Chladni figures in Andreev billiards

We study wave functions and their nodal patterns in Andreev billiards consisting of a normal-conducting (N) ballistic quantum dot in contact with a superconductor (S). The bound states in such systems feature an electron and a hole component which are coherently coupled by the scattering of electrons into holes at the S-N interface. The wave function “lives” therefore on two sheets of configuration space, each of which features, in general, distinct nodal patterns. By comparing the wave functions and their nodal patterns for holes and electrons detailed tests of semiclassical predictions become possible. One semiclassical theory based on ideal Andreev retroreflection predicts the electron- and hole eigenstates to perfectly mirror each other. We probe the limitations of validity of this model both in terms of the spectral density of the eigenstates and the shape of the wavefunctions in the electron and hole sheet. We identify cases where the Chladni figures for the electrons and holes drastically differ from each other and explain these discrepancies by limitations of the retroreflection picture.     

Viscous fingering and the shape of an electronic droplet in the quantum Hall regime

We show that the semiclassical dynamics of an electronic droplet, confined in a plane in a quantizing inhomogeneous magnetic field in the regime where the electrostatic interaction is negligible, is similar to viscous (Saffman-Taylor) fingering on the interface between two fluids with different viscosities confined in a Hele-Shaw cell. Both phenomena are described by the same equations with scales differing by a factor of up to 10(-9). We also report the quasiclassical wave function of the droplet in an inhomogeneous magnetic field.     

Magnon heat transport in doped La2CuO4

We present results of the thermal conductivity of La2CuO4 and La(1.8)Eu(0.2)CuO4 single crystals which represent model systems for the two-dimensional spin-1/2 Heisenberg antiferromagnet on a square lattice. We find large anisotropies of the thermal conductivity which are explained in terms of two-dimensional heat conduction by magnons within the CuO2 planes. Nonmagnetic Zn substituted for Cu gradually suppresses this magnon thermal conductivity kappa(mag). A semiclassical analysis of kappa(mag) is shown to yield a magnon mean free path which scales linearly with the reciprocal concentration of Zn ions.     

Bosonization,topological solitons and fractional charges in two-dimensional quantum field theory

We further develop the quantization of topological solitons in two-dimensional quantum field theory in terms of Euclidean region functional integrals. Our approach is nonperturbative and mathematically rigorous. We apply it to construct physical states with fractional fermion number in models of interacting bosons and fermions without recurring to a semiclassical approximation. A related issue discussed in this paper is two-dimensional chiral bosonization.     

Homogeneous polymer blend microparticles with a tunable refractive index

We show that homogeneous polymer blend microparticles can be prepared in situ from droplets of dilute solution of codissolved polymers. Provided that the droplet of solution is small enough (<10 mum), solvent evaporation is rapid enough to inhibit phase separation. Thus the polymers that are being mixed need not be miscible, which greatly enhances the applicability of the technique. From analysis of two-dimensional Fraunhofer diffraction (angular scattering) patterns, we show that both the real and the imaginary parts of the refractive index can be tuned by adjustment of the relative weight fractions of polymers in solution.     

Deposition and characterization of lines printed through laser-induced forward transfer

The possibility of printing two-dimensional micropatterns of biomolecule solutions is of great interest in many fields of research in biomedicine, from cell-growth and development studies to the investigation of the mechanisms of communication between cells. Although laser-induced forward transfer (LIFT) has been extensively used to print micrometric droplets of biological solutions, the fabrication of complex patterns depends on the feasibility of the technique to print micron-sized lines of aqueous solutions. In this study we investigate such a possibility through the analysis of the influence of droplet spacing of a water and glycerol solution on the morphology of the features printed by LIFT. We prove that it is indeed possible to print long and uniform continuous lines by controlling the overlap between adjacent droplets. We show how, depending on droplet spacing, several printed morphologies are generated, and we offer, in addition, a simple explanation of the observed behavior based on the jetting dynamics characteristic of the LIFT of liquids.     

Thermodynamics of a two-dimensional interacting Bose gas trapped in a quartic potential

We have studied the Bose-Einstein condensation (BEC) of an interacting Bose gas confined in a two-dimensional (2D) quartic potential by using a mean-field, semiclassical two-fluid model. A thermodynamic analysis including the chemical potential, condensate fraction, total energy, and specific heat has been carried out by considering different values of the interaction strength. Finally, we have found that the behaviour of the condensate fraction and specific heat of quartically trapped bosons differs from those of bosons trapped in a harmonic potential.     

Magnetotransport in a modulated two-dimensional electron gas

We propose a semiclassical theory of dc magnetotransport in a two-dimensional electron gas modulated along one direction with weak electrostatic modulations. We show that oscillations of the magnetoresistivity ρ_∥ corresponding to the current driven along the modulation lines observed at moderately low magnetic fields can be explained as commensurability oscillations.     

A Semiclassical Theory of a Dissipative Henon—Heiles System

A semiclassical theory of a dissipative Henon—Heiles system is proposed. Based on -scaling of an equation for the evolution of the Wigner quasiprobability distribution function in the presence of dissipation and thermal diffusion, we derive a semiclassical equation for quantum fluctuations, governed by the dissipation and the curvature of the classical potential. We show how the initial quantum noise gets amplified by classical chaotic diffusion, which is expressible in terms of a correlation of stochastic fluctuations of the curvature of the potential due to classical chaos, and ultimately settles down to equilibrium under the influence of dissipation. We also establish that there exists a critical limit to the expansion of phase space. The limit is set by chaotic diffusion and dissipation. Our semiclassical analysis is corroborated by numerical simulation of a quantum operator master equation.     

Chaotic Eigenfunctions in Phase Space

We study individual eigenstates of quantized area-preserving maps on the 2-torus which are classically chaotic. In order to analyze their semiclassical behavior, we use the Bargmann–Husimi representations for quantum states as well as their stellar parametrization, which encodes states through a minimal set of points in phase space (the constellation of zeros of the Husimi density). We rigorously prove that a semiclassical uniform distribution of Husimi densities on the torus entails a similar equidistribution for the corresponding constellations. We deduce from this property a universal behavior for the phase patterns of chaotic Bargmann eigenfunctions which is reminiscent of the WKB approximation for eigenstates of integrable systems (though in a weaker sense). In order to obtain more precise information on chaotic eigenconstellations, we then model their properties by ensembles of random states, generalizing former results on the 2-sphere to the torus geometry. This approach yields statistical predictions for the constellations which fit quite well the chaotic data. We finally observe that specific dynamical information, e.g., the presence of high peaks (like scars) in Husimi densities, can be recovered from the knowledge of a few long-wavelength Fourier coefficients, which therefore appear as valuable order parameters at the level of individual chaotic eigenfunctions.     

Why does the intrinsic spin Hall effect in a Rashba two-dimensional electron gas disappear in the dc limit?

Based on a self-consistent semiclassical approach, in this Letter we try to contribute to the basic physical understanding of some controversial issues about the intrinsic spin Hall effect in a Rashba two-dimensional electron gas. We show that for a Rashba two-dimensional electron gas in the diffusive transport thermodynamic limit, there exist some simple but much clear physical reasons which explain naturally why the intrinsic spin Hall effect in such a system cannot survive in the dc limit. The physical pictures established in this Letter resolve some puzzles existed in some previous theoretical treatments about this extraordinary effect.     

Inverse cascade regime in shell models of two-dimensional turbulence

We consider shell models that display an inverse energy cascade similar to two-dimensional turbulence (together with a direct cascade of an enstrophylike invariant). Previous attempts to construct such models ended negatively, stating that shell models give rise to a "quasiequilibrium" situation with equipartition of the energy among the shells. We show analytically that the quasiequilibrium state predicts its own disappearance upon changing the model parameters in favor of the establishment of an inverse cascade regime with Kolmogorov scaling. The latter regime is found where predicted, offering a useful model to study inverse cascades.     

Theory of forward glory scattering for chemical reactions: New derivation of a uniform semiclassical formula for the scattering amplitude

The theory of forward glory scattering is investigated for a state-to-state chemical reaction whose scattering amplitude can be written as a Legendre partial wave series. Legendre series occur in the exact quantum theory of reactive scattering when the initial and final helicity quantum numbers are zero, as well as in many approximate theories of chemical reactions. The starting point for the semiclassical theory is a two-dimensional integral representation for the scattering amplitude. A uniform semiclassical approximation is derived that is valid for angles both on, and off, the axial caustic associated with the glory. The derivation is the first application to a concrete problem in molecular physics of a method outlined by J. N. L. Connor and H. R. Mayne in 1979 for the uniform semiclassical evaluation of multidimensional integrals. The approach exploits the theory of singularities of differential mappings. The key step in the derivation is an exact one-to-one change of variables in the neighbourhood of the stationary phase points that locally reduce the two-dimensional phase of the integrand to a non-polynomial canonical form. The derivation complements a different semiclassical glory analysis reported in a companion paper.     

No-boundary measure of the universe

We consider the no-boundary proposal for homogeneous isotropic closed universes with a cosmological constant and a scalar field with a quadratic potential. In the semiclassical limit, it predicts classical behavior at late times if the scalar field is large enough. The classical histories may be singular in the past or bounce at a finite radius. This probability measure selects inflationary histories but is biased towards small numbers of e-foldings N. However, to obtain the probability of our observations in our past light cone these probabilities should be multiplied by exp(3N). This volume weighting is similar to that in eternal inflation. In a landscape potential, it would predict that the Universe underwent a large amount of inflation and could have always been semiclassical.     

The shapes of bowed interfaces in the two-dimensional Ising model

We show that properly normalized net energy fluctuations associated with interfaces in two-dimensional Ising models are described, asymptotically, by random walk partition functions. Two examples are investigated: one is a droplet on a wall, and the other is two nearby, ideally parallel interfaces; the mean shapes of the interfaces in both cases prove to be elliptic, bowed outward from the wall or from each other, the semiminor axis of the latter ellipse being 1/2 that of the former, in accord with random walk results.     

Effect of noise on interference phenomena in resonance spectroscopy

It is shown that, unlike the semiclassical theory of radiation, quantum theory predicts coherent reflection of resonance radiation from media for any ratios between the molecular density in the ground and excited states.     

Quantized dispersion of two-dimensional magnetoplasmons detected by photoconductivity spectroscopy

We find that the long-wavelength magnetoplasmon, resistively detected by photoconductivity spectroscopy in high-mobility two-dimensional electron systems, deviates from its well-known semiclassical nature as uncovered in conventional absorption experiments. A clear filling-factor dependent plateau-type dispersion is observed that reveals a so far unknown relation between the magnetoplasmon and the quantum Hall effect.     

二维可积系统的求迹公式和周期轨道的量子化

从Berry–Tabor求迹公式出发,导出了二维可积系统周期轨道作用量的半经典量子化条件.利用此量子化条件,考虑周期轨道满足的周期条件,得到了二维无关联四次振子系统周期轨道作用量的半经典量子化条件,并给出了半经典能级公式.对能级与周期轨道的对应关系做了分析.     

Interference oscillations in the angular distribution of laser-ionized electrons near ionization threshold

We analyze the two-dimensional momentum distribution of electrons ionized by few-cycle laser pulses in the transition regime from multiphoton absorption to tunneling by solving the time-dependent Schr?dinger equation and by a classical-trajectory Monte-Carlo simulation with tunneling (CTMC-T). We find a complex two-dimensional interference pattern that resembles above threshold ionization (ATI) rings at higher energies and displays Ramsauer-Townsend-type diffraction oscillations in the angular distribution near threshold. CTMC-T calculations provide a semiclassical explanation for the dominance of selected partial waves. While the present calculation pertains to hydrogen, we find surprising qualitative agreement with recent experimental data for rare gases [A. Rudenko, J. Phys. B 37, L407 (2004)].     

Semiclassical theory of spin-orbit interactions using spin coherent states

We formulate a semiclassical theory for systems with spin-orbit interactions. Using spin coherent states, we start from the path integral in an extended phase space, formulate the classical dynamics of the coupled orbital and spin degrees of freedom, and calculate the ingredients of Gutzwiller's trace formula for the density of states. For a two-dimensional quantum dot with a spin-orbit interaction of Rashba type, we obtain satisfactory agreement with fully quantum-mechanical calculations. The mode-conversion problem, which arose in an earlier semiclassical approach, has hereby been overcome.