This article establishes a proof of dynamical localization for a random scattering zipper model. The scattering zipper operator is the product of two unitary by blocks operators, multiplicatively perturbed on the left and right by random unitary phases. One of the operator is shifted so that this configuration produces a random 5-diagonal unitary o...
Published in Nonlinearity
We prove Anderson localization for all Diophantine frequencies and all non-resonant phases for a model that arises from a 2D quantum walk model subject to an external magnetic field, also known as the unitary almost Mathieu operator. Our work provides the first localization results for all Diophantine frequencies in quasi-periodic quantum walk and ...
Published in Journal of Physics A: Mathematical and Theoretical
This paper concerns the Z2 classification of Fermionic Time-Reversal (FTR) symmetric partial differential Hamiltonians on the Euclidean plane. We consider the setting of two insulators separated by an interface. Hamiltonians that are invariant with respect to spatial translations along the interface are classified into two categories depending on w...
Published in Journal of Physics A: Mathematical and Theoretical
A conceptual quantity—the minimal effective amount of a quantum state ϕ(rj) in d-dimensional systems, defined by N∗=∑j=1Nmin{N|ϕ(rj)|2,1} , is newly proposed, where system sizes N=Ld . The effective dimension d IR can be calculated by N∗=h∗(L)LdIR , where h∗(L) does not change faster than any nonzero power. However, the nature of h∗(L) is unknown p...
Published in Physica Scripta
The topological funneling effect, i.e., the motion of an arbitrary excitation to a focal point of the lattice no matter where the lattice is excited, is a dynamical effect due to the non-Hermitian skin effect. This effect disappears in the presence of strong disorder where the system is topologically trivial. In Anderson localized regime with compl...
Anderson localization is a multiple-scattering phenomenon of linear waves propagating within a disordered medium. Discovered in the late 50s for electrons, it has since been observed experimentally with cold atoms and with classical waves (optics, microwaves, and acoustics), but whether wave localization is enhanced or weakened for nonlinear waves ...
In this short note we we give the proper rate of exponential decay for the Initial Length-Scale Estimate in the case of quasi-one-dimensional random operators of Schrödinger type. This corrects the statement and the demonstration of Proposition 5 in : H. Boumaza, Localization for a matrix-valued Anderson model, Math. Phys. Anal. Geom. 12(3), 255-28...
Published in Physica Scripta
We consider the localization and dynamical properties of a one dimensional spin orbit coupled Bose–Einstein condensate trapped by a disordered speckle potential. We numerically solve coupled Gross–Pitaevskii equation to obtain ground sate solutions. The effects of spin–orbit coupling and detuning parameter on localization are investigated. It is fo...
In a broad sense, the term wave localization refers to a phenomenon where waves are spatially confined in small regions of the space without any bounding material barriers.In this Thesis, we investigate (analytically, numerically and experimentally) different physical collective mechanisms to spatially localize, and therefore, to control electromag...
Published in Frontiers in Physics
