arXiv subjects

Ziad H. Musslimani

Publications and source records attributed to Ziad H. Musslimani.

23 records · Page 2Linked to original sources

arXiv2015

Constant-intensity waves and their modulation instability in non-Hermitian potentials

In all of the diverse areas of science where waves play an important role, one of the most fundamental solutions of the corresponding wave equation is a stationary wave with constant intensity. The most familiar example is that of a plane wave propagating in free space. In the presence of any Hermitian potential, a wave's constant intensity is, however, immediately destroyed due to scattering. Here we show that this fundamental restriction is conveniently lifted when working with non-Hermitian potentials. In particular, we present a whole new class of waves that have constant intensity in the presence of linear as well as of nonlinear inhomogeneous media with gain and loss. These solutions allow us to study, for the first time, the fundamental phenomenon of modulation instability in an inhomogeneous environment. Our results pose a new challenge for the experiments on non-Hermitian scattering that have recently been put forward.

physics.optics↗

arXiv2014

Continuous and discrete Schrodinger systems with PT-symmetric nonlinearities

We investigate the dynamical behavior of continuous and discrete Schrodinger systems exhibiting parity-time (PT) invariant nonlinearities. We show that such equations behave in a fundamentally different fashion than their nonlinear Schrodinger counterparts. In particular, the PT-symmetric nonlinear Schrodinger equation can simultaneously support both bright and dark soliton solutions. In addition, we study a two-element discretized version of this PT nonlinear Schrödinger equation. By obtaining the underlying invariants, we show that this system is fully integrable and we identify the PT-symmetry breaking conditions. This arrangement is unique in the sense that the exceptional points are fully dictated by the nonlinearity itself.

nlin.PS↗

arXiv2009

Modulation theory for self-focusing in the nonlinear Schrödinger-Helmholtz equation

The nonlinear Schrödinger-Helmholtz (SH) equation in $N$ space dimensions with $2σ$ nonlinear power was proposed as a regularization of the classical nonlinear Schrödinger (NLS) equation. It was shown that the SH equation has a larger regime ($1\leσ<\frac{4}{N}$) of global existence and uniqueness of solutions compared to that of the classical NLS ($0<σ<\frac{2}{N}$). In the limiting case where the Schrödinger-Helmholtz equation is viewed as a perturbed system of the classical NLS equation, we apply modulation theory to the classical critical case ($σ=1,\:N=2$) and show that the regularization prevents the formation of singularities of the NLS equation. Our theoretical results are supported by numerical simulations

math-ph↗

arXiv2007

Nonlinear Schrodinger-Helmholtz Equation as Numerical Regularization of the Nonlinear Schrodinger Equation

A regularized $α-$system of the Nonlinear Schrödinger Equation (NLS) with $2σ$ nonlinear power in dimension $N$ is studied. We prove existence and uniqueness of local solution in the case $1 \le σ<\frac{4}{N-2}$ and existence and uniqueness of global solution in the case $1 \le σ< \frac{4}{N}$. When $α\to 0^+$, this regularized system will converge to the classical NLS in the appropriate range. In particular, the purpose of this numerical regularization is to shed light on the profile of the blow up solutions of the original Nonlinear Schrödinger Equation in the range $\frac{2}{N}\le σ<\frac{4}{N}$, and in particular for the critical case $σ= \frac{2}{N}$.

math.AP↗

arXiv1995

Enhancement of Persistent Currents by Hubbard Interactions In Disordered 1D Rings: Avoided Level Crossings Interpretation

We study effects of local electron interactions on the persistent current of one dimensional disordered rings. For different realizations of disorder we compute the current as a function of Aharonov-Bohm flux to zeroth and first orders in the Hubbard interaction. We find that the persistent current is {\em enhanced} by onsite interactions. Using an avoided level crossings approach, we derive analytic formulas which explain the numerical results at weak disorder. The same approach also explains the opposite effect (suppression) found for spinless fermion models with intersite interactions.

cond-mat↗