相关论文: On the groundstate of octonionic matrix models in …

This paper is concerned with the nonlinear Schrodinger lattice with nonlinear hopping. Via variation approach and the Nehari manifold argument, we obtain two types of solution: periodic ground state and localized ground state. Moreover, we…

We formulate part I of a rigorous theory of ground states for classical, finite, Heisenberg spin systems. The main result is that all ground states can be constructed from the eigenvectors of a real, symmetric matrix with entries comprising…

In this paper we give an abstract definition of solitary wave and soliton and we develop an abstract existence theory. This theory provides a powerful tool to study the existence of solitons for the Klein-Gordon equations as well as for…

We continue the development of the study of the equisingularity of isolated singularities, in the determinantal case. This version of the paper includes a substantial amount of new material (76% larger). The new material introduces the idea…

We investigate excitations in Matrix Theory on T^2 corresponding to bound states of strings. We demonstrate the Dirichlet aspect of R-R charged vacua through a non-trivial connection between the U(1) and SU(n) sectors of the matrix SYM.

An important but little-studied property of spin glasses is the stability of their ground states to changes in one or a finite number of couplings. It was shown in earlier work that, if multiple ground states are assumed to exist, then…

We consider the focusing nonlinear Schr\"odinger equation on a large class of rotationally symmetric, noncompact manifolds. We prove the existence of a solitary wave by perturbing off the flat Euclidean case. Furthermore, we study the…

This paper considers ground states of mass subcritical rotational nonlinear Schr\"{o}dinger equation \begin{equation*} -\Delta u+V(x)u+i\Omega(x^\perp\cdot\nabla u)=\mu u+\rho^{p-1}|u|^{p-1}u \,\ \text{in} \,\ \mathbb{R}^2, \end{equation*}…

We survey our recent results on stability of 3D crystals in the Schr\"odinger-Poisson-Newton model. We establish orbital stability for the ground state in the case of finite crystal and linear stability for infinite crystals under novel…

Let G(d,n) denote the Grassmannian of d-planes in C^n and let T be the torus (C^*)^n/diag(C^*) which acts on G(d,n). Let x be a point of G(d,n) and let \bar{Tx} be the closure of the T-orbit through x. Then the class of the structure sheaf…

We point out an effect which may stabilize a supersymmetric membrane moving on a manifold with boundary, and lead to a light-cone Hamiltonian with a discrete spectrum of eigenvalues. The analysis is carried out explicitly for a closed…

We present a simple proof of a sufficient condition for the uniqueness of non-equilibrium steady states of Gorini-Kossakowski-Sudarshan-Lindblad equations. We demonstrate the applications of the sufficient condition using examples of the…

A gauge-invariant wavefunctional is proposed as an approximation to the ground state of Yang-Mills theory in 2+1 dimensions, quantized in temporal gauge. The proposed vacuum state is the true ground state of the appropriate Hamiltonian in…

We examine the behaviour of a charged particle in a two-dimensional confining potential, in the presence of a magnetic field. The confinement serves to remove the otherwise infinite degeneracy, but additional ingredients are required to…

We study a supersymmetric model for strongly interacting lattice fermions in the presence of a staggering parameter. The staggering is introduced as a tunable parameter in the manifestly supersymmetric Hamiltonian. We obtain analytic…

Inhomogeneity in the ground state is an intriguing, emergent phenomenon in magnetism. Recently, it has been observed in the magnetostructural channel of the geometrically frustrated $\alpha$-NaMnO$_2$, for the first time in the absence of…

In N=1 supersymmetric SO(N)/USp(2N) gauge theories with the tree-level superpotential W(\Phi) that is an arbitrary polynomial of the adjoint matter \Phi, the massless fluctuations about each quantum vacuum are described by U(1)^n gauge…

We study uniqueness of solutions to degenerate parabolic problems, posed in bounded domains, where no boundary conditions are imposed. Under suitable assumptions on the operator, uniqueness is obtained for solutions that satisfy an…

The hopping motion of classical particles on a chain coupled to reservoirs at both ends is studied for parallel dynamics with arbitrary probabilities. The stationary state is obtained in the form of an alternating matrix product. The…

We study a singular nonlinear ordinary differential equation on intervals $[0,R)$ with $R\le +\infty$, motivated by the Ginzburg-Landau models in superconductivity and Landau-de Gennes models in liquid crystals. We prove existence and…