相关论文: On the groundstate of octonionic matrix models in …
We investigate the ground state of a system of interacting particles in small nonlinear lattices with M > 2 sites, using as a prototypical example the discrete nonlinear Schroedinger equation that has been recently used extensively in the…
Existence and uniqueness are investigated for a nonlinear diffusion problem of phase-field type, consisting of a parabolic system of two partial differential equations, complemented by Neumann homogeneous boundary conditions and initial…
We explicitly describe certain components of the finite size groundstate of the inhomogeneous transfer matrix of the O(n=1) loop model on a strip with non-trivial boundaries on both sides. In addition we compute explicitly the groundstate…
The matrix product state formalism is used to simulate Hamiltonian lattice gauge theories. To this end, we define matrix product state manifolds which are manifestly gauge invariant. As an application, we study 1+1 dimensional one flavour…
We present a numerical study of the SU(N) Heisenberg model with the fundamental representation at each site for the kagome lattice (for N=3) and the checkerboard lattice (for N=4), which are the line graphs of the honeycomb and square…
We study the qualitative properties of groundstates of the time-independent magnetic semilinear Schr\"odinger equation \[ - (\nabla + i A)^2 u + u = |u|^{p-2} u, \qquad \text{ in } \mathbb{R}^N, \] where the magnetic potential $A$ induces a…
In this paper, we first provide an alternative proof of the uniqueness of the ground state solution for NLS with inverse square potential and power nonlinearity $|u|^pu$ for all $0<p<\frac 4{d-2}$ in dimensions $d\ge 3$. While the…
We construct the generalised Eigenfunctions of the entries of the monodromy matrix of the $N$-site modular XXZ magnet and show, in each case, that these form a complete orthogonal system in $L^2(\mathbb{R}^N)$. In particular, we develop a…
We focus on the study of ground-states for the system of $M$ coupled semilinear Schr\"odinger equations with power-type nonlinearities and couplings. General results regarding existence and characterization are derived using a variational…
We investigate the existence of ground states of prescribed mass, for the nonlinear Schroedinger energy on a noncompact metric graph G. While in some cases the topology of G may rule out or, on the contrary, guarantee the existence of…
A waveguide coincides with a three-dimensional domain G having finitely many cylindrical outlets to infinity; the boundary of G is smooth. In G, we consider the stationary Maxwell system with real spectral parameter k and identity matrices…
We consider the problem of uniqueness of ground states of prescribed mass for the Nonlinear Schr\"odinger Energy with power nonlinearity on noncompact metric graphs. We first establish that the Lagrange multiplier appearing in the NLS…
We prove basic theorems about the ground states of the S=1 Bose-Hubbard model. The results are quite universal and depend only on the coefficient U_2 of the spin-dependent interaction. We show that the ground state exhibits saturated…
Matrix mechanics is developed to describe the bound state spectra in few- and many-electron atoms, ions and molecules. Our method is based on the matrix factorization of many-electron (or many-particle) Coulomb Hamiltonians which are…
I construct the ground state, up to first nonperturbative order, of the stochastic stabilization of the zero dimensional matrix model which defines 2D Quantum Gravity. It is given by the linear combination of a perturbative wave function…
We state and prove two theorems about the ground state of magnetic systems described by very general Heisenberg-type models and discuss their implications for magnetic neutron scattering. The first theorem states that two models cannot have…
We prove a linear and a nonlinear generalization of the Lax-Milgram theorem. In particular we give sufficient conditions for a real-valued function defined on the product of a reflexive Banach space and a normed space to represent all…
We determine and study the ground states of a focusing Schr\"odinger equation in dimension one with a power nonlinearity $|\psi|^{2\mu} \psi$ and a strong inhomogeneity represented by a singular point perturbation, the so-called…
The dynamic properties of normalized ground states for the Hartree equation with a harmonic potential are addressed. The existence of normalized ground state for any prescribed mass is confirmed according to mass-energy constrained…
In this manuscript, we present a method to prove constructively the existence and spectral stability of solitary waves in both the Whitham and the capillary-gravity Whitham equations. By employing Fourier series analysis and computer-aided…