We study the localization transitions which arise in both one and two dimensions when quantum mechanical particles described by a random Schr\"odinger equation are subjected to constant imaginary vector potential. A path-integral formulation relates transition flux lines depinned from columnar defects transverse magnetic field superconductors. The theory predicts that Meissner effect is accompanied stretched exponential relaxation of into bulk diverging penetration depth at transition.

We propose a new measure of the communicability complex network, which is broad generalization concept shortest path. According to measure, most real-world networks display largest between connected (popular) nodes network (assortative communicability). There are also several with disassortative communicability, where "popular" communicate very poorly each other. Using this information we classify diverse set systems into small number universality classes based on their structure-dynamic...

A delocalization phenomenon is studied in a class of non-Hermitian random quantum-mechanical problems. Delocalization arises response to sufficiently large constant imaginary vector potential. The transition related depinning flux lines from extended defects type-II superconductors subject tilted external magnetic field. physical meaning the complex eigenvalues and currents system elucidated terms properties vortex lines. singular behavior penetration length describing stretched exponential...

We consider the agreement problem over random information networks. In a network, existence of an channel between pair elements at each time instance is probabilistic and independent other channels; hence, topology network varies time. such framework, we address asymptotic for networked via notions from stochastic stability. Furthermore, delineate on rate convergence as it relates to algebraic connectivity graphs.

We consider the agreement problem over random information networks. In a network, existence of an channel between pair units at each time instance is probabilistic and independent other channels; hence, topology network varies time. such framework, we address asymptotic for networked via notions from stochastic stability. Furthermore, delineate on rate convergence as it relates to algebraic connectivity graphs.

Recent literature on delocalization in non-Hermitian systems has stressed criteria based sensitivity of eigenvalues to boundary conditions and the existence a nonzero current. We emphasize here that also shows up clearly eigenfunctions, provided one studies product left right as required physical grounds, not simply squared modulii eigenfunctions themselves. discuss ground state delocalized regime suggest behavior these functions, when considered separately, may be viewed ``intermediate''...

We present a novel microscopic model of sorption and convection ions in heterogeneous media. Our is based on an analogy to electron transport semiconductor. A new feature our power law random distribution the adsorption time ions. Diverging standard deviation function yields anomalous ion transport. show that this explains concentration profile with long tail has been observed column experiments. successfully fit recent experimental data. Finally, we propose experiments by which can check...

We explore the spectra and localization properties of N-site banded one-dimensional non-Hermitian random matrices that arise naturally in sparse neural networks. Approximately equal numbers excitatory inhibitory connections lead to spatially localized eigenfunctions, an intricate eigenvalue spectrum complex plane controls spontaneous activity induced response. A finite fraction eigenvalues condense onto real or imaginary axes. For large N, has remarkable symmetries not only with respect...

We point out that the Rashba and Dresselhaus spin-orbit interactions in two dimensions can be regarded as a Yang-Mills non-Abelian gauge field. The physical field generated by gives electron wave function spin-dependent phase which is frequently called Aharonov-Casher phase. Applying on an $AB$ ring this together with usual vector potential, we make interference condition completely destructive for one component of spin while constructive other over entire energy range. This enables us to...

The resonant state of the open quantum system is studied from viewpoint outgoing momentum flux. We show that number particles conserved for a state, if we use an expanding volume integration in order to take account flux; would decay exponentially fixed integration. Moreover, introduce new numerical methods treating with effective potential. first give method finding resonance pole complex energy plane. seeks eigenvalue iteratively. found our leads super-convergence, convergence exponential...

We study a simple open quantum system with $\mathcal{PT}$-symmetric defect potential as prototype in order to illustrate number of general features systems; however, the itself could be mimicked by $\mathcal{PT}$ systems that have been experimentally studied quite recently. One key feature is resonance continuum (RIC), which appears both discrete spectrum and scattering such systems. The RIC wave function forms standing extending throughout spatial extent this sense represents between...

Mesoscopic thermoelectric heat engine is much anticipated as a device that allows us to utilize with high efficiency wasted inaccessible by conventional engines. However, the derivation of current in this seems be either not general or described too briefly, even inappropriately some cases. In paper, we give clear-cut suitable assumptions beyond linear-response regime. It resolves confusion definition After verifying can construct same formalism cyclic engine, find following two interesting...

The Lindblad equation for a two-level system under an electric field is analyzed by mapping to linear with non-Hermitian matrix. Exceptional points of the matrix are found be extensive; second-order ones located on lines in two-dimensional parameter space, while third-order one at point.

We examine the efficiency of an effective two-terminal thermoelectric device under broken time-reversal symmetry. The setup is derived from a three-terminal comprising thermal terminal and two electronic contacts, magnetic field. find that breaking symmetry in presence inelastic electron-phonon processes can significantly enhance figure merit for delivering electric power by supplying heat phonon bath, beyond one producing investing current. such bounded non-negativity entropy production...

Quantum thermodynamics explores novel thermodynamic phenomena that emerge when interactions between macroscopic systems and microscopic quantum ones go into action. Among various issues, heat engines, in particular, have attracted much attention as a critical step theoretical formulation of investigation efficient use by means resources. In the present paper, we focus on absorption emission processes well work extraction Otto cycle. We describe former non-Markovian dynamics, thereby find...

The electronic thermoelectric coefficients are analyzed in the vicinity of one and two Anderson localization thresholds three dimensions. For a single mobility edge, we correct extend previous studies, find universal approximants which allow to deduce critical exponent for zero-temperature conductivity from measurements. In particular, that at non-zero low temperatures Seebeck coefficient efficiency can be very large on "insulating" side, chemical potentials below (zero-temperature)...

We study a limit cycle of quantum Otto engine whose every consists two finite-time isochoric (heating or cooling) processes and adiabatic work-extracting processes. Considering two-level system as working substance that weakly interacts with reservoirs comprising an infinite number bosons, we investigate the non-Markovian effect [short-time behavior reduced dynamics in (QIPs)] on work extraction after repetition cycles. focus parameter region where energy transferred to reservoir can come...

We report the prediction of quasibound states (resonant with very long lifetimes) that occur in eigenvalue continuum propagating for certain systems which is formed by two overlapping energy bands. illustrate this effect using a quantum wire system channels and an attached adatom. When bands overlap, would-be bound state lays just below upper band slightly destabilized lower thereby becomes resonant lifetime (a second such above band). Unlike predicted von Neumann Wigner, these wide region...