Isolated resonances in conductance fluctuations in ballistic billiards

We study numerically quantum transport through a billiard with a classically mixed phase space. In particular, we calculate the conductance and Wigner delay time by employing a recursive Green's function method. We find sharp, isolated resonances with a broad distribution of resonance widths in both the conductance and the Wigner time, in contrast to the well-known smooth conductance fluctuations of completely chaotic billiards. In order to elucidate the origin of the isolated resonances, we calculate the associated scattering states as well as the eigenstates of the corresponding closed system. As a result, we find a one-to-one correspondence between the resonant scattering states and eigenstates of the closed system. The broad distribution of resonance widths is traced to the structure of the classical phase space. Husimi representations of the resonant scattering states show a strong overlap either with the regular regions in phase space or with the hierarchical parts surrounding the regular regions. We are thus lead to a classification of the resonant states into regular and hierarchical, depending on their phase space portrait.Comment: 2 pages, 5 figures, to be published in J. Phys. Soc. Jpn., proceedings Localisation 2002 (Tokyo, Japan

Universal Power-law Decay in Hamiltonian Systems?

The understanding of the asymptotic decay of correlations and of the distribution of Poincar\'e recurrence times $P(t)$ has been a major challenge in the field of Hamiltonian chaos for more than two decades. In a recent Letter, Chirikov and Shepelyansky claimed the universal decay $P(t) \sim t^{-3}$ for Hamiltonian systems. Their reasoning is based on renormalization arguments and numerical findings for the sticking of chaotic trajectories near a critical golden torus in the standard map. We performed extensive numerics and find clear deviations from the predicted asymptotic exponent of the decay of $P(t)$. We thereby demonstrate that even in the supposedly simple case, when a critical golden torus is present, the fundamental question of asymptotic statistics in Hamiltonian systems remains unsolved.Comment: Phys. Rev. Lett., in pres

Resonance-assisted tunneling in deformed optical microdisks with a mixed phase space

The lifetimes of optical modes in whispering-gallery cavities depend crucially on the underlying classical ray dynamics, and they may be spoiled by the presence of classical nonlinear resonances due to resonance-assisted tunneling. Here we present an intuitive semiclassical picture that allows for an accurate prediction of decay rates of optical modes in systems with a mixed phase space. We also extend the perturbative description from near-integrable systems to systems with a mixed phase space, and we find equally good agreement. Both approaches are based on the approximation of the actual ray dynamics by an integrable Hamiltonian, which enables us to perform a semiclassical quantization of the system and to introduce a ray-based description of the decay of optical modes. The coupling between them is determined either perturbatively or semiclassically in terms of complex paths

Efficient Diagonalization of Kicked Quantum Systems

We show that the time evolution operator of kicked quantum systems, although a full matrix of size NxN, can be diagonalized with the help of a new method based on a suitable combination of fast Fourier transform and Lanczos algorithm in just N^2 ln(N) operations. It allows the diagonalization of matrizes of sizes up to N\approx 10^6 going far beyond the possibilities of standard diagonalization techniques which need O(N^3) operations. We have applied this method to the kicked Harper model revealing its intricate spectral properties.Comment: Text reorganized; part on the kicked Harper model extended. 13 pages RevTex, 1 figur

Structure of resonance eigenfunctions for chaotic systems with partial escape

Physical systems are often neither completely closed nor completely open, but instead are best described by dynamical systems with partial escape or absorption. In this paper we introduce classical measures that explain the main properties of resonance eigenfunctions of chaotic quantum systems with partial escape. We construct a family of conditionally invariant measures with varying decay rates by interpolating between the natural measures of the forward and backward dynamics. Numerical simulations in a representative system show that our classical measures correctly describe the main features of the quantum eigenfunctions: their multifractal phase-space distribution, their product structure along stable and unstable directions, and their dependence on the decay rate. The (Jensen-Shannon) distance between classical and quantum measures goes to zero in the semiclassical limit for long- and short-lived eigenfunctions, while it remains finite for intermediate cases

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

Dimer Decimation and Intricately Nested Localized-Ballistic Phases of Kicked Harper

Dimer decimation scheme is introduced in order to study the kicked quantum systems exhibiting localization transition. The tight-binding representation of the model is mapped to a vectorized dimer where an asymptotic dissociation of the dimer is shown to correspond to the vanishing of the transmission coefficient thru the system. The method unveils an intricate nesting of extended and localized phases in two-dimensional parameter space. In addition to computing transport characteristics with extremely high precision, the renormalization tools also provide a new method to compute quasienergy spectrum.Comment: There are five postscript figures. Only half of the figure (3) is shown to reduce file size. However, missing part is the mirror image of the part show

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 x 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.Comment: 10 pages, 4 figs on request, RevTeX3.0, Europhysics Letters, in pres