Related papers: Finite Size Spectrum of SU(N) Principal Chiral Fie…
We describe some field theoretic methods for studying quantum spin systems in one dimension. These include the nonlinear sigma-model approach which is particularly useful for large values of the spin, the idea of Luttinger liquids and…
We consider systems of nonlinear magnetostatics and quasistatics that typically arise in the modeling and simulation of electric machines. The nonlinear problems, eventually obtained after time discretization, are usually solved by…
The general features of the 1/N expansion in statistical mechanics and quantum field theory are briefly reviewed both from the theoretical and from the phenomenological point of view as an introduction to a more detailed analysis of the…
The two-dimensional self-dual Chern--Simons equations are equivalent to the conditions for static, zero-energy solutions of the $(2+1)$-dimensional gauged nonlinear Schr\"odinger equation with Chern--Simons matter-gauge dynamics. In this…
In this paper we study the ground state properties of a ladder Hamiltonian with chiral $SU(2)$-invariant spin interactions, a possible first step towards the construction of truly two dimensional non-trivial systems with chiral properties…
We investigate neutrinoless double beta decay ($0\nu\beta\beta$) in the presence of sterile neutrinos with Majorana mass terms. These gauge-singlet fields are allowed to interact with Standard-Model (SM) fields via renormalizable Yukawa…
By solving the Schr\"odinger equation one obtains the whole energy spectrum, both the bound and the continuum states. If the Hamiltonian depends on a set of parameters, these could be tuned to a transition from bound to continuum states.…
We discuss some properties of the soliton equations of the type, partial derivative u/partial derivative t = S [u, (u) over bar], where S is a nonlinear operator differential in x, and present the additivity theorems of the class of the…
After we derive the Serre system of equations of water wave theory from a generalized variational principle, we present some of its structural properties. We also propose a robust and accurate finite volume scheme to solve these equations…
We derive a set of bilinear functional equations of Hirota type for the partition functions of the $sl(2)$ related integrable statistical models defined on a random lattice. These equations are obtained as deformations of the Hirota…
We derive a finite set of nonlinear integral equations (NLIE) for the thermodynamics of the one-dimensional sl(4)-symmetric Uimin-Sutherland model. Our NLIE can be evaluated numerically for arbitrary finite temperature and chemical…
The Hirota equation is an integrable higher order nonlinear Schr\"{o}dinger type equation which describes the propagation of ultrashort light pulses in optical fibers. We present a standard Darboux transformation for the Hirota equation and…
Using a ten dimensional dual string background, we study aspects of the physics of finite temperature large N four dimensional SU(N) gauge theory, focusing on the dynamics of fundamental quarks in the presence of a background magnetic…
We study the local properties of positive solutions of the equation -Delta u= exp(u) in a punctured domain Omega of RN in the range of parameters q > 1 and M > 0. We prove a series of a priori estimates near a singular point. In the case of…
The new method of solving quantum mechanical problems is proposed. The finite, i.e. cut off, Hilbert space is algebraically implemented in the computer code with states represented by lists of variable length. Complete numerical solution of…
We study Yang Mills theory in 2+1 dimensions, as an array of coupled (1+1)-dimensional principal chiral sigma models. This can be understood as an anisotropic limit where one of the space-time dimensions is discrete and the others are…
Under investigation in this work is the robust inverse scattering transform of the discrete Hirota equation with nonzero boundary conditions, which is applied to solve simultaneously arbitrary-order poles on the branch points and spectral…
We consider an O(N) version of a massive, interacting, chiral supersymmetry model solved exactly in the large N limit. We demonstrate that the system approaches a stable attractor at high energy densities, corresponding to a…
Applying the inverse scattering transform to study a focusing two-component Hirota equation with nonzero boundary conditions at infinity. Through the spectral problem and the adjoint spectral problem, the analyticity properties and symmetry…
An implicit Euler finite-volume scheme for a spinorial matrix drift-diffusion model for semiconductors is analyzed. The model consists of strongly coupled parabolic equations for the electron density matrix or, alternatively, of weakly…