Soliton transmission through disordered system

An exact formula for the transmission time in the disordered nonlinear soliton-bearing classical one-dimensional system is obtained

Anderson localization in metamaterials and other complex media

We review some recent (mostly ours) results on the Anderson localization of light and electron waves in complex disordered systems, including: (i) left-handed metamaterials, (ii) magnetoactive optical structures, (iii) graphene superlattices, and (iv) nonlinear dielectric media. First, we demonstrate that left-handed metamaterials can significantly suppress localization of light and lead to an anomalously enhanced transmission. This suppression is essential at the long-wavelength limit in the case of normal incidence, at specific angles of oblique incidence (Brewster anomaly), and in the vicinity of the zero-ε or zero-μ frequencies for dispersive metamaterials. Remarkably, in disordered samples comprised of alternating normal and left-handed metamaterials, the reciprocal Lyapunov exponent and reciprocal transmittance increment can differ from each other. Second, we study magnetoactive multilayered structures, which exhibit nonreciprocal localization of light depending on the direction of propagation and on the polarization. At resonant frequencies or realizations, such nonreciprocity results in effectively unidirectional transport of light. Third, we discuss the analogy between the wave propagation through multilayered samples with metamaterials and the charge transport in graphene, which enables a simple physical explanation of unusual conductive properties of disordered graphene superlatices. We predict disorder-induced resonances of the transmission coefficient at oblique incidence of the Dirac quasiparticles. Finally, we demonstrate that an interplay of nonlinearity and disorder in dielectric media can lead to bistability of individual localized states excited inside the medium at resonant frequencies. This results in nonreciprocity of the wave transmission and unidirectional transport of light

Localization of solitons: linear response of the mean-field ground state to weak external potentials

Two aspects of bright matter-wave solitons in weak external potentials are discussed. First, we briefly review recent results on the Anderson localization of an entire soliton in disordered potentials [Sacha et al. PRL 103, 210402 (2009)], as a paradigmatic showcase of genuine quantum dynamics beyond simple perturbation theory. Second, we calculate the linear response of the mean-field soliton shape to a weak, but otherwise arbitrary external potential, with a detailed application to lattice potentials.Comment: Selected paper presented at the 2010 Spring Meeting of the Quantum Optics and Photonics Section of the German Physical Society. V2: minor changes, published versio

Localized states in 2D semiconductors doped with magnetic impurities in quantizing magnetic field

A theory of magnetic impurities in a 2D electron gas quantized by a strong magnetic field is formulated in terms of Friedel-Anderson theory of resonance impurity scattering. It is shown that this scattering results in an appearance of bound Landau states with zero angular moment between the Landau subbands. The resonance scattering is spin selective, and it results in a strong spin polarization of Landau states, as well as in a noticeable magnetic field dependence of the $g$ factor and the crystal field splitting of the impurity $d$ levels.Comment: 12 pages, 4 figures Submitted to Physical Review B This version is edited and updated in accordance with recent experimental dat

Self-trapping transition for nonlinear impurities embedded in a Cayley tree

The self-trapping transition due to a single and a dimer nonlinear impurity embedded in a Cayley tree is studied. In particular, the effect of a perfectly nonlinear Cayley tree is considered. A sharp self-trapping transition is observed in each case. It is also observed that the transition is much sharper compared to the case of one-dimensional lattices. For each system, the critical values of $\chi$ for the self-trapping transitions are found to obey a power-law behavior as a function of the connectivity $K$ of the Cayley tree.Comment: 6 pages, 7 fig

Magnetic properties of conventional superconductors with columnar defects

Equilibrium vortex configuration in conventional type II superconductors containing short-range columnar defects is investigated theoretically. In the bulk superconductor near the upper critical field Hс₂ a single defect causes a strong local deformation of the vortex lattice which has C₃ or C₆ point symmetry. The vortices can collapse onto attractive defect, while in the case of repulsion the regions free of vortices appear near a defect. Increasing the applied magnetic field results in an abrupt change of the configuration of vortices related to the formation of multiquantum vortices and giving rise to reentering transitions between configurations with C₃ or C₆ symmetry. In the case of a small concentration of defects these transitions manifest themselves as jumps of magnetization and discontinuities of the magnetic susceptibility. Columnar defects also essentially influence the magnetic properties of a mesoscopic superconducting disc. They help the penetration of vortices into the sample, thereby decreasing the sample magnetization and reducing its upper critical field. Even the presence of weak defects splits a giant vortex state (usually appearing in a clean disc in the vicinity of the transition to a normal state) into a number of vortices with smaller topological charges. In a disc with a sufficient number of strong enough defects vortices are always placed onto defects. The presence of defects lead to the appearance of additional magnetization jumps related to the redistribution of vortices which are already present on the defects and not to the penetration of new vortices

Magnetic properties of irradiated quasi 2D type II superconductors

Persistent scaling behavior of magnetization in layered high Tc superconductors with short-range columnar defects is explained within the Ginzburg-Landau theory. In the weak field region, the scaling function differs from that of a clean sample and the critical temperature is renormalized due to defects. In the strong field region, defects are effectively suppressed and the scaling function, as well as the critical temperature are the same as in a clean superconductor. This picture is consistent with recent experimental results

Nonlinear delocalization on disordered Stark ladder

05.45.-a Nonlinear dynamics and chaos, 63.50.-x Vibrational states in disordered systems, 03.75.Kk Dynamic properties of condensates; collective and hydrodynamic excitations, superfluid flow,