Anomalous Transport Regimes Research Articles

Anomalous transport in periodic photonic chains with designed loss

Here we show that a coherent random walk in a perfectly periodic chain of bosonic modes with designed loss can exhibit a variety of different anomalous transfer regimes in dependence on the initial state of the chain. In particular, for any given finite initial time-interval there is a set of initial states leading to a hyperballistic transport regime. Also, there are initial states allowing one to achieve a subdiffusive regime or even localization for a given time-interval, or change an asymptotic long-time diffusion rate. We show how these anomalous transport regimes can be practically realized in a laser-written network of single-mode waveguides in balk glass or how a planar system of coupled single-mode waveguides can be realized with an integrated photonic platform.

Anomalous transport regime in a non-Hermitian Anderson-localized hybrid system

In a disordered environment, the average transmission of a propagating wave falls with increasing disorder. Beyond a crossover, transport is arrested because the wave is trapped in the bulk of the sample with exponentially decaying coupling to the boundaries due to Anderson localization. Here, we report the experimental demonstration of anomalous transport of hybrid particles under localizing disorder in a non-Hermitian setting. We create hybrid polariton-photon states in a one-dimensional copper sample with a comb-shaped periodic microstructure designed for microwave frequencies. Non-Hermiticity arises from multiple loss channels existing in the real experimental sample. Disorder is introduced by deliberate alterations of the periodic microstructure. Direct measurement of wave functions was achieved by a near-field probe. At a particular disorder, we observe the onset of Anderson localization of the hybrid states attested to by the exponential tails of the wave function. However, at stronger disorder and under conditions that support localization, an unexpected enhancement in the transmission was facilitated by an emergent miniband. The transmission was traced to the hopping of the hybrid particle over multiple coexisting localized resonances that exchange energy due to the nonorthogonality. These emergent states are manifested in all configurations under strong disorder, suggesting a novel transport regime. This is verified by measuring the averaged conductance which indicates an anomalous transport regime in the hybrid, non-Hermitian environment under strong disorder. These experimental observations open up new unexplored avenues in the ambit of disorder under non-Hermitian conditions.

Anomalous transport of a classical wave-particle entity in a tilted potential.

A classical wave-particle entity in the form of a millimetric walking droplet can emerge on the free surface of a vertically vibrating liquid bath. Such wave-particle entities have been shown to exhibit hydrodynamic analogs of quantum systems. Using an idealized theoretical model of this wave-particle entity in a tilted potential, we explore its transport behavior. The integro-differential equation of motion governing the dynamics of the wave-particle entity transforms to a Lorenz-like system of ordinary differential equations that drives the particle's velocity. Several anomalous transport regimes such as absolute negative mobility, differential negative mobility, and lock-in regions corresponding to force-independent mobility are observed. These observations motivate experiments in the hydrodynamic walking-droplet system for the experimental realizations of anomalous transport phenomena.

Dual current anomalies and quantum transport within extended reservoir simulations

Quantum transport simulations are rapidly evolving and now encompass well-controlled tensor network techniques for many-body limits. One powerful approach combines matrix product states with extended reservoirs. In this method, continuous reservoirs are represented by explicit, discretized counterparts and a chemical potential or temperature drop is maintained by external relaxation. Currents are strongly influenced by relaxation when it is very weak or strong, resulting in a simulation analog of Kramers' turnover for solution-phase chemical reactions. At intermediate relaxation, the intrinsic conductance, that given by the Landauer or Meir-Wingreen expressions, moderates the current. We demonstrate that strong impurity scattering (i.e., a small steady-state current) reveals anomalous transport regimes within this methodology at weak-to-moderate and moderate-to-strong relaxation. The former is due to virtual transitions and the latter to unphysical broadening of the populated density of states. Thus, the turnover analog has $five$ standard transport regimes, further constraining the parameters that lead to recovery of the intrinsic conductance. In the worst case, the common strategy of choosing a relaxation strength proportional to the reservoir level spacing can prevent convergence to the continuum limit. This advocates a simulation strategy where one utilizes the current versus relaxation turnover profiles to identify simulation parameters that most efficiently reproduce the intrinsic physical behavior.

Tuning the phonon transport in bilayer graphene to an anomalous regime dominated by electron-phonon scattering

Recent studies have revealed the significance of electron-phonon interaction (EPI) in phonon transport at intermediate temperatures. In some metals, the EPI can even dominate over the anharmonic phonon-phonon (ph-ph) scattering, leading to an anomalous phonon transport regime in which the lattice thermal conductivity ${\ensuremath{\kappa}}_{L}$ becomes nearly temperature ($T$) independent in contrast to the usual $1/T$ dependence. However, the experimental verification of this anomalous transport regime is very challenging due to the difficulty in separating the phonon contributions from the dominating electron ones to the measured total thermal conductivity in metals. In this work, using first-principles calculations, we predict that in bilayer graphene, the phonon transport can be driven to the anomalous regime by tuning the doping level. At high doping levels close to the Van Hove singularity, the EPI can result in a fivefold reduction of ${\ensuremath{\kappa}}_{L}$ at room temperature, and ${\ensuremath{\kappa}}_{L}$ becomes $T$ independent. This anomalous behavior is found to have its origin in three aspects: (i) mirror symmetry breaking enables direct coupling between flexural phonons, the dominant carriers of ${\ensuremath{\kappa}}_{L}$, and electrons; (ii) dominance of normal processes in the anharmonic ph-ph scattering facilitates the EPI to be more prominent; (iii) dominance of these normal ph-ph processes induces the indirect effect of EPI on ${\ensuremath{\kappa}}_{L}$. This is distinct from monolayer graphene, where the mirror symmetry prohibits the direct scattering of the flexural phonons by electrons and only the indirect EPI affects ${\ensuremath{\kappa}}_{L}$. This work gives insight into the manipulation of heat conduction via externally induced EPI in two-dimensional materials in which mirror symmetry breaks and normal processes dominate the ph-ph scattering.

Kinetic and hydrodynamic regimes in multi-particle-collision dynamics of a one-dimensional fluid with thermal walls

The Authors consider nonequilibrium steady states of a one-dimensional fluid of particles interacting by multi-particle collisions and in contact with two thermal-wall reservoirs, and observe a crossover from a normal to anomalous transport regimes above a characteristic size.

Quantum transport in graphene in presence of strain-induced pseudo-Landau levels

We report on mesoscopic transport fingerprints in disordered graphene caused by strain-field induced pseudomagnetic Landau levels (pLLs). Efficient numerical real space calculations of the Kubo formula are performed for an ordered network of nanobubbles in graphene, creating pseudomagnetic fields up to several hundreds of Tesla, values inaccessible by real magnetic fields. Strain-induced pLLs yield enhanced scattering effects across the energy spectrum resulting in lower mean free path and enhanced localization effects. In the vicinity of the zeroth order pLL, we demonstrate an anomalous transport regime, where the mean free paths increases with disorder. We attribute this puzzling behavior to the low-energy sub-lattice polarization induced by the zeroth order pLL, which is unique to pseudomagnetic fields preserving time-reversal symmetry. These results, combined with the experimental feasibility of reversible deformation fields, open the way to tailor a metal-insulator transition driven by pseudomagnetic fields.

Non-classical regimes of colloid-facilitated impurity transport in statistically homogeneous double porosity media

In the context of impurity transport study it is shown how complexity of the system leads to emergence of anomalous transport regimes, moreover the power-law behavior of which changes with time. Specifically, a model of nonequillibrium colloid-facilitated transport in statistically homogeneous double porosity media is presented and possible transport regimes are simulated. Depending on the medium and colloids characteristics different sequences of transport regimes can realize. Temporal interval exists where anomalous transport regimes (sub-diffusion and quasi-diffusion) occur. At asymptotically large times the transport is described by the classical advection-diffusion with modified parameters.

Advection of an impurity in percolation media with a finite correlation length

The impurity transport regimes in percolation media with a finite correlation length, which are caused by advection and diffusion mechanisms, have been analyzed. It has been shown that the change in the transport characteristics of a medium from the self-similar type to the statistically homogeneous type occurs through two stages because of the structural features of percolation clusters (presence of a backbone and dead ends). As a result, new anomalous transport regimes appear in the system. The quasi-isotropic and moderately and strongly anisotropic media have been considered.

How molecular motors work in the crowded environment of living cells: coexistence and efficiency of normal and anomalous transport.

Recent experiments reveal both passive subdiffusion of various nanoparticles and anomalous active transport of such particles by molecular motors in the molecularly crowded environment of living biological cells. Passive and active microrheology reveals that the origin of this anomalous dynamics is due to the viscoelasticity of the intracellular fluid. How do molecular motors perform in such a highly viscous, dissipative environment? Can we explain the observed co-existence of the anomalous transport of relatively large particles of 100 to 500 nm in size by kinesin motors with the normal transport of smaller particles by the same molecular motors? What is the efficiency of molecular motors in the anomalous transport regime? Here we answer these seemingly conflicting questions and consistently explain experimental findings in a generalization of the well-known continuous diffusion model for molecular motors with two conformational states in which viscoelastic effects are included.

Surface electronic structure of the topological Kondo-insulator candidate correlated electron system SmB6

The Kondo insulator SmB6 has long been known to exhibit low-temperature transport anomalies whose origin is of great interest. Here we uniquely access the surface electronic structure of the anomalous transport regime by combining state-of-the-art laser and synchrotron-based angle-resolved photoemission techniques. We observe clear in-gap states (up to ~4 meV), whose temperature dependence is contingent on the Kondo gap formation. In addition, our observed in-gap Fermi surface oddness tied with the Kramers' point topology, their coexistence with the two-dimensional transport anomaly in the Kondo hybridization regime, as well as their robustness against thermal recycling, taken together, collectively provide strong evidence for protected surface metallicity with a Fermi surface whose topology is consistent with the theoretically predicted topological Fermi surface. Our observations of systematic surface electronic structure provide the fundamental electronic parameters for the anomalous Kondo ground state of correlated electron material SmB6.

Negative mobility induced by colored thermal fluctuations

Anomalous transport of non-Markovian thermal Brownian particle dynamics in spatially periodic symmetric systems that is driven by time-periodic symmetric driving and constant bias is investigated numerically. The Brownian dynamics is modeled by a generalized Langevin equation with exponentially correlated Gaussian thermal noise, obeying the fluctuation-dissipation theorem. We study the role of nonzero correlation time of thermal fluctuations for the occurrence of absolute negative (linear) mobility (ANM) near zero bias, negative-valued, nonlinear mobility (NNM), and negative differential mobility (NDM) at finite bias away from equilibrium. We detect that a nonzero thermal correlation time can either enhance or also diminish the value of ANM. Moreover, finite thermal noise correlation can induce NDM and NNM in regions of parameter space for which such ANM and NNM behaviors are distinctly absent for limiting white thermal noise. In parts of the parameter space, we find a complex structure of regions of linear and nonlinear negative mobility: islands and tongues which emerge and vanish under parameters manipulation. While certain such anomalous transport regimes fade away with increasing temperature some specific regions interestingly remain rather robust. Outside those regimes with anomalous mobility, the ac/dc driven transport is either normal or the driven Brownian particles are not transported at all.

Anomalous transport regimes and asymptotic concentration distributions in the presence of advection and diffusion on a comb structure

We study the transport of impurity particles on a comb structure in the presence of advection. The main body concentration and asymptotic concentration distributions are obtained. Seven different transport regimes occur on the comb structure with finite teeth: classical diffusion, advection, quasidiffusion, subdiffusion, slow classical diffusion, and two kinds of slow advection. Quasidiffusion deserves special attention. It is characterized by a linear growth of the mean-square displacement. However, quasidiffusion is an anomalous transport regime. We established that a change in transport regimes in time leads to a change in regimes in space. Concentration tails have a cascade structure, namely, consisting of several parts.

Vortical structures of trajectories and transport of tracers advected by turbulent fluids

Tracer transport in two-dimensional incompressible turbulent fluids is studied using the nested subensemble method, a semi-analytical statistical approach. Quasi-coherent vortical structures of trajectories are shown to appear when the stream function has slow time variation. In the presence of weak perturbation the structures are not destroyed and they determine anomalous transport regimes.

Nonclassical Transport Processes in Geologic Media: Review of Field and Laboratory Observations and Basic Physical Concepts

We present an overview of the problem of solute transport in unsaturated heterogeneous media. We first review field and laboratory observations that demonstrate nonclassical flow and transport behavior. The main physical principles causing anomalous transport regimes in fractured rock media are identified. The basic factors and physical concepts needed to describe anomalous transport in saturated and unsaturated fractured rock are discussed in detail.

Universal Fano factor and anomalousI−Vcharacteristics in weakly interacting quantum dots

We study interaction effects in quantum dots coupled to perfectly conducting leads via barriers of arbitrary transparencies and embedded in an electromagnetic environment characterized by a fixed external impedance. Combining a recently proposed renormalization group equation for the semiclassical regime of this system with an extended version of circuit theory, we study the Fano factor and the $I\text{\ensuremath{-}}V$ characteristics in the low-temperature and low-energy regime. The Fano factor exhibits a sequence of universal plateaus as a function of the transparencies of the barriers. We also show that a recently discovered quantum transition, at intermediate values of the barrier's transparencies, leads to an anomalous transport regime characterized by a Fano factor that is the harmonic average of its values in adjacent plateaus. Our result extends a previous classification scheme for mesoscopic conductors.

Anomalous transport regimes in a stochastic advection-diffusion model

A general solution to the stochastic advection-diffusion problem is obtained for a fractal medium with long-range correlated spatial fluctuations. A particular transport regime is determined by two basic parameters: the exponent 2h of power-law decay of the two-point velocity correlation function and the mean advection velocity u. The values of these parameters corresponding to anomalous diffusion are determined, and anomalous behavior of the tracer distribution is analyzed for various combinations of u and h. The tracer concentration is shown to decrease exponentially at large distances, whereas power-law decay is predicted by fractional differential equations. Equations that describe the essential characteristics of the solution are written in terms of coupled space-time fractional differential operators. The analysis relies on a diagrammatic technique and makes use of scale-invariant properties of the medium.

Spatial behavior of anomalous transport.

We present a general derivation of one-dimensional spatial concentration distributions for anomalous transport regimes. Such transport can be captured in the framework of a continuous time random walk with a broad transition time distribution. This general theory includes a Fokker-Planck equation as a particular limiting case. All of the concentration profiles, as well as the associated temporal first passage time distributions, can be written in terms of a single special function (that belongs to the class of Fox functions). In addition, we consider the first two moments of the spatial concentration distributions, and determine not only their scaling behavior with time but also the coefficients and correction terms.

The Kubo number as a parameter governing the level of chaos in magnetic turbulence

It is well known that the Kubo number R allows to classify the transport regimes in turbulent systems. A small Kubo number leads to the so-called quasilinear diffusion coefficient, while a large Kubo number corresponds to the percolative diffusion coefficient. Here we show, by means of a numerical simulation of magnetic field line transport in a three-dimensional anisotropic magnetic turbulence, in which the magnetic fluctuating level and the correlation lengths can be varied independently of each other, that the Kubo number also determines the level of chaos of the magnetic-field lines. We find weak chaos, closed magnetic surfaces, and anomalous transport regimes for R⪡1; widespread chaos, destroyed magnetic surfaces, and quasilinear scaling of the diffusion coefficient for R≳0.3; and global stochasticity as well as the percolation scaling of the diffusion coefficient for R⪢1.

Anomalous, quasilinear, and percolative regimes for magnetic-field-line transport in axially symmetric turbulence

We studied a magnetic turbulence axisymmetric around the unperturbed magnetic field for cases having different ratios l( ||)/l( perpendicular). We find, in addition to the fact that a higher fluctuation level deltaB/B(0) makes the system more stochastic, that by increasing the ratio l( ||)/l( perpendicular) at fixed deltaB/B(0), the stochasticity increases. It appears that the different transport regimes can be organized in terms of the Kubo number R=(deltaB/B(0))(l( ||)/l( perpendicular)). The simulation results are compared with the two analytical limits, that is the percolative limit and the quasilinear limit. When R<<1 weak chaos, closed magnetic surfaces, and anomalous transport regimes are found. When R approximately 1 the diffusion regime is Gaussian, and the quasilinear scaling of the diffusion coefficient D( perpendicular) approximately (deltaB/B(0))(2) is recovered. Finally, for R>>1 the percolation scaling of the diffusion coefficient D( perpendicular) approximately (deltaB/B(0))(0.7) is obtained.