Ground states for nonlinear Maxwell–Dirac system with magnetic field

Ground States and Bound States of a Nonlinear Schrödinger System

This paper concerns existence and multiplicity of ground states and bound states of the time-independent Schrödinger system    −∆uj + λjuj = N ∑ i=1 βiju 2 i uj in R, uj(x) → 0 as |x| → ∞, j = 1, . . . , N, where n = 2, 3, N ≥ 2, λj > 0 for j = 1, · · · , N , βjj > 0 for j = 1, · · · , N , and βij = βji. In the attractive case we give sufficient condition for existence of co-existing groun...

MAT 1061: notes on Nonlinear Ground States

Soliton Dynamics for the Nonlinear Schrödinger Equation with Magnetic Field

Abstract. The semiclassical regime of a nonlinear focusing Schrödinger equation in presence of non-constant electric and magnetic potentials V, A is studied by taking as initial datum the ground state solution of an associated autonomous stationary equation. The concentration curve of the solutions is a parameterization of the solutions of the second order ordinary equation ẍ = −∇V (x) − ẋ × B(...

Coherent states for a 2-sphere with a magnetic field

We consider a particle moving on a 2-sphere in the presence of a constant magnetic field. Building on our earlier work in the nonmagnetic case we construct coherent states for this system. The coherent states are labeled by points in the associated phase space, the (co)tangent bundle of S2. They are constructed as eigenvectors for certain annihilation operators and expressed in terms of a certa...

Josephson junction with a magnetic-field tunable ground state.

We consider an asymmetric 0-π Josephson junction consisting of 0 and π regions of different lengths L(0) and L(π). As predicted earlier this system can be described by an effective sine-Gordon equation for the spatially averaged phase ψ so that the effective current-phase relation of this system includes a negative second harmonic ∝sin(2ψ). If its amplitude is large enough, the ground state of ...