数学物理

We show future global non-linear stability of surface symmetric solutions of the Einstein-Vlasov system with a positive cosmological constant. Estimates of higher derivatives of the metric and the matter terms are obtained using an…

We consider a non-self-adjoint third order operator $(y''+py)'+py'+qy$ with 1-periodic coefficients $p,q$. This operator is the L-operator in the Lax pair for the good Boussinesq equation on the circle. In 1981, McKean introduced a…

The method of variational completion allows one to transform an (in principle, arbitrary) system of partial differential equations -- based on an intuitive ``educated guess'' -- into the Euler-Lagrange one attached to a Lagrangian, by…

We consider the problem of calculation of correlation functions in the six-vertex model with domain wall boundary conditions. To this aim, we formulate the model as a scalar product of off-shell Bethe states, and, by applying the quantum…

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 consider a gas of bosons interacting through a three-body hard-core potential in the thermodynamic limit. We derive an upper bound on the ground state energy of the system at the leading order using a Jastrow factor. Our result matches…

Anisotropic laminates with a negative Poisson's ratio for at least some directions are called auxetic. In this paper, we consider the conditions for optimizing the auxeticity of an orthotropic laminate, namely: for a laminate composed by a…

We consider a model of a one-dimensional Bose gas with attraction. We study ground state equal-time correlation functions in this model using the algebraic Bethe ansatz. In cases of strong interaction or/and large-volume systems, we obtain…

Extending our previous results, we study the double-scaling limit SYK (DSSYK) model with an additional diagonal matrix with a fixed number $c$ of nonzero constant entries $\theta$. This constant diagonal term can be rewritten in terms of…

This work proposes a closed formula for the leading term of the long-distance and large-time asymptotics in a cone of the space-like regime for the transverse dynamical two-point functions of the XXZ spin 1/2 chain at finite temperatures.…

Classical mechanical systems with internal constraints will be examined using the extended symplectic formalism of Faddeev-Jackiw. We will derive the generalized brackets of the theory and the corresponding equations of motion. The…

In this survey article, we present two applications of surface curvatures in theoretical physics. The first application arises from biophysics in the study of the shape of cell vesicles involving the minimization of a mean curvature type…

We consider the problem of construction of determinant formulas for the partition function of the six-vertex model with domain wall boundary conditions. In pioneering works of Korepin and Izergin a determinant formula was proposed and…

We consider the dressed energy $\varepsilon$ of the XXZ chain in the massless antiferromagnetic parameter regime at $0 < \Delta < 1$ and at finite magnetic field. This function is defined as a solution of a Fredholm integral equation of the…

A novel method for finding the eigenvalues of a Sturm-Liouville problem is developed. Following the minimalist approach the problem is transformed to a single first-order differential equation with appropriate boundary conditions. Although…

Sensitivity of an eigenvalue $\lambda_i$ to the perturbation of matrix elements is controlled by the eigenvalue condition number defined as $\kappa_i = \sqrt{\left< L_i | L_i\right> \left< R_i|R_i \right> }$, where $\left<L_i\right|$ and…

One of many manifestations of a deep relation between the topology of the moduli spaces of algebraic curves and the theory of integrable systems is a recent construction of Arsie, Lorenzoni, Rossi, and the first author associating an…

A new kind of quantum Calogero model is proposed, based on a hyperbolic Kac-Moody algebra. We formulate nonrelativistic quantum mechanics on the Minkowskian root space of the simplest rank-3 hyperbolic Lie algebra $AE_3$ with an…

A well known procedure to get quantum hydrodynamical models for charge transport is to resort to the Wigner equations and deduce the hierarchy of the moment equations as in the semiclassical approach. If one truncates the moment hierarchy…

Ising machines (IM) have recently been proposed as unconventional hardware-based computation accelerators for solving NP-hard problems. In this work, we present a model for a time-multiplexed IM based on the nonlinear oscillations in a…