相关论文: Number-Rigidity and $\beta$-Circular Riesz gas

We study the Restricted Phase Space Thermodynamics (RPST) of magnetically charged Anti de Sitter (AdS) black holes sourced by nonlinear electrodynamics(NED). The first law and the corresponding Euler relation are examined using the scaling…

We study the two-dimensional two-component Coulomb gas in the canonical ensemble and at inverse temperature $\beta>2$. In this regime, the partition function diverges and the interaction needs to be cut off at a length scale $\lambda\in…

In this paper we prove the boundedness of the Gaussian Riesz potentials $I_{\beta}$, for $\beta\geq 1$ on $L^{p(\cdot)}(\gamma_d)$, the Gaussian variable Lebesgue spaces under a certain additional condition of regularity on $p(\cdot)$…

Dunkel and Hilbert, "Consistent thermostatistics forbids negative absolute temperatures," Nature Physics, {\bf 10}, 67 (2014), and Hilbert, H\"anggi, and Dunkel, "Thermodynamic laws in isolated systems," Phys. Rev. E {\bf 90}, 062116 (2014)…

Given a square box $\Lambda_n\subseteq\mathbb Z^2$ of side length $L^n$ with $L,n>1$, we study hierarchical random fields $\{\phi_x\colon x\in\Lambda_n\}$ with law proportional to ${\rm…

Thermodynamic properties of extensive but nonadditive systems are investigated. The precise definitions of additivity and extensivity are presented, and we will see that additivity derives several important properties including the…

We investigate a family of radially symmetric Coulomb gas systems at inverse temperature $\beta = 2$. The family is characterised by the property that the density of the equilibrium measure vanishes on a ring at radius $r_*$, which lies…

It is believed that the $\pm J$ Ising spin-glass does not order at finite temperatures in dimension $d=2$. However, using a graphical representation and a contour argument, we prove rigorously the existence of a finite-temperature phase…

We consider a particle system of the squared Bessel processes with index $\nu > -1$ conditioned never to collide with each other, in which if $-1 < \nu < 0$ the origin is assumed to be reflecting. When the number of particles is finite, we…

We introduce and study a model of a logarithmic gas with inverse temperature $\beta$ on an arbitrary smooth closed contour in the plane. This model generalizes Dyson's gas (the $\beta$-ensemble) on the unit circle. We compute the…

A numerical model is presented, designed to simulate the kinetic and thermal behaviour of a porous pellet in which any gas-solid reaction is taking place. Its novelty consists in the fact that it can deal with reactions whether they are…

In the semi-classical limit, the quantum mechanics of a stationary beam of counter-streaming relativistic electrons and ions is described by a nonlinear system of finite-temperature Thomas-Fermi equations. In the high temperature / low…

We prove a Central Limit Theorem for the linear statistics of two-dimensional Coulomb gases, with arbitrary inverse temperature and general confining potential, at the macroscopic and mesoscopic scales and possibly near the boundary of the…

The zero-temperature dynamical structure factor of the one-dimensional Bose gas with delta-function interaction (Lieb-Liniger model) is computed using a hybrid theoretical/numerical method based on the exact Bethe Ansatz solution, which…

Mathematical models in equilibrium statistical mechanics describe physical systems with many particles interacting with an external force and with one another. Gibbs measure is a fundamental concept in this theory. In existing literature…

We introduce and prove a maximum principle for a natural quantity related to the $k$-point correlation function of the classical one-component Coulomb gas. As an application, we show that the gas is confined to the droplet by a well-known…

We prove that the grand canonical Gibbs state of an interacting quantum Bose gas converges to the Gibbs measure of a nonlinear Schr\"odinger equation in the mean-field limit, where the density of the gas becomes large and the interaction…

We study the occurrence of number rigidity and deletion singularity in a class of point processes that we call {\it projected perturbed lattices}. These are generalizations of processes of the form…

In this paper, we study the homogeneous multi-component Curie-Weiss-Potts model with $q \geq 3$ spins. The model is defined on the complete graph $K_{Nm}$, whose vertex set is equally partitioned into $m$ components of size $N$. For a…

Reduced one-dimensional equations for the stationary, isothermal rotational spinning process of slender fibers are considered for the case of large Reynolds ($\delta=3/\text{Re}\ll 1$) and small Rossby numbers ($\varepsilon \ll 1$). Surface…