of Polytropic gas as a candidate for dark energy. We use the general arguments of thermodynamics to investigate its properties and behavior. We find that a Polytropic gas may exhibit the dark energy…
We give a characterization of limits of dihedral groups in the space of finitely generated marked groups. We also describe the topological closure of dihedral groups in the space of marked groups on a fixed number of generators.
We introduce a numerical method to obtain approximate eigenvalues for some problems of Sturm-Liouville type. As an application, we consider an infinite square well in one dimension in which the mass is a function of the position. Two…
We predict the effect of the roton instability for a two-dimensional weakly interacting gas of tilted dipoles in a single homogeneous quantum layer. Being typical for strongly correlated systems, the roton phenomena appear to occur in a…
We present experimental investigations of antibubbles. Such an unusual fluid object is a thin spherical air shell surrounding a liquid globule. We explain how to produce them and we study their stability. By overweighting antibubbles with a…
The classical (i.e. non-quantum) equilibrium statistical mechanics of a two-dimensional one-component plasma (a system of charged point-particles embedded in a neutralizing background) living on a pseudosphere (an infinite surface of…
In the present Supplementary notes to our work "Arresting bubble coarsening: A two-bubble experiment to investigate grain growth in presence of surface elasticity" (accepted in EPL), we derive the expression of the gas pressure inside a…
We prove uniform linear bounds on the volume variation under drilling and filling operations on finite volume hyperbolic 3-manifolds.
Some theorems for a static prefect fluid sphere, i.e. a star, in the presence of a positive cosmological constant are proved. These theorems put bounds on the pressure profile and internal compactness of the star.