Anderson-like Localization Research Articles

Turbulence spreading by resonant wave-wave interactions: A fractional kinetics approach.

This paper is concerned with the processes of spatial propagation and penetration of turbulence from the regions where it is locally excited into initially laminar regions. The phenomenon has come to be known as "turbulence spreading" and witnessed a renewed attention in the literature recently. Here, we propose a comprehensive theory of turbulence spreading based on fractional kinetics. We argue that the use of fractional-derivative equationspermits a general approach focusing on fundamentals of the spreading process regardless of a specific turbulence model and/or specific instability type. The starting point is the Hamiltonian of resonant wave-wave interactions, from which a family of scaling laws for the asymptotic spreading is derived. Both three- and four-wave interactions are considered. The results span from a subdiffusive spreading in the parameter range of weak chaos to avalanche propagation in regimes with population inversion. Attention is paid to how nonergodicity introduces weak mixing, memory and intermittency into spreading dynamics, and how the properties of non-Markovianity and nonlocality emerge from the presence of islands of regular dynamics in phase space. Also we resolve an existing question concerning turbulence spillover into gap regions, where the instability growth is locally suppressed, and show that the spillover occurs through exponential (Anderson-like) localization in case of four-wave interactions and through an algebraic (weak) localization in case of triad interactions. In the latter case an inverse-cubic behavior of the spillover function is found. Wherever relevant, we contrast our findings against the available observational and numerical evidence, and we also commit ourselves to establish connections with the models of turbulence spreading proposed previously.

Stable interaction-induced Anderson-like localization embedded in standing waves

We uncover the interaction-induced stable self-localization of few bosons in finite-size disorder-free superlattices. In these nonthermalized multi-particle states, one of the particles forms a superposition of multiple standing waves, so that it provides a quasi-random potential to localize the other particles. We derive effective Hamiltonians for self-localized states and find their energy level spacings obeying the Poisson statistics. The spatial distribution of the localized particles decays exponentially, which is refered to Anderson-like localization (ALL). Surprisingly, we find that the correlated self-localization can be solely induced by interaction in the well-studied Bose–Hubbard models, which has been overlooked for a long time. We propose a dynamical scheme to detect self-localization, where long-time quantum walks of a single particle form a superposition of multiple standing waves for trapping the subsequently loaded particles. Our work provides an experimentally feasible way to realize stable ALL in translation-invariant disorder-free few-body systems.

Quantum simulation of rogue waves in Bose-Einstein condensate: An exact analytical method

A quantum simulator environment is considered in Bose-Einstein condensate under bichromatic optical lattice, manifesting rogue waves. We report an exact analytical model to produce rogue wave excitations, the dynamics of which is investigated by solving the corresponding scalar Gross-Pitaevskii equation. A qualitative understanding of the formation mechanism at various trap parameters is provided by assuming the rogue wave excitation as a mixture of bright and dark solitary waves, which offers a novel illustration of the previous conjecture for rogue waves in Bose-Einstein condensate. We identify the lattice parameters for controlling the spatio-temporal variations of the condensate density. An Anderson-like localization is identified where the condensate is seen to preserve the rogue wave nature at the central frustrated site for larger lattice frustration.

Formation of Matter-Wave Droplet Lattices in Multi-Color Periodic Confinements

In the paper, we introduce a new model that addresses the generation of quantum droplets (QDs) in the binary Bose–Einstein condensate (BEC) mixture with mutually symmetric spinor components loaded in multi-color optical lattices (MOLs) of commensurate wavelengths and tunable intensities. The considered MOL confinement is the combination of the four-color optical lattice with an exponential periodic trap, which includes the complete set of the Fourier harmonics. Employing the one-dimensional (1D) extended Gross–Pitäevskii equation (eGPE), we calculate the exact analytical form of the wavefunction, MF/BMF nonlinearities, and MOL trap parameters. Utilizing the exact solutions, the formation of supersolid-like spatially periodic matter-wave droplet lattices and superlattices is illustrated under the space-periodic nonlinearity management. The precise positioning of the density maxima/minima of the droplet patterns at the center of the trap and tunable Anderson-like localization are observed by tuning the symmetry and amplitude of the considered MOL trap. The stability of the obtained solution is confirmed using the Vakhitov–Kolokolov (VK) criterion.

Synergy between the negative absolute temperature and the external trap for a Bose-Einstein condensate under optical lattices

We provide a generic but exact analytical model for realizing negative absolute temperature in ultracold atoms under a quasi-periodic optical lattice (bi-chromatic) and an expulsive trap. We keep freedom for maximum tunability for both kinds of trap profile, where bi-chromatic lattice is quasi-periodic except two tunable limits, from a pure optical lattice to another doubly periodic optical lattice. The expulsive trap can be tuned from zero to a stronger one. All the required conditions for achieving negative temperature domain have been explored by identifying appropriate trap parameters. Condensate density in each lattice site is controlled and Anderson-like localization is emphasized. A thorough study of a quantitative estimate of the temperature is performed in the negative domain by controlling the trap, where the roles of all the trap parameters are precisely identified. A numerical stability analysis by Fourier split-step method makes the study more useful and the proposed family of solution are found quite stable. This is also connected to the merit of negative temperature through mean deviation data with varied trap parameters.

Exact Solutions for Solitary Waves in a Bose-Einstein Condensate under the Action of a Four-Color Optical Lattice

We address dynamics of Bose-Einstein condensates (BECs) loaded into a one-dimensional four-color optical lattice (FOL) potential with commensurate wavelengths and tunable intensities. This configuration lends system-specific symmetry properties. The analysis identifies specific multi-parameter forms of the FOL potential which admits exact solitary-wave solutions. This newly found class of potentials includes more particular species, such as frustrated double-well superlattices, and bichromatic and three-color lattices, which are subject to respective symmetry constraints. Our exact solutions provide options for controllable positioning of density maxima of the localized patterns, and tunable Anderson-like localization in the frustrated potential. A numerical analysis is performed to establish dynamical stability and structural stability of the obtained solutions, which makes them relevant for experimental realization. The newly found solutions offer applications to the design of schemes for quantum simulations and processing quantum information.

Disorder-induced Anderson-like localization for bidimensional thermoelectrics optimization

Disorder-induced Anderson-like localization for bidimensional thermoelectrics optimization

Disorder-Induced Anderson-Like Localization for Bidimensional Thermoelectrics Optimization

Thermoelectric materials, which can generate electricity from waste heat or be used as solid-state Peltier coolers, couldplay an important role in global sustainable energy. However, improving thermoelectric efficiency has proven difficult, largelydue to the complex interdependence of electronic properties of solids. Early work by Ioffe has developed into the standardthermoelectric optimization paradigm of tuning the electronic carrier concentration in semiconductors. Although the localizationtheory of electrons by Anderson and Mott has developed in parallel, its potential for thermoelectrics optimization has notbeen explored. Here, we show that electron localization induced by structural disorder also provides an effective optimizationstrategy for thermoelectric materials. By using a transport model that includes the relevant physics of localization it is shownthat the maximum thermoelectric figure-of-merit can be increased ~20% by tuning both carrier concentration and disorder.This approach is demonstrated in two model Ge-Sb-Te material systems and confirms that the peak figure-of-merit occursin slightly disordered materials. Particularly for highly degenerate semiconductors this bidimensional optimization strategyprovides a new methodology to attain high thermoelectric performance.

Energy transport and Anderson-like localization in non-Hermitian electrical transmission line

We investigate on the right and left-handed (RH/LH) balanced gain and loss non-Hermitian electrical transmission lines (ETL) modeled using an imaginary resistor. The hamiltonian of each system is successfully derived in the framework of the tight-binding theory. We discuss the underlying symmetries and calculate the breaking thresholds of the Parity time (PT) and Anti PT (APT) symmetry phase transitions. Moreover, the modes dynamic characterization reveal the existence of critical points beyond which operation requires thresholdless transition and the eigen modes are either real or complex. We also present a self-consistent theory to investigate on their scattering properties. In particular, we demonstrate that the Anderson-like localized modes mostly emerge in the broken phase where eigen modes are complex with the localization length proportional to the cell numbers. Importantly, the mode localization is most likely to occur in structures consisting of a large cells number for RH ETL while LH ETL will confined modes even for infinitesimal small cell numbers. These results unveil embryonic applications in cryptography, switching and system control.

Transient diffusion and two-regime localization of discrete breatherlike excitations in nonlinear Schrödinger lattice with disorder.

We systematically simulate and analyze the motion of discrete breatherlike excitations (DBEs) in the nonlinear Schrödinger lattice with random potentials. A universal transient diffusion of the DBEs is observed for short timescales (t≲10^{3}). For longer timescales (t up to 10^{5}), the DBEs become localized. Such localization, depending on the DBE powers, has two different regimes: Regime I is the Anderson-like localization induced by the disorder, while Regime II is an enhanced localization attributed to both the disorder and discreteness. Our study is expected to shed light on understanding the interplay between disorder and strong nonlinearity, from the diffusive transport and localization properties of nonlinear localized excitations in random media.

Anderson-like localization transition of random walks with resetting

We study several lattice random walk models with stochastic resetting to previously visited sites which exhibit a phase transition between an anomalous diffusive regime and a localization regime where diffusion is suppressed. The localized phase settles above a critical resetting rate, or rate of memory use, and the probability density asymptotically adopts in this regime a non-equilibrium steady state similar to that of the well known problem of diffusion with resetting to the origin. The transition occurs because of the presence of a single impurity site where the resetting rate is lower than on other sites, and around which the walker spontaneously localizes. Near criticality, the localization length diverges with a critical exponent that falls in the same class as the self-consistent theory of Anderson localization of waves in random media. The critical dimensions are also the same in both problems. Our study provides analytically tractable examples of localization transitions in path-dependent, reinforced stochastic processes, which can also be useful for understanding spatial learning by living organisms.

Phase diagram of the incommensurate off-diagonal Aubry–André model with p-wave pairing

Using exact numerical methods, we study the interplay between p-wave superconductivity and off-diagonal modulation in the incommensurate off-diagonal Aubry–André model with p-wave pairing. When chemical potential is zero, the modulation not only leads to an Anderson-like localization with all bulk states changing into critical ones, but also induces a topological phase transition accompanying the disappearing of exponentially localized zero-energy edge Majorana fermions. These two transitions happen at different places and true Anderson localization is absent. With a finite chemical potential, the quasi-periodicity of the modulation causes band splitting and drives the system into a band insulator phase. It has a fixed incommensurate particle density which is determined by the modulation frequency. Phase diagrams are identified, and can be tested with existing proposals for experimental realizations of the effective off-diagonal disorder and the p-wave pairing.

Chaos and Anderson-like localization in polydisperse granular chains.

We investigate the dynamics of highly polydisperse finite granular chains. From the spatiospectral properties of small vibrations, we identify which particular single-particle displacements lead to energy localization. Then, we address a fundamental question: Do granular nonlinearities and the resulting chaotic dynamics destroy this energy localization? Our numerical simulations show that for moderate nonlinearities, the overall system behaves chaotically, and spreading of energy occurs. However, long-lasting chaotic energy localization is observed for particular single-particle excitations in the presence of the nonsmooth nonlinearities. On the other hand, for sufficiently strong nonlinearities, the granular chain reaches energy equipartition. In this case, an equilibrium chaotic state is reached independent of the initial position excitation.

Localization transition in SU(3) gauge theory

We study the Anderson-like localization transition in the spectrum of the Dirac operator of quenched QCD. Above the deconfining transition we determine the temperature dependence of the mobility edge separating localized and delocalized eigenmodes in the spectrum. We show that the temperature where the mobility edge vanishes and localized modes disappear from the spectrum, coincides with the critical temperature of the deconfining transition. We also identify topological charge related close to zero modes in the Dirac spectrum and show that they account for only a small fraction of localized modes, a fraction that is rapidly falling as the temperature increases.

A simulator for discrete quantum walks on lattices

In this paper, we present a simulator for two-particle quantum walks on the line and one-particle on a two-dimensional squared lattice. It can be used to investigate the equivalence between the two cases (one- and two-particle walks) for various boundary conditions (open, circular, reflecting, absorbing and their combinations). For the case of a single walker on a two-dimensional lattice, the simulator can also implement the Möbius strip. Furthermore, other topologies for the walker are also simulated by the proposed tool, like certain types of planar graphs with degree up to 4, by considering missing links over the lattice. The main purpose of the simulator is to study the genuinely quantum effects on the global properties of the two-particle joint probability distribution on the entanglement between the walkers/axis. For that purpose, the simulator is designed to compute various quantities such as: the entanglement and classical correlations, (classical and quantum) mutual information, the average distance between the two walkers, different hitting times and quantum discord. These quantities are of vital importance in designing possible algorithmic applications of quantum walks, namely in search, 3-SAT problems, etc. The simulator can also implement the static partial measurements of particle(s) positions and dynamic breaking of the links between certain nodes, both of which can be used to investigate the effects of decoherence on the walker(s). Finally, the simulator can be used to investigate the dynamic Anderson-like particle localization by varying the coin operators of certain nodes on the line/lattice. We also present some illustrative and relevant examples of one- and two-particle quantum walks in various scenarios. The tool was implemented in C and is available on-line at http://qwsim.weebly.com/ .

Facilitation Dynamics and Localization Phenomena in Rydberg Lattice Gases with Position Disorder

We explore the dynamics of Rydberg excitations in an optical tweezer array under antiblockade (or facilitation) conditions. Because of the finite temperature the atomic positions are randomly spread, an effect that leads to quenched correlated disorder in the interatomic interaction strengths. This drastically affects the facilitation dynamics as we demonstrate experimentally on the elementary example of two atoms. To shed light on the role of disorder in a many-body setting we show that here the dynamics is governed by an Anderson-Fock model, i.e., an Anderson model formulated on a lattice with sites corresponding to many-body Fock states. We first consider a one-dimensional atom chain in a limit that is described by a one-dimensional Anderson-Fock model with disorder on every other site, featuring both localized and delocalized states. We then illustrate the effect of disorder experimentally in a situation in which the system maps on a two-dimensional Anderson-Fock model on a trimmed square lattice. We observe a clear suppression of excitation propagation, which we ascribe to the localization of the many-body wave functions in Hilbert space.

Long-range transverse Ising model built with dipolar condensates in two-well arrays

Dipolar Bose–Einstein condensates in an array of double-well potentials realize an effective transverse Ising model with peculiar inter-layer interactions, that may result under proper conditions in an anomalous first-order ferromagnetic–antiferromagnetic phase transition, and non-trivial phases due to frustration. The considered setup allows as well for the study of Kibble–Zurek defect formation, whose kink statistics follows that expected from the universality class of the mean-field one-dimensional transverse Ising model. Furthermore, random occupation of each layer of the stack leads to random effective Ising interactions and local transverse fields, that may lead to the Anderson-like localization of imbalance perturbations.

Fano resonance and resonant localization of excitonic wave in one-dimensional quantum dot array with a ring

The Fano interference of excitonic wave transmitting through a quantum dot chain array with a ring and the Anderson-like localization of the excitonic wave in the ring side are studied. In the quantum dot chain array with a ring, propagating excitonic waves via resonant dipole–dipole interaction interfere with the scattered excitonic wave from the ring and results in the Fano resonance. The excitation energy through the ring is transmitted, reflected, or localized depending on the dipole–dipole couplings to the Fano defect in the ring and transition energy detuning of the defect. Consequently, under some particular conditions, the excitation is resonantly localized in the ring side in the sense of Anderson-like localization by the destructive interference of the totally reflected wave from the ring with the incoming excitonic wave.

Anderson localization of multichannel excitations in disordered two-dimensional waveguide arrays

We considered the transfer of multi-spot optical patterns through disordered two-dimensional waveguide arrays with shallow refractive index modulation. In computer simulations, it was uncovered that statistically averaged output intensity distributions of complex inputs retain their structural features for suitable disorder strengths due to the Anderson-like localization of light. To characterize the quality of the input-output pattern similarity, we introduced corresponding criteria and analyzed their variations with the disorder level.

Light propagation management by disorder and nonlinearity in one-dimensional photonic lattices

We study managing of light beam propagation by competing disorder and nonlinearity in one-dimensional disordered, nonlinear photonic lattices (PLs). The system is modeled by a paraxial time-independent Helmholtz equation, which includes the nonlinear saturable self-interacting term and the quenched or nonquenched disordered PL potential. Diverse PL structures with alternating length of the regular and disordered parts are investigated showing the possibility to change the light propagation from ballistic to the propagation of the transversely localized structures originating from the Anderson-like localization or self-trapping mechanism. Dynamical calculations indicate the possibility of guiding light through the lattice by proper lattice management.