We give a method to solve the time-dependent Schrödinger equation for a system of one-dimensional bosons interacting via a repulsive delta function potential. The method uses the ideas of Bethe Ansatz but does not use the spectral theory of the associated Hamiltonian.

The Fourier transform of a skeletal delta function that characterizes the most striking features of experimental quasi-crystal diffraction patterns is evaluated. The result plays a role analogous to the Poisson summation formula for periodic delta functions that underlie classical crystallography. The real-space distribution can be interpreted in terms of a backbone comprising a system of inter...

Abstract. In this article, we propose a model describing the transport of trapped particles in a surface potential. The potential confines particles close to the surface increasing the number of surface collisions. First, we consider the case of non charged particles. From a kinetic description, we rigorously derive a two dimensional Boltzmann equation. In the case of charged particles we intro...

The three-dimensional Schrödinger propogator e , H = −△+V , is a bounded map from L to L∞ with norm controlled by |t|−3/2 provided the potential satisfies two conditions: An integrability condition limiting the singularities and decay of V , and a zero-energy spectral condition on H . This is shown by expressing the spectral measure of H in terms of its resolvents and proving a family of L mapp...

We consider deformations in R of an infinite linear chain of atoms where each atom interacts with all others through a two-body potential. We compute the effect of an external force applied to the chain. At equilibrium, the positions of the particles satisfy an Euler-Lagrange equation. For large classes of potentials, we prove that every solution is well approximated by the solution of a contin...

We consider deformations in R3 of an infinite general nanotube of atoms where each atom interacts with all the other through a two-body potential. We compute the effect of an external force applied to the nanotube. At the equilibrium, the positions of the atoms satisfy an Euler-Lagrange equation. For large classes of potentials (including Lennard-Jones potential) and under suitable stability as...

We compute the Bohmian trajectories of the incoming scattering plane waves for Klein’s potential step in explicit form. For finite norm incoming scattering solutions we derive their asymptotic space-time localization and we compute some Bohmian trajectories numerically. The paradox, which appears in the traditional treatments of the problem based on the outgoing scattering asymptotics, is absent.

During periods of market stress, electricity prices can rise dramatically. This paper treats these abnormal episodes or price spikes as count events and attempts to build a model of the spiking process. In contrast to the existing literature, which either ignores temporal dependence in the spiking process or attempts to model the dependence solely in terms of deterministic variables (like seaso...

An infinite family of classical superintegrable Hamiltonians defined on the N dimensional spherical, Euclidean and hyperbolic spaces are shown to have a common set of (2N − 3) functionally independent constants of the motion. Among them, two different subsets of N integrals in involution (including the Hamiltonian) can always be explicitly identified. As particular cases, we recover in a straig...

Massively-parallel molecular dynamics simulation is applied to systems containing electrolytes, vapour-liquid interfaces, and biomolecules in contact with water-oil interfaces. Novel molecular models of alkali halide salts are presented and employed for the simulation of electrolytes in aqueous solution. The enzymatically catalysed hydroxylation of oleic acid is investigated by molecular dynami...