Impeded thermal transport in aperiodic BN/C nanotube superlattices due to phonon Anderson localization

Anderson localization of phonons is a kind of phonon wave effect,which has been proved to occur in many structures with disorders.In this work,we introduced aperiodicity to boron nitride/carbon nanotube superlattices(BN/C NT SLs),and used molecular dynamics to calculate the thermal conductivity and the phonon transmission spectrum of the models.The existence of phonon Anderson localization was proved in this quasi one-dimensional structure by analyzing the phonon transmission spectra.Moreover,we introduced interfacial mixing to the aperiodic BN/C NT SLs and found that the coexistence of the two disorder entities(aperiodicity and interfacial mixing)can further decrease the thermal conductivity.In addition,we also showed that anharmonicity can destroy phonon localization at high temperatures.This work provides a reference for designing thermoelectric materials with low thermal conductivity by taking advantage of phonon localization.

Anderson Localization in the Induced Disorder System

We propose a coherently prepared three-level atomic medium that can provide a flexible disordered scheme for realizing the Anderson localization. Different disorder levels can be attained by modulating the intensity ratio between the two control beams. Due to the real-time tunability, the localization of the signal beam is observable and controllable. The influences of the induced disorder level, atomic density and the initial waist radius of the signal beam on the Anderson localization in the medium are also discussed.

Hidden Anderson localization in disorder-free Ising–Kondo lattice

Anderson localization (AL) phenomena usually exist in systems with random potential. However, disorder-free quantum many-body systems with local conservation can also exhibit AL or even many-body localization transition. We show that the AL phase exists in a modified Kondo lattice without external random potential. The density of state, inverse participation ratio and temperature-dependent resistance are computed by classical Monte Carlo simulation, which uncovers an AL phase from the previously studied Fermi liquid and Mott insulator regimes. The occurrence of AL roots from quenched disorder formed by conservative localized moments. Interestingly, a many-body wavefunction is found, which captures elements in all three paramagnetic phases and is used to compute their quantum entanglement. In light of these findings, we expect that the disorder-free AL phenomena can exist in generic translation-invariant quantum many-body systems.

Anderson localization of a spin–orbit coupled Bose–Einstein condensate in disorder potential

We present numerical results of a one-dimensional spin–orbit coupled Bose–Einstein condensate expanding in a speckle disorder potential by employing the Gross–Pitaevskii equation.Localization properties of a spin–orbit coupled Bose–Einstein condensate in zero-momentum phase,magnetic phase and stripe phase are studied.It is found that the localizing behavior in the zero-momentum phase is similar to the normal Bose–Einstein condensate.Moreover,in both magnetic phase and stripe phase,the localization length changes non-monotonically as the fitting interval increases.In magnetic phases,the Bose–Einstein condensate will experience spin relaxation in disorder potential.

Anderson Localization Light Guiding in a Two-Phase Glass

Anderson localization has been realized in several different systems over the years. In this paper we describe a rather unique manifestation of the phenomenon occurring in a two-phase glass composition that guides light. The glasses are a borate or alkali borosilicate composition that when heated separates into two distinct phases of different compositions, a high index phase and a low index phase. When the glass is heated with a specific thermal schedule to develop the phase separation it is then drawn into a rod or fiber, the particulate phase forms elongated strands resulting in a random cross-sectional refractive index pattern. This pattern of refractive index is maintained along the length producing a light guiding behavior over a significant distance that we propose is a manifestation of an Anderson localization phenomenon.

Anderson Localization for Jacobi Matrices Associated with High-Dimensional Skew Shifts

In this paper,the authors establish Anderson localization for a class of Jacobi matrices associated with skew shifts on Td,d≥3.

Mobility edges and reentrant localization in one-dimensional dimerized non-Hermitian quasiperiodic lattice

The mobility edges and reentrant localization transitions are studied in one-dimensional dimerized lattice with non-Hermitian either uniform or staggered quasiperiodic potentials.We find that the non-Hermitian uniform quasiperiodic disorder can induce an intermediate phase where the extended states coexist with the localized ones,which implies that the system has mobility edges.The localization transition is accompanied by the PT symmetry breaking transition.While if the non-Hermitian quasiperiodic disorder is staggered,we demonstrate the existence of multiple intermediate phases and multiple reentrant localization transitions based on the finite size scaling analysis.Interestingly,some already localized states will become extended states and can also be localized again for certain non-Hermitian parameters.The reentrant localization transitions are associated with the intermediate phases hosting mobility edges.Besides,we also find that the non-Hermiticity can break the reentrant localization transition where only one intermediate phase survives.More detailed information about the mobility edges and reentrant localization transitions are presented by analyzing the eigenenergy spectrum,inverse participation ratio,and normalized participation ratio.

Periodic electron oscillation in coupled two-dimensional lattices

We study the time evolution of electron wavepacket in the coupled two-dimensional(2D)lattices with mirror symmetry,utilizing the tight-binding Hamiltonian framework.We show analytically that the wavepacket of an electron initially located on one atomic layer in the coupled 2D square lattices exhibits a periodic oscillation in both the transverse and longitudinal directions.The frequency of this oscillation is determined by the strength of the interlayer hopping.Additionally,we provide numerical evidence that a damped periodic oscillation occurs in the coupled 2D disordered lattices with degree of disorderW,with the decay time being inversely proportional to the square ofW and the frequency change being proportional to the square of W,which is similar to the case in the coupled 1D disordered lattices.Our numerical results further confirm that the periodic and damped periodic electron oscillations are universal,independent of lattice geometry,as demonstrated in AA-stacked bilayer and tri-layer graphene systems.Unlike the Bloch oscillation driven by electric fields,the periodic oscillation induced by interlayer coupling does not require the application of an electric field,has an ultrafast periodicity much shorter than the electron decoherence time in real materials,and can be tuned by adjusting the interlayer coupling.Our findings pave the way for future observation of periodic electron oscillation in material systems at the atomic scale.

Colossal negative magnetoresistance from hopping in insulating ferromagnetic semiconductors

Ferromagnetic semiconductor Ga_(1–x)Mn_(x)As_(1–y)P_(y) thin films go through a metal–insulator transition at low temperature where electrical conduction becomes driven by hopping of charge carriers.In this regime,we report a colossal negative magnetoresistance(CNMR)coexisting with a saturated magnetic moment,unlike in the traditional magnetic semiconductor Ga_(1–x)Mn_(x)As.By analyzing the temperature dependence of the resistivity at fixed magnetic field,we demonstrate that the CNMR can be consistently described by the field dependence of the localization length,which relates to a field dependent mobility edge.This dependence is likely due to the random environment of Mn atoms in Ga_(1-x)Mn_(x)As_(1-y)P_(y) which causes a random spatial distribution of the mobility that is suppressed by an increasing magnetic field.

Invariable mobility edge in a quasiperiodic lattice

We analytically and numerically study a 1 D tight-binding model with tunable incommensurate potentials.We utilize the self-dual relation to obtain the critical energy,namely,the mobility edge.Interestingly,we analytically demonstrate that this critical energy is a constant independent of strength of potentials.Then we numerically verify the analytical results by analyzing the spatial distributions of wave functions,the inverse participation rate and the multifractal theory.All numerical results are in excellent agreement with the analytical results.Finally,we give a brief discussion on the possible experimental observation of the invariable mobility edge in the system of ultracold atoms in optical lattices.

Energy spreading,equipartition,and chaos in lattices with non-central forces

We numerically study a one-dimensional,nonlinear lattice model which in the linear limit is relevant to the study of bending(flexural)waves.In contrast with the classic one-dimensional mass-spring system,the linear dispersion relation of the considered model has different characteristics in the low frequency limit.By introducing disorder in the masses of the lattice particles,we investigate how different nonlinearities in the potential(cubic,quadratic,and their combination)lead to energy delocalization,equipartition,and chaotic dynamics.We excite the lattice using single site initial momentum excitations corresponding to a strongly localized linear mode and increase the initial energy of excitation.Beyond a certain energy threshold,when the cubic nonlinearity is present,the system is found to reach energy equipartition and total delocalization.On the other hand,when only the quartic nonlinearity is activated,the system remains localized and away from equipartition at least for the energies and evolution times considered here.However,for large enough energies for all types of nonlinearities we observe chaos.This chaotic behavior is combined with energy delocalization when cubic nonlinearities are present,while the appearance of only quadratic nonlinearity leads to energy localization.Our results reveal a rich dynamical behavior and show differences with the relevant Fermi–Pasta–Ulam–Tsingou model.Our findings pave the way for the study of models relevant to bending(flexural)waves in the presence of nonlinearity and disorder,anticipating different energy transport behaviors.

Phase diagram of a family of one-dimensional nearest-neighbor tight-binding models with an exact mobility edge

Recently, an interesting family of quasiperiodic models with exact mobility edges（MEs） has been proposed（Phys.Rev. Lett. 114 146601（2015））. It is self-dual under a generalized duality transformation. However, such transformation is not obvious to map extended（localized） states in the real space to localized（extended） ones in the Fourier space. Therefore,it needs more convictive evidences to confirm the existence of MEs. We use the second moment of wave functions, Shannon information entropies, and Lypanunov exponents to characterize the localization properties of the eigenstates, respectively.Furthermore, we obtain the phase diagram of the model. Our numerical results support the existing analytical findings.

Disordered quantum walks in two-dimensional lattices

The properties of the two-dimensional quantum walk with point, line, and circle disorders in phase are reported.Localization is observed in the two-dimensional quantum walk with certain phase disorder and specific initial coin states.We give an explanation of the localization behavior via the localized stationary states of the unitary operator of the walker＋ coin system and the overlap between the initial state of the whole system and the localized stationary states.

State vector evolution localized over the edges of a square tight-binding lattice

We study thc time evolution of a state vector in a square tight-binding lattice, focusing on its evolution localized over the system surfaces. In this tight-binding lattice, the energy of atomic orbital centred at surface site is different from that at the interior （bulky） site by an energy shift U. It is shown that for the state vector initially localized on a surface, there exists an exponential law （y = ae^x/b ＋ Y0） determined by the absolute value of the energy shift, ｜U｜, which describes the transition of the state evolving on the square tight-binding lattice, from delocalized over the whole lattice to localized over the surfaces.

Transport dynamics of an interacting binary Bose Einstein condensate in an incommensurate optical lattice

We investigate the transport dynamics of an interacting binary Bose-Einstein condensate in an incommensurate optical lattice and predict a novel splitting of a matter wavepacket induced by disorder potential and inter-species interaction. The effect of atomic interaction on the dynamics of the mobile and localized atoms are also studied in detail. We also discuss the behavior of the balanced and inbalanced mixtures in the incommensurate optical lattice.

Energy relaxation in disordered lattice φ4 system:The combined effects of disorder and nonlinearity

We address the issue of how disorder together with nonlinearity affect energy relaxation in the latticeφ~4 system.The absence of nonlinearity leads such a model to only supporting fully localized Anderson modes whose energies will not relax.However,through exploring the time decay behavior of each Anderson mode’s energy–energy correlation,we find that adding nonlinearity,three distinct relaxation details can occur.(i)A small amount of nonlinearity causes a rapid exponential decay of the correlation for all modes.(ii)In the intermediate value of nonlinearity,this exponential decay will turn to power-law with a large scaling exponent close to-1.(iii)Finally,all Anderson modes’energies decay in a power-law manner but with a quite small exponent,indicating a slow long-time tail decay.Obviously,the last two relaxation details support a new localization mechanism.As an application,we show that these are relevant to the nonmonotonous nonlinearity dependence of thermal conductivity.Our results thus provide new information for understanding the combined effects of disorder and nonlinearity on energy relaxation.

Uncertainties of clock and shift operators for an electron in one-dimensional nonuniform lattice systems

The clock operator U and shift operator V are higher-dimensional Pauli operators. Just recently, tighter uncertainty relations with respect to U and V were derived, and we apply them to study the electron localization properties in several typical one-dimensional nonuniform lattice systems. We find that uncertainties △U^2 are less than, equal to, and greater than uncertainties △V^2 for extended, critical, and localized states, respectively. The lower bound LB of the uncertainty relation is relatively large for extended states and small for localized states. Therefore, in combination with traditional quantities,for instance inverse participation ratio, these quantities can be as novel indexes to reflect Anderson localization.

Effects of Interactions and Temperature in Disordered Ultra-Cold Bose Gases

We simulate ultra-cold interacting bosons in quasi-one-dimensional, incommensurate optical lattices. In the tight-binding limit, these lattices have pseudo-random on-site energies and thus can potentially lead to Anderson localization. We use the Hartree-Fock-Bogoliubov formalism in the Bose-Hubbard model to explore the parameter regimes that lead to exponential localization of the ground state in a 3-colour optical lattice and investigate the role of repulsive interactions, harmonic confinement and finite temperature.

Quantitative Green's function estimates for lattice quasi-periodic Schrodinger operators

In this paper,we establish quantitative Green’s function estimates for some higher-dimensional lattice quasi-periodic(QP)Schrodinger operators.The resonances in the estimates can be described via a pair of symmetric zeros of certain functions,and the estimates apply to the sub-exponential-type non-resonance conditions.As the application of quantitative Green’s function estimates,we prove both the arithmetic version of Anderson localization and the finite volume version of(1/2-)-Holder continuity of the integrated density of states(IDS)for such QP Schrodinger operators.This gives an affirmative answer to Bourgain’s problem in Bourgain(2000).

Deep-learning cell imaging through Anderson localizing optical fiber

We demonstrate a deep-learning-based fiber imaging system that can transfer real-time artifact-free cell images through a meter-long Anderson localizing optical fiber.The cell samples are illuminated by an incoherent LED light source.A deep convolutional neural network is applied to the image reconstruction process.The network training uses data generated by a setup with straight fiber at room temperature(∼20°C)but can be utilized directly for high-fidelity reconstruction of cell images that are transported through fiber with a few degrees bend or fiber with segments heated up to 50°C.In addition,cell images located several millimeters away from the bare fiber end can be transported and recovered successfully without the assistance of distal optics.We provide evidence that the trained neural network is able to transfer its learning to recover images of cells featuring very different morphologies and classes that are never“seen”during the training process.