The Makeenko-Migdal loop equation is non-linear and first order in the area derivative, but we show that for simple loops in QCD2 it is possible to reformulate this equation as a linear equation with second order derivatives. This equation is a bound state Schrödinger equation with a three dimensional Coulomb potential. Thus, loop dynamics leads to a surprising new picture of confinement, where...

Unlike noncommutative space, when space and time are noncommutative, it seems necessary to modify the usual scheme of quantum mechanics. We propose in this paper a simple generalization of the time evolution equation in quantum mechanics to incorporate the feature of a noncommutative spacetime. This equation is much more constraining than the usual Schrödinger equation in that the spatial dimen...

By considering the three-dimensional incompressible Euler equations, a 4-vector ζ is constructed out of a combination of scalar and vector products of the vorticity ω and the vortex stretching vector ω · ∇u = Sω. The evolution equation for ζ can then be cast naturally into a quaternionic Riccati equation. This is easily transformed into a quaternionic zero-eigenvalue Schrödinger equation whose ...

Huygens’ principle following from the d’Alembert wave equation is not valid in two–dimensional space. A Schrödinger particle of vanishing angular momentum moving freely in two dimensions experiences an attractive force – the quantum anti–centrifugal force – towards its center. We connect these two phenomena by comparing and contrasting the radial propagators of the d’Alembert wave equation and ...

We provide some numerical computations for the soliton dynamics of the nonlinear Schrödinger equation with an external potential. After computing the ground state solution r of a related elliptic equation we show that, in the semi-classical regime, the center of mass of the solution with initial datum modelled on r is driven by the solution of ẍ = −∇V (x). Finally, we provide some examples and ...

We show that initial data near an unperturbed stable plane wave can evolve into a regime of spatiotemporal chaos in the slightly forced conservative periodic one-dimensional nonlinear Schrödinger equation. Statistical measures are employed to demonstrate that this spatiotemporal chaos is intermittent: there are windows in time for which the solution gains spatial coherence. The parameters and i...

The metric of some Lorentzian wormholes in the background of the FRW universe is obtained. It is shown that for a de Sitter space-time the new solution is supported by Phantom Energy. The wave equation for a scalar field in such backgrounds is separable. The form of the potential for the Schrödinger type one dimensional wave equation is found. PACS numbers: 04.20.-q, 04.20.Jb

We develop the basic formalism of complex q-analysis to study the solutions of second order q-difference equations which reduce, in the q → 1 limit, to the ordinary Laplace equation in Euclidean and Minkowski space. After defining an inner product on the function space we construct and study the properties of the solutions, and then apply this formalism to the Schrödinger equation and two-dimen...

We prove rigorously that the one-particle density matrix of three dimensional interacting Bose systems with a short-scale repulsive pair interaction converges to the solution of the cubic nonlinear Schrödinger equation in a suitable scaling limit. The result is extended to k-particle density matrices for all positive integer k. AMS Classification Number (2000): 35Q55, 81Q15, 81T18, 81V70. Runni...

We investigate stability of (2+1)-dimensional ring solitons of the nonlinear Schrödinger equation with focusing cubic and defocusing quintic nonlinearities. Computing eigenvalues of the linearised equation, we show that rings with spin (topological charge) s = 1 and s = 2 are linearly stable, provided that they are very broad. The stability regions occupy, respectively, 9% and 8% of the corresp...