Quantum Lissajous Scars.

A quantum scar-an enhancement of a quantum probability density in the vicinity of a classical periodic orbit-is a fundamental phenomenon connecting quantum and classical mechanics. Here we demonstrate that some of the eigenstates of the perturbed two-dimensional anisotropic (elliptic) harmonic oscillator are strongly scarred by the Lissajous orbits of the unperturbed classical counterpart. In particular, we show that the occurrence and geometry of these quantum Lissajous scars are connected to the anisotropy of the harmonic confinement, but unlike the classical Lissajous orbits the scars survive under a small perturbation of the potential. This Lissajous scarring is caused by the combined effect of the quantum (near) degeneracies in the unperturbed system and the localized character of the perturbation. Furthermore, we discuss experimental schemes to observe this perturbation-induced scarring.

Dynamical tunneling versus fast diffusion for a non-convex Hamiltonian.

This paper attempts to resolve the issue of the nature of the 0.01-0.1 cm(-1) peak splittings observed in high-resolution IR spectra of polyatomic molecules. One hypothesis is that these splittings are caused by dynamical tunneling, a quantum-mechanical phenomenon whereby energy flows between two disconnected regions of phase-space across dynamical barriers. However, a competing classical mechanism for energy flow is Arnol'd diffusion, which connects different regions of phase-space by a resonance network known as the Arnol'd web. The speed of diffusion is bounded by the Nekhoroshev theorem, which guarantees stability on exponentially long time scales if the Hamiltonian is steep. Here we consider a non-convex Hamiltonian that contains the characteristics of a molecular Hamiltonian, but does not satisfy the Nekhoroshev theorem. The diffusion along the Arnol'd web is expected to be fast for a non-convex Hamiltonian. While fast diffusion is an unlikely competitor for longtime energy flow in molecules, we show how dynamical tunneling dominates compared to fast diffusion in the nearly integrable regime for a non-convex Hamiltonian, as well as present a new kind of dynamical tunneling.

The Degree of Ergodicity of ortho- and para-Aminobenzonitrile in an Electric Field.

We study the dynamics of the two molecules ortho-aminobenzonitrile (OABN) and para-aminobenzonitrile (PABN). They are structural isomers, with differing asymmetries and dipole moments. In this paper, we show that the dynamics of the system strongly depends on the region of phase space of the initial rotational state, the asymmetry of the molecule, and on the direction of the dipole. We also show that the ergodicity of the system varies gradually with energy, except where the rotational energy of the initial state is much less than the Stark interaction. In this regime, the projection of the dipole along the lab-frame z-axis varies linearly with increasing energy and follows the microcanonical ergodic estimate. Both molecules are far from full chaos for total angular momentum quanta J ∈ [0,45]. However, the initial rotational states in OABN access much more of the available phase space than in PABN. We show that this is a likely cause for the experimental discrepancies in molecular beam deflection experiments.

Fractal dynamics in chaotic quantum transport.

Despite several experiments on chaotic quantum transport in two-dimensional systems such as semiconductor quantum dots, corresponding quantum simulations within a real-space model have been out of reach so far. Here we carry out quantum transport calculations in real space and real time for a two-dimensional stadium cavity that shows chaotic dynamics. By applying a large set of magnetic fields we obtain a complete picture of magnetoconductance that indicates fractal scaling. In the calculations of the fractality we use detrended fluctuation analysis-a widely used method in time-series analysis-and show its usefulness in the interpretation of the conductance curves. Comparison with a standard method to extract the fractal dimension leads to consistent results that in turn qualitatively agree with the previous experimental data.

Imaging coherent transport in graphene. Part I: mapping universal conductance fluctuations.

Graphene provides a fascinating testbed for new physics and exciting opportunities for future applications based on quantum phenomena. To understand the coherent flow of electrons through a graphene device, we employ a nanoscale probe that can access the relevant length scales--the tip of a liquid-He-cooled scanning probe microscope (SPM) capacitively couples to the graphene device below, creating a movable scatterer for electron waves. At sufficiently low temperatures and small size scales, the diffusive transport of electrons through graphene becomes coherent, leading to universal conductance fluctuations (UCF). By scanning the tip over a device, we map these conductance fluctuations versus scatterer position. We find that the conductance is highly sensitive to the tip position, producing delta G approximately e(2)/h fluctuations when the tip is displaced by a distance comparable to half the Fermi wavelength. These measurements are in good agreement with detailed quantum simulations of the imaging experiment and demonstrate the value of a cooled SPM for probing coherent transport in graphene.

Freak waves in the linear regime: a microwave study.

Microwave transport experiments have been performed in a quasi-two-dimensional resonator with randomly distributed conical scatterers. At high frequencies, the flow shows branching structures similar to those observed in stationary imaging of electron flow. Semiclassical simulations confirm that caustics in the ray dynamics are responsible for these structures. At lower frequencies, large deviations from Rayleigh's law for the wave height distribution are observed, which can only partially be described by existing multiple-scattering theories. In particular, there are "hot spots" with intensities far beyond those expected in a random wave field. The results are analogous to flow patterns observed in the ocean in the presence of spatially varying currents or depth variations in the sea floor, where branches and hot spots lead to an enhanced frequency of freak or rogue wave formation.

Guided Gaussian wave packets.

We discuss several semiclassical Gaussian wave packet approaches with emphasis on one that is not very well-known, that is, the off-center guiding approach. Off-center guiding of (thawed) Gaussian wave packets uses the same information as other Gaussian propagation schemes, that is, the full van Vleck determinant and multiple trajectories. It retains the well-known caustic smoothing property of Gaussians. The off-center guiding of Gaussians can handle hard chaos and other highly nonlinear situations, where the van Vleck propagator, for example, has over 30,000 separate branches.

Thermal averages in a quantum point contact with a single coherent wave packet.

A novel formal equivalence between thermal averages of coherent properties (e.g., conductance) and time averages of a single wave packet arises for Fermi gases and certain geometries. In the case of one open channel in a quantum point contact (QPC), only one wave packet history, with the wave packet width equal to the thermal length, completely determines the thermally averaged conductance. The formal equivalence moreover allows very simple physical interpretations of interference features surviving under thermal averaging. Simply put, pieces of the thermal wave packet returning to the QPC along independent paths must arrive at the same time in order to interfere. Remarkably, one immediate result of this approach is that higher temperature leads to narrower wave packets and therefore better resolution of events in the time domain. In effect, experiments at 4.2 K are performing time-gated experiments at better than a gigahertz. Experiments involving thermally averaged ballistic conductance in 2DEGS are presented as an application of this picture.

Imaging electron interferometer.

An imaging interferometer was created in a two-dimensional electron gas by reflecting electron waves emitted from a quantum point contact with a circular mirror. Images of electron flow obtained with a scanning probe microscope at liquid He temperatures show interference fringes when the mirror is energized. A quantum phase shifter was created by moving the mirror via its gate voltage, and an interferometric spectrometer can be formed by sweeping the tip over many wavelengths. Experiments and theory demonstrate that the interference signal is robust against thermal averaging.

Replacement manifolds: a method to uniformize semiclassical wave functions.

We present a semiclassical technique that relies on replacing complicated classical manifold structure with simpler manifolds, which are then evaluated by the usual semiclassical rules. Under circumstances where the original manifold structure gives poor or useless results semiclassically the replacement manifolds can yield remarkable accuracy. We give several working examples to illustrate the theory presented here.

Scarring effects on tunneling in chaotic double-well potentials.

The connection between scarring and tunneling in chaotic double-well potentials is studied in detail through the distribution of level splittings. The mean level splitting is found to have oscillations as a function of energy, as expected if scarring plays a role in determining the size of the splittings, and the spacing between peaks is observed to be periodic of period 2 pi Planck's over 2 pi in action. Moreover, the size of the oscillations is directly correlated with the strength of scarring. These results are interpreted within the theoretical framework of Creagh and Whelan. The semiclassical limit and finite-Planck's over 2 pi effects are discussed, and connections are made with reaction rates and resonance widths in metastable wells.

Localization of eigenfunctions in the stadium billiard.

We present a systematic survey of scarring and symmetry effects in the stadium billiard. The localization of individual eigenfunctions in Husimi phase space is studied first, and it is demonstrated that on average there is more localization than can be accounted for by random-matrix theory, even after removal of bouncing-ball states and visible scars. A major point of the paper is that symmetry considerations, including parity and time-reversal symmetries, enter to influence the total amount of localization. The properties of the local density of states are also investigated, as a function of phase space location. Aside from the bouncing-ball region of phase space, excess localization is found on short periodic orbits and along certain symmetry-related lines; the origin of all these sources of localization is discussed quantitatively and comparison is made with analytical predictions. Scarring is observed to be present in all the energy ranges considered. In light of our results, the excess localization in individual eigenstates is interpreted as being primarily due to symmetry effects.

Parametric evolution for a deformed cavity.

We consider a classically chaotic system that is described by a Hamiltonian H(Q,P;x), where (Q,P) describes a particle moving inside a cavity, and x controls a deformation of the boundary. The quantum eigenstates of the system are /n(x)>. We describe how the parametric kernel P(n/m)=//(2), also known as the local density of states, evolves as a function of deltax=x-x(0). We illuminate the nonunitary nature of this parametric evolution, the emergence of nonperturbative features, the final nonuniversal saturation, and the limitations of random-wave considerations. The parametric evolution is demonstrated numerically for two distinct representative deformation processes.

Scattering theory of Kondo mirages and observation of single Kondo atom phase shift.

We explain the origin of the Kondo mirage seen in recent quantum corral scanning tunneling microscope experiments with a scattering theory of electrons on the surfaces of metals. Our theory, combined with experimental data, provides a direct observation of a single Kondo atom phase shift. The Kondo mirage observed at the empty focus of an elliptical quantum corral is shown to arise from multiple electron bounces off the corral wall adatoms. We demonstrate our theory with direct quantitive comparison to experimental data.

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.

Measuring scars of periodic orbits.

The phenomenon of periodic orbit scarring of eigenstates of classically chaotic systems is attracting increasing attention. Scarring is one of the most important "corrections" to the ideal random eigenstates suggested by random matrix theory. This paper discusses measures of scars and in so doing also tries to clarify the concepts and effects of eigenfunction scarring. We propose a universal scar measure which takes into account an entire periodic orbit and the linearized dynamics in its vicinity. This measure is tuned to pick out those structures which are induced in quantum eigenstates by unstable periodic orbits and their manifolds. It gives enhanced scarring strength as measured by eigenstate overlaps and inverse participation ratios, especially for longer orbits. We also discuss off-resonance scars which appear naturally on either side of an unstable periodic orbit.

A novel synergistic stimulation of Swiss 3T3 cells by extracellular ATP and mitogens with opposite effects on cAMP levels.

In Swiss 3T3 mouse fibroblasts, the mitogenic effect of extracellular ATP depends on stimulation of adenylyl cyclase. Lysophosphatidic acid (LPA) and phosphatidic acid (PA) inhibited adenylyl cyclase but synergized with ATP in mitogenic stimulation. This unusual synergism of two mitogens with opposite effects on cAMP levels was further investigated. LPA and PA inhibited the elevation of cAMP caused by cholera toxin, prostaglandin E2, or forskolin, but not the rise induced by ATP. In fact, ATP overcame the inhibitory effects of LPA or PA on cAMP levels. Indeed, in the presence of ATP and either cholera toxin or prostaglandin E2, LPA became a stimulator of adenylyl cyclase. Stimulation of DNA synthesis and inhibition of cAMP accumulation by LPA were inhibited by pertussis toxin, but with different dose-response characteristics. In addition, a normal mitogenic response to LPA was obtained in transfected mutant cells with a defective regulatory subunit for protein kinase A and in cells whose regulation of cAMP levels was abnormal because of overproduction of cAMP phosphodiesterase. The data support the hypothesis that the mitogenic effect of LPA involves a PTX-sensitive Gi protein but not inhibition of adenylyl cyclase.