arXiv subjects

T. Geisel

Publications and source records attributed to T. Geisel.

At least 19 recordsLinked to original sources

arXiv2012

How branching can change the conductance of ballistic semiconductor devices

We demonstrate that branching of the electron flow in semiconductor nanostructures can strongly affect macroscopic transport quantities and can significantly change their dependence on external parameters compared to the ideal ballistic case even when the system size is much smaller than the mean free path. In a corner-shaped ballistic device based on a GaAs/AlGaAs two-dimensional electron gas we observe a splitting of the commensurability peaks in the magnetoresistance curve. We show that a model which includes a random disorder potential of the two-dimensional electron gas can account for the random splitting of the peaks that result from the collimation of the electron beam. The shape of the splitting depends on the particular realization of the disorder potential. At the same time magnetic focusing peaks are largely unaffected by the disorder potential.

cond-mat.mes-hall↗

arXiv2012

Beyond mean-field dynamics in open Bose-Hubbard chains

We investigate the effects of phase noise and particle loss on the dynamics of a Bose-Einstein condensate in an optical lattice. Starting from the many-body master equation, we discuss the applicability of generalized mean-field approximations in the presence of dissipation as well as methods to simulate quantum effects beyond mean-field by including higher-order correlation functions. It is shown that localized particle dissipation leads to surprising dynamics, as it can suppress decay and restore the coherence of a Bose-Einstein condensate. These effects can be applied to engineer coherent structures such as stable discrete breathers and dark solitons.

cond-mat.quant-gas↗

arXiv2008

Avalanches of Bose-Einstein Condensates in Leaking Optical Lattices

One of the most fascinating experimental achievements of the last decade was the realization of Bose-Einstein Condensation (BEC) of ultra-cold atoms in optical lattices (OL's). The extraordinary level of control over these structures allows us to investigate complex solid state phenomena and the emerging field of ``atomtronics'' promises a new generation of nanoscale devices. It is therefore of fundamental and technological importance to understand their dynamical properties. Here we study the outgoing atomic flux of BECs loaded in an one-dimensional OL with leaking edges, using a mean field description provided by the Discrete Non-Linear Schrodinger Equation (DNLSE). We demonstrate that the atom population inside the OL decays in avalanches of size $J$. For intermediate values of the interatomic interaction strength their distribution ${\cal P}(J)$ follows a power law i.e. ${\cal P}(J)\sim1/J^{\alpha}$ characterizing systems at phase transition. This scale free behaviour of ${\cal P}(J)$ reflects the complexity and the hierarchical structure of the underlying classical mixed phase space. Our results are relevant in a variety of contexts (whenever DNLSE is adequate), most prominently the light emmitance from coupled non-linear optics waveguides.

cond-mat.stat-mech↗

arXiv2007

Fractal Conductance Fluctuations of Classical Origin

In mesoscopic systems conductance fluctuations are a sensitive probe of electron dynamics and chaotic phenomena. We show that the conductance of a purely classical chaotic system with either fully chaotic or mixed phase space generically exhibits fractal conductance fluctuations unrelated to quantum interference. This might explain the unexpected dependence of the fractal dimension of the conductance curves on the (quantum) phase breaking length observed in experiments on semiconductor quantum dots.

cond-mat.mes-hall↗

arXiv2006

Complexity in parametric Bose-Hubbard Hamiltonians and structural analysis of eigenstates

We consider a family of chaotic Bose-Hubbard Hamiltonians (BHH) parameterized by the coupling strength $k$ between neighboring sites. As $k$ increases the eigenstates undergo changes, reflected in the structure of the Local Density of States. We analyze these changes, both numerically and analytically, using perturbative and semiclassical methods. Although our focus is on the quantum trimer, the presented methodology is applicable for the analysis of longer lattices as well.

cond-mat.other↗

arXiv2006

The scaling laws of human travel

The dynamic spatial redistribution of individuals is a key driving force of various spatiotemporal phenomena on geographical scales. It can synchronise populations of interacting species, stabilise them, and diversify gene pools [1-3]. Human travelling, e.g. is responsible for the geographical spread of human infectious disease [4-9]. In the light of increasing international trade, intensified human mobility and an imminent influenza A epidemic [10] the knowledge of dynamical and statistical properties of human travel is thus of fundamental importance. Despite its crucial role, a quantitative assessment of these properties on geographical scales remains elusive and the assumption that humans disperse diffusively still prevails in models. Here we report on a solid and quantitative assessment of human travelling statistics by analysing the circulation of bank notes in the United States. Based on a comprehensive dataset of over a million individual displacements we find that dispersal is anomalous in two ways. First, the distribution of travelling distances decays as a power law, indicating that trajectories of bank notes are reminiscent of scale free random walks known as Levy flights. Secondly, the probability of remaining in a small, spatially confined region for a time T is dominated by algebraically long tails which attenuate the superdiffusive spread. We show that human travelling behaviour can be described mathematically on many spatiotemporal scales by a two parameter continuous time random walk model to a surprising accuracy and conclude that human travel on geographical scales is an ambivalent effectively superdiffusive process.

cond-mat.stat-mech↗

arXiv2005

Wavepacket Dynamics, Quantum Reversibility and Random Matrix Theory

We introduce and analyze the physics of "driving reversal" experiments. These are prototype wavepacket dynamics scenarios probing quantum irreversibility. Unlike the mostly hypothetical "time reversal" concept, a "driving reversal" scenario can be realized in a laboratory experiment, and is relevant to the theory of quantum dissipation. We study both the energy spreading and the survival probability in such experiments. We also introduce and study the "compensation time" (time of maximum return) in such a scenario. Extensive effort is devoted to figuring out the capability of either Linear Response Theory (LRT) or Random Matrix Theory (RMT) in order to describe specific features of the time evolution. We explain that RMT modeling leads to a strong non-perturbative response effect that differs from the semiclassical behavior.

cond-mat.mes-hall↗

arXiv2004

Action Potential Onset Dynamics and the Response Speed of Neuronal Populations

The result of computational operations performed at the single cell level are coded into sequences of action potentials (APs). In the cerebral cortex, due to its columnar organization, large number of neurons are involved in any individual processing task. It is therefore important to understand how the properties of coding at the level of neuronal populations are determined by the dynamics of single neuron AP generation. Here we analyze how the AP generating mechanism determines the speed with which an ensemble of neurons can represent transient stochastic input signals. We analyze a generalization of the $θ$-neuron, the normal form of the dynamics of Type-I excitable membranes. Using a novel sparse matrix representation of the Fokker-Planck equation, which describes the ensemble dynamics, we calculate the transmission functions for small modulations of the mean current and noise noise amplitude. In the high-frequency limit the transmission function decays as $ω^{-γ}$, where $γ$ surprisingly depends on the phase $θ_{s}$ at which APs are emitted. In a physiologically plausible regime up to 1kHz the typical response speed is, however, independent of the high-frequency limit and is set by the rapidness of the AP onset, as revealed by the full transmission function. In this regime modulations of the noise amplitude can be transmitted faithfully up to much higher frequencies than modulations in the mean input current. We finally show that the linear response approach used is valid for a large regime of stimulus amplitudes.

q-bio.NC↗

arXiv2004

Forecast and Control of Epidemics in a Globalized World

The rapid worldwide spread of the severe acute respiratory syndrome (SARS) demonstrated the potential threat an infectious disease poses in a closely interconnected and interdependent world. Here we introduce a probabilistic model which describes the worldwide spreading of infectious diseases and demonstrate that a forecast of the geographical spread of epidemics is indeed possible. It combines a stochastic local infection dynamics between individuals with stochastic transport in a worldwide network which takes into account the national and international civil aviation traffic. Our simulations of the SARS outbreak are in suprisingly good agreement with published case reports. We show that the high degree of predictability is caused by the strong heterogeneity of the network. Our model can be used to predict the worldwide spreading of future infectious diseases and to identify endangered regions in advance. The performance of different control strategies is analyzed and our simulations show that a quick and focused reaction is essential to inhibit the global spreading of epidemics.

cond-mat.dis-nn↗

arXiv2004

Fingerprints of classical diffusion in open 2D mesoscopic systems in the metallic regime

We investigate the distribution of the resonance widths ${\cal P}(Γ)$ and Wigner delay times ${\cal P}(τ_W)$ for scattering from two-dimensional systems in the diffusive regime. We obtain the forms of these distributions (log-normal for large $τ_W$ and small $Γ$, and power law in the opposite case) for different symmetry classes and show that they are determined by the underlying diffusive classical dynamics. Our theoretical arguments are supported by extensive numerical calculations.

cond-mat.mes-hall↗

arXiv2003

Particle Dispersion on Rapidly Folding Random Hetero-Polymers

We investigate the dynamics of a particle moving randomly along a disordered hetero-polymer subjected to rapid conformational changes which induce superdiffusive motion in chemical coordinates. We study the antagonistic interplay between the enhanced diffusion and the quenched disorder. The dispersion speed exhibits universal behavior independent of the folding statistics. On the other hand it is strongly affected by the structure of the disordered potential. The results may serve as a reference point for a number of translocation phenomena observed in biological cells, such as protein dynamics on DNA strands.

cond-mat.stat-mech↗

arXiv2003

Levy Flights in Inhomogeneous Media

We investigate the impact of external periodic potentials on superdiffusive random walks known as Levy flights and show that even strongly superdiffusive transport is substantially affected by the external field. Unlike ordinary random walks, Levy flights are surprisingly sensitive to the shape of the potential while their asymptotic behavior ceases to depend on the Levy index $μ$. Our analysis is based on a novel generalization of the Fokker-Planck equation suitable for systems in thermal equilibrium. Thus, the results presented are applicable to the large class of situations in which superdiffusion is caused by topological complexity, such as diffusion on folded polymers and scale-free networks.

cond-mat.stat-mech↗

arXiv2002

Signatures of Prelocalized States in Classically Chaotic Systems

We investigate the statistics of eigenfunction intensities ${\cal P}(|ψ|^2)$ in dynamical systems with classical chaotic diffusion. Our results contradict some recent theoretical considerations which challenge the applicability of field theoretical predictions, derived in a different framework for diffusive disordered samples. For two-dimensional systems, the tails of ${\cal P}(|ψ|^2)$ contradict the results of the optimal fluctuation method, but agree very well with the predictions of the non-linear $σ-$model.

cond-mat.mes-hall↗

arXiv2001

Mesoscopic Rectifiers Based on Ballistic Transport: Playing off Classical against Quantum Mechanics

Recent experiments on symmetry-broken mesoscopic semiconductor structures have exhibited an amazing rectifying effect in the transverse current-voltage characteristics with promising prospects for future applications. We present a simple microscopic model, which takes into account the energy dependence of current-carrying modes and explains the rectifying effect by an interplay of fully quantized and quasi-classical transport channels in the system. It also suggests the design of a ballistic rectifier with an optimized rectifying signal and predicts voltage oscillations which may provide an experimental test for the mechanism considered here.

cond-mat.mes-hall↗

arXiv2001

Superballistic spreading of wave packets

We demonstrate for various systems that the variance of a wave packet $M(t)\propto t^ν$, can show a {\it superballistic} increase with $2<ν\le3$, for parametrically large time intervals. A model is constructed which explains this phenomenon and its predictions are verified numerically for various disordered and quasi-periodic systems.

cond-mat.dis-nn↗

arXiv2001

Taming chaos by impurities in two-dimensional oscillator arrays

The effect of impurities in a two-dimensional lattice of coupled nonlinear chaotic oscillators and their ability to control the dynamical behavior of the system are studied. We show that a single impurity can produce synchronized spatio-temporal patterns, even though all oscillators and the impurity are chaotic when uncoupled. When a small number of impurities is arranged in a way, that the lattice is divided into two disjoint parts, synchronization is enforced even for small coupling. The synchronization is not affected as the size of the lattice increases, although the impurity concentration tends to zero.

nlin.CD↗

arXiv2001

Quantum mechanical relaxation of open quasiperiodic systems

We study the time evolution of the survival probability $P(t)$ in open one-dimensional quasiperiodic tight-binding samples of size $L$, at critical conditions. We show that it decays algebraically as $P(t)\sim t^{-α}$ up to times $t^*\sim L^γ$, where $α= 1-D_0^E$, $γ=1/D_0^E$ and $D_0^E$ is the fractal dimension of the spectrum of the closed system. We verified these results for the Harper model at the metal-insulator transition and for Fibonacci lattices. Our predictions should be observable in propagation experiments with electrons or classical waves in quasiperiodic superlattices or dielectric multilayers.

cond-mat.mes-hall↗

arXiv2000

Metal-insulator transitions in cyclotron resonance of periodic nanostructures due to avoided band crossings

A recently found metal-insulator transition in a model for cyclotron resonance in a two-dimensional periodic potential is investigated by means of spectral properties of the time evolution operator. The previously found dynamical signatures of the transition are explained in terms of avoided band crossings due to the change of the external electric field. The occurrence of a cross-like transport is predicted and numerically confirmed.

cond-mat.mes-hall↗