Ragnar Fleischmann

Coherent branched flow in a two-dimensional electron gas.

Semiconductor nanostructures based on two-dimensional electron gases (2DEGs) could form the basis of future devices for sensing, information processing and quantum computation. Although electron transport in 2DEG nanostructures has been well studied, and many remarkable phenomena have already been discovered (for example, weak localization, quantum chaos, universal conductance fluctuations), fundamental aspects of the electron flow through these structures have so far not been clarified. However, it has recently become possible to image current directly through 2DEG devices using scanning probe microscope techniques. Here, we use such a technique to observe electron flow through a narrow constriction in a 2DEG—a quantum point contact. The images show that the electron flow from the point contact forms narrow, branching strands instead of smoothly spreading fans. Our theoretical study of this flow indicates that this branching of current flux is due to focusing of the electron paths by ripples in the background potential. The strands are decorated by interference fringes separated by half the Fermi wavelength, indicating the persistence of quantum mechanical phase coherence in the electron flow. These findings may have important implications for a better understanding of electron transport in 2DEGs and for the design of future nanostructure devices.Semiconductor nanostructures based on two dimensional electron gases (2DEGs) have the potential to provide new approaches to sensing, information processing, and quantum computation. Much is known about electron transport in 2DEG nanostructures and many remarkable phenomena have been discovered (e.g. weak localization, quantum chaos, universal conductance fluctuations)1,2 - yet a fundamental aspect of these devices, namely how electrons move through them, has never been clarified. Important details about the actual pattern of electron flow are not specified by statistical measures such as the mean free path. Scanned probe microscope (SPM) measurements allow spatial investigations of nanostructures, and it has recently become possible to directly image electron flow through 2DEG devices using newly developed SPM techniques3-13. Here we present SPM images of electron flow from a quantum point contact (QPC) which show unexpected dynamical channeling - the electron flow forms persistent, narrow, branching channels rather than smoothly spreading fans. Theoretical study of this flow, including electron scattering by impurities and donor atoms, shows that the channels are not due to deep valleys in the potential, but rather are caused by the indirect cumulative effect of small angle scattering. Surprisingly, the channels are decorated by interference fringes well beyond where the simplest thermal averaging arguments suggest they should be found. These findings may have important implications for 2DEG physics and for the design of future nanostructure devices.

The nature and perception of fluctuations in human musical rhythms

Although human musical performances represent one of the most valuable achievements of mankind, the best musicians perform imperfectly. Musical rhythms are not entirely accurate and thus inevitably deviate from the ideal beat pattern. Nevertheless, computer generated perfect beat patterns are frequently devalued by listeners due to a perceived lack of human touch. Professional audio editing software therefore offers a humanizing feature which artificially generates rhythmic fluctuations. However, the built-in humanizing units are essentially random number generators producing only simple uncorrelated fluctuations. Here, for the first time, we establish long-range fluctuations as an inevitable natural companion of both simple and complex human rhythmic performances. Moreover, we demonstrate that listeners strongly prefer long-range correlated fluctuations in musical rhythms. Thus, the favorable fluctuation type for humanizing interbeat intervals coincides with the one generically inherent in human musical performances.

Quenched and Negative Hall Effect in Periodic Media: Application to Antidot Superlattices

We find the counterintuitive result that electrons move in opposite direction to the free-electron (E × B)-drift when subject to a two-dimensional periodic potential. We show that this phenomenon arises from chaotic channeling trajectories and by a subtle mechanism leads to a negative value of the Hall resistivity for small magnetic fields. The effect is present also in experimentally recorded Hall curves in antidot arrays on semiconductor heterojunctions but so far has remained unexplained.

Optical structures with local PT-symmetry

We propose a new class of optical synthetic materials that are described by non-Hermitian Hamiltonians. The building blocks of such systems are coupled -symmetric elements (dimers), with coupling t. Despite the lack of global -symmetry, these systems have a robust parameter region of real spectra (exact phase) even in cases where the complex refractive index n = ? + i? of each dimer is random. The validity of our proposition is confirmed for representative cases where we calculate the borders of the exact phase in terms of ?, ? and t.

Musical rhythms: The science of being slightly off

With a statistical understanding of our natural rhythmic imperfections, one can make computer-generated music sound more human.

Avalanches of Bose–Einstein condensates in leaking optical lattices

We study the decay of an atomic Bose–Einstein condensate (BEC) population N(τ) from the leaking boundaries of an optical lattice (OL). For a rescaled interatomic interaction strength Λ>Λb, discrete breathers (DBs) are created that prevent the atoms from reaching the leaking boundaries. Collisions of other lattice excitations with the outermost DBs result in avalanches, i.e. steps in N(τ), which for a whole range of Λ-values follow a scale-free distribution P(J=δN)~1/Jα. A theoretical analysis of the mixed phase space of the system indicates that 1

Statistics of Extreme Waves in Random Media

Waves traveling through random media exhibit random focusing that leads to extremely high wave intensities even in the absence of nonlinearities. Although such extreme events are present in a wide variety of physical systems and the statistics of the highest waves is important for their analysis and forecast, it remains poorly understood in particular in the regime where the waves are highest. We suggest a new approach that greatly simplifies the mathematical analysis and calculate the scaling and the distribution of the highest waves valid for a wide range of parameters.

Experimental Observation of a Fundamental Length Scale of Waves in Random Media

Waves propagating through a weakly scattering random medium show a pronounced branching of the flow accompanied by the formation of freak waves, i.e., extremely intense waves. Theory predicts that this strong fluctuation regime is accompanied by its own fundamental length scale of transport in random media, parametrically different from the mean free path or the localization length. We show numerically how the scintillation index can be used to assess the scaling behavior of the branching length. We report the experimental observation of this scaling using microwave transport experiments in quasi-two-dimensional resonators with randomly distributed weak scatterers. Remarkably, the scaling range extends much further than expected from random caustics statistics.

NONLINEAR DYNAMICS OF COMPOSITE FERMIONS IN NANOSTRUCTURES

We outline a theory describing the quasi-classical dynamics of composite fermions in the fractional quantum Hall regime in the potentials of arbitrary nanostructures. By an appropriate parametrization of time we show that their trajectories are independent of their mass and dispersion. This allows to study the dynamics in terms of an effective Hamiltonian although the actual dispersion is as yet unknown. The applicability of the theory is verified in the case of antidot arrays where it explains details of magnetoresistance measurements and thus confirms the existence of these quasiparticles.

Quantum diffusion, fractal spectra, and chaos in semiconductor microstructures

Abstract We review how unbounded quantum mechanical diffusion is related to multifractal properties of the spectrum, its level statistics, and to the algebraic decay of correlations. This new field could be called “quantum chaology” of fractal spectra and should be contrasted with the dynamical localization of the kicked rotator and other previously studied quantum systems. These fascinating properties are found in systems described by a quasiperiodic Schrodinger equation, e.g. the Fibonacci chain for quasicrystals and the Harper model, a single-band description of Bloch electrons in magnetic fields. The semiclassical limit of Bloch electrons in magnetic fields is realized in recent experiments on lateral surface superlattices. There we show that classical chaos and nonlinear resonances are clearly reflected in the magnetotransport and thereby explain a series of magnetoresistance peaks observed in antidot arrays on semiconductor heterojunctions. We also find the counterintuitive result that electrons move in opposite direction to the free electron E × B - drift when subject to a two-dimensional periodic potential. This phenomenon arises from chaotic channeling trajectories and by a subtle mechanism leads to a negative value of the Hall resistivity for small magnetic fields.