相关论文: Quasi-classical expansion of a hyperbolic solution…
A new solution to the star-triangle relation is given, for an Ising type model that involves interacting spins, that contain integer and real valued components. Boltzmann weights of the model are given in terms of the lens elliptic-gamma…
In this paper, we study quasi-linear hyperbolic systems. Our goal in this paper is to provide a new proof of local existence of a classical solution for the system. Most difficult point is to prove the convergence of the derivative of…
In this paper, we consider the lens hyperbolic gamma solution to the star-star relation and the flipping relation from three-dimensional $\mathcal{N}=2$ supersymmetric gauge theories on $S^3_b/\mathbb{Z}_r$. We explore that a certain limit…
We have developed a semiclassical approach to solving the Bogoliubov - de Gennes equations for superconductors. It is based on the study of classical orbits governed by an effective Hamiltonian corresponding to the quasiparticles in the…
In this paper we present a new solution of the star-triangle relation having positive Boltzmann weights. The solution defines an exactly solvable two-dimensional Ising-type (edge interaction) model of statistical mechanics where the local…
We establish existence and uniqueness results for the singular initial value problem associated with a class of quasilinear, symmetric hyperbolic, partial differential equations of Fuchsian type in several space dimensions. This is an…
In this paper we give an overview of exactly solved edge-interaction models, where the spins are placed on sites of a planar lattice and interact through edges connecting the sites. We only consider the case of a single spin degree of…
We construct the hyperbolic and trigonometric solutions to the star-star relation via the gauge/YBE correspondence by using the three-dimensional lens partition function and superconformal index for a certain N=2 supersymmetric gauge dual…
We obtain a new solution to the star-triangle relation for an Ising-type model with two kinds of spin variables at each lattice site, taking continuous real values and arbitrary integer values, respectively. The Boltzmann weights are…
The aim of the present paper is to consider the hyperbolic limit of an elliptic hypergeometric sum/integral identity, and associated lattice model of statistical mechanics previously obtained by the second author. The hyperbolic…
We present a semiclassical study of the spectrum of a few-body system consisting of two short-range interacting bosonic particles in one dimension, a particular case of a general class of integrable many-body systems where the energy…
We consider boundary value problems for quasilinear first-order one-dimensional hyperbolic systems in a strip. The boundary conditions are supposed to be of a smoothing type, in the sense that the $L^2$-generalized solutions to the…
We develop a framework for understanding the existence of asymptotically flat solutions to the static vacuum Einstein equations with prescribed boundary data consisting of the induced metric and mean curvature on a 2-sphere. A partial…
This course introduces the use of semigroup methods in the solution of linear and nonlinear (quasi-linear) hyperbolic partial differential equations, with particular application to wave equations and Hermitian hyperbolic systems. Throughout…
We generalise the covariant Tolman-Oppenheimer-Volkoff equations proposed in arXiv:1709.02818 [gr-qc] to the case of static and spherically symmetric spacetimes with anisotropic sources. The extended equations allow a detailed analysis of…
We present a novel numerical solver for the systems of coupled non-linear elliptical differential equations. The solver partitions the computational domain into a set of rectangular pseudo-spectral collocation subdomains and is especially…
We show that the equality of 2d $\mathcal{N}$=(2,2) supersymmetric indices in Seiberg-type duality leads to a new integrable Ising-type model. The emergence of the new model is the result of correspondence between the supersymmetric $SU(2)$…
The classical soliton solution, quantized by means of suitable translational and rotational collective coordinates, is embedded into the one-particle irreductible representation of the Poincare group corresponding to a definite spin. It is…
A set of equations is derived from the Boltzmann kinetic equation describing charge transport in semiconductors. The unknowns of these equations depend on the space-time coordinates and the electron energy. The non-parabolic and parabolic…
The two-point correlation function of chaotic systems with spin 1/2 is evaluated using periodic orbits. The spectral form factor for all times thus becomes accessible. Equivalence with the predictions of random matrix theory for the…