相关论文: The one-dimensional log-gas free energy has a uniq…

Sandier and Serfaty studied the one-dimensional Log-gas model, in particular they gave a crystallization result by showing that the one-dimensional lattice $\mathbb{z}$ is a minimizer for the so-called renormalized energy which they…

We study the statistical mechanics of a one-dimensional log gas with general potential and arbitrary beta, the inverse of temperature, according to the method we introduced for two-dimensional Coulomb gases in [SS2]. Such ensembles…

We define a notion of logarithmic, Coulomb and Riesz interactions in any dimension for random systems of infinite charged point configurations with a uniform background of opposite sign. We connect this interaction energy with the…

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…

We consider overdamped Langevin dynamics for the attractive log gas on the torus $\mathbb{T}^\mathsf{d}$, for $\mathsf{d}\geq 1$. In dimension $\mathsf{d}=2$, this model coincides with a periodic version of the parabolic-elliptic…

We consider a one-dimensional continuum gas of pointlike positive and negative unit charges interacting via a logarithmic potential. The mapping onto a two-dimensional boundary sine-Gordon field theory with zero bulk mass provides the full…

We investigate Sine$_\beta$, the universal point process arising as the thermodynamic limit of the microscopic scale behavior in the bulk of one-dimensional log-gases, or $\beta$-ensembles, at inverse temperature $\beta>0$. We adopt a…

We prove a lower bound for the free energy (per unit volume) of the two-dimensional Bose gas in the thermodynamic limit. We show that the free energy at density $\rho$ and inverse temperature $\beta$ differs from the one of the…

In this article, we study the smallest gaps of the log-gas $\beta$-ensemble on the unit circle (C$\beta$E), where $\beta$ is any positive integer. The main result is that the smallest gaps, after being normalized by $n^{\frac…

We prove a central limit theorem for the linear statistics of one-dimensional log-gases, or $\beta$-ensembles. We use a method based on a change of variables which allows to treat fairly general situations, including multi-cut and, for the…

We give an expression for the partition function of a one-dimensional log-gas comprised of particles of (possibly) different integer charge at inverse temperature {\beta} = 1 (restricted to the line in the presence of a neutralizing field)…

We consider a one-dimensional gas of positive and negative unit charges interacting via a logarithmic potential, which is in thermal equilibrium at the (dimensionless) inverse temperature $\beta$. In a previous paper [Samaj, L.: J. Stat.…

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 prove the universality of the $\beta$-ensembles with convex analytic potentials and for any $\beta>0$, i.e. we show that the spacing distributions of log-gases at any inverse temperature $\beta$ coincide with those of the Gaussian…

We prove, for any $\beta >0$, a central limit theorem for the fluctuations of linear statistics in the Sine-$\beta$ process, which is the infinite volume limit of the random microscopic behavior in the bulk of one-dimensional log-gases at…

We prove an upper bound for the free energy (per unit volume) of the dilute Bose gas in the thermodynamic limit, showing that the free energy at density $\rho$ and inverse temperature $\beta$ differs from that of the non-interacting system…

The physics of the attractive one-dimensional Bose gas (Lieb-Liniger model) is investigated with techniques based on the integrability of the system. Combining a knowledge of particle quasi-momenta to exponential precision in the system…

We consider $\mathbb{S}^2$-valued maps on a domain $\Omega\subset\mathbb{R}^N$ minimizing a perturbation of the Dirichlet energy with vertical penalization in $\Omega$ and horizontal penalization on $\partial\Omega$. We first show 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…

We present a rigorous study of the Bose-Einstein condensation in the Luttinger-Sy model. We prove the existence of the condensation in this one-dimensional model of the perfect boson gas placed in the Poisson random potential of singular…