Related papers: Mutual distribution of two partial solutions in 1D…
A Lyapunov-based approach for the trajectory generation of an $N$-dimensional Schr{\"o}dinger equation in whole $\RR^N$ is proposed. For the case of a quantum particle in an $N$-dimensional decaying potential the convergence is precisely…
We study the propagation of wave packets for a one-dimensional system of two coupled Schr\"odinger equations with a cubic nonlinearity, in the semi-classical limit. Couplings are induced by the nonlinearity and by the potential, whose…
A systematic solution of a general model for Copper-Oxides reveals a line of transitions $T = T_p (x)$ for $x$, the doping away from half-filling less than a critical value, to a phase with broken time reversal and rotational symmetry but…
This contribution is devoted to cover some technical aspects related to the use of the recently proposed energy probability distribution zeros in the study of phase transitions. This method is based on the partial knowledge of the partition…
For the stationary one-dimensional nonlinear Schr\"odinger equation (or Gross-Pitaevskii equation) nonlinear resonant transmission through a finite number of equidistant identical barriers is studied using a (semi-) analytical approach. In…
Electronic transport through a material depends on the response to local perturbations induced by defects or impurities in the material. The scattering processes can be described in terms of phase shifts and corresponding cross sections.…
Resonant light interacting with matter can support different phases of a polarizable medium, and optical bistability where two such phases coexist. Here we identify signatures of optical phase transitions and optical bistability mapped onto…
We consider the totally asymmetric simple exclusion process, a model in the KPZ universality class. We focus on the fluctuations of particle positions starting with certain deterministic initial conditions. For large time t, one has regions…
We study the uniform boundedness of solutions to reaction-diffusion systems possessing a Lyapunov-like function and satisfying an {\it intermediate sum condition}. This significantly generalizes the mass dissipation condition in the…
We consider a version of the stationary phase method in one dimension of A. Erd\'elyi, allowing the phase to have stationary points of non-integer order and the amplitude to have integrable singularities. After having completed the original…
We investigate a system of harmonically coupled identical nonlinear constituents subject to noise in different spatial arrangements. For global coupling we find for infinitely many constituents the coexistence of several ergodic components…
We present an analytic proof of the existence of phase transition in the large $N$ limit of certain random noncommutaitve geometries. These geometries can be expressed as ensembles of Dirac operators. When they reduce to single matrix…
In this communication we report on a peculiar property of barrier transmission that systems governed by the nonlinear Schroedinger equation share with the linear one: For unit transmission the potential can be divided at an arbitrary point…
In this paper we study the asymptotic phase space energy distribution of solution of the Schr\"{o}dinger equation with a time-dependent random potential. The random potential is assumed to be with slowly decaying correlations. We show that…
In this paper, the development of a mathematical method is presented to explore spatially non-uniform phases with no long-range order in mathematical models of first order phase transitions. We use essential results regarding the…
This paper is devoted to the averaged controllability of the random Schr\"odinger equation, with diffusivity as a random variable drawn from a general probability distribution. First, we show that the solutions to these random Schr\"odinger…
We consider the evolution of a quantum particle hopping on a cubic lattice in any dimension and subject to a potential consisting of a periodic part and a random part that fluctuates stochastically in time. If the random potential evolves…
The purpose of this work is to find the time dependent distributions of directions and positions of a particle that undergoes multiple elastic scattering. The angular cross section is given and the scatterers are randomly placed. The…
We derive a self-duality relation for a one-dimensional model of branching and annihilating random walkers with an even number of offsprings. With the duality relation and by deriving exact results in some limiting cases involving fast…
We rigorously calculate the propagation and scattering of electromagnetic waves by rectangular and random arrays of dielectric cylinders in a uniform medium. For regular arrays, the band structures are computed and complete bandgaps are…