Tunable Fano Resonances in Transport through Microwave Billiards

We present a tunable microwave scattering device that allows the controlled variation of Fano line shape parameters in transmission through quantum billiards. Transport in this device is nearly fully coherent. By comparison with quantum calculations, employing the modular recursive Green's-function method, the scattering wave function and the degree of residual decoherence can be determined. The parametric variation of Fano line shapes in terms of interacting resonances is analyzed.Comment: 5 pages, 4 figures, submitted to Phys. Rev.

Formation of long-lived, scarlike modes near avoided resonance crossings in optical microcavities

We study the formation of long-lived states near avoided resonance crossings in open systems. For three different optical microcavities (rectangle, ellipse, and semi-stadium) we provide numerical evidence that these states are localized along periodic rays, resembling scarred states in closed systems. Our results shed light on the morphology of long-lived states in open mesoscopic systems.Comment: 4 pages, 5 figures (in reduced quality), to appear in Phys. Rev. Let

Classical limit of transport in quantum kicked maps

We investigate the behavior of weak localization, conductance fluctuations, and shot noise of a chaotic scatterer in the semiclassical limit. Time resolved numerical results, obtained by truncating the time-evolution of a kicked quantum map after a certain number of iterations, are compared to semiclassical theory. Considering how the appearance of quantum effects is delayed as a function of the Ehrenfest time gives a new method to compare theory and numerical simulations. We find that both weak localization and shot noise agree with semiclassical theory, which predicts exponential suppression with increasing Ehrenfest time. However, conductance fluctuations exhibit different behavior, with only a slight dependence on the Ehrenfest time.Comment: 17 pages, 13 figures. Final versio

Comparing periodic-orbit theory to perturbation theory in the asymmetric infinite square well

An infinite square well with a discontinuous step is one of the simplest systems to exhibit non-Newtonian ray-splitting periodic orbits in the semiclassical limit. This system is analyzed using both time-independent perturbation theory (PT) and periodic-orbit theory and the approximate formulas for the energy eigenvalues derived from these two approaches are compared. The periodic orbits of the system can be divided into classes according to how many times they reflect from the potential step. Different classes of orbits contribute to different orders of PT. The dominant term in the second-order PT correction is due to non-Newtonian orbits that reflect from the step exactly once. In the limit in which PT converges the periodic-orbit theory results agree with those of PT, but outside of this limit the periodic-orbit theory gives much more accurate results for energies above the potential step.Comment: 22 pages, 2 figures, 2 tables, submitted to Physical Review

Noise resistance of adiabatic quantum computation using random matrix theory

Besides the traditional circuit-based model of quantum computation, several quantum algorithms based on a continuous-time Hamiltonian evolution have recently been introduced, including for instance continuous-time quantum walk algorithms as well as adiabatic quantum algorithms. Unfortunately, very little is known today on the behavior of these Hamiltonian algorithms in the presence of noise. Here, we perform a fully analytical study of the resistance to noise of these algorithms using perturbation theory combined with a theoretical noise model based on random matrices drawn from the Gaussian Orthogonal Ensemble, whose elements vary in time and form a stationary random process.Comment: 9 pages, 3 figure

First Experimental Observation of Superscars in a Pseudointegrable Barrier Billiard

With a perturbation body technique intensity distributions of the electric field strength in a flat microwave billiard with a barrier inside up to mode numbers as large as about 700 were measured. A method for the reconstruction of the amplitudes and phases of the electric field strength from those intensity distributions has been developed. Recently predicted superscars have been identified experimentally and - using the well known analogy between the electric field strength and the quantum mechanical wave function in a two-dimensional microwave billiard - their properties determined.Comment: 4 pages, 5 .eps figure

Fractal Weyl law for chaotic microcavities: Fresnel's laws imply multifractal scattering

We demonstrate that the harmonic inversion technique is a powerful tool to analyze the spectral properties of optical microcavities. As an interesting example we study the statistical properties of complex frequencies of the fully chaotic microstadium. We show that the conjectured fractal Weyl law for open chaotic systems [W. T. Lu, S. Sridhar, and M. Zworski, Phys. Rev. Lett. 91, 154101 (2003)] is valid for dielectric microcavities only if the concept of the chaotic repeller is extended to a multifractal by incorporating Fresnel's laws.Comment: 8 pages, 12 figure

Poisson-to-Wigner crossover transition in the nearest-neighbor spacing statistics of random points on fractals

We show that the nearest-neighbor spacing distribution for a model that consists of random points uniformly distributed on a self-similar fractal is the Brody distribution of random matrix theory. In the usual context of Hamiltonian systems, the Brody parameter does not have a definite physical meaning, but in the model considered here, the Brody parameter is actually the fractal dimension. Exploiting this result, we introduce a new model for a crossover transition between Poisson and Wigner statistics: random points on a continuous family of self-similar curves with fractal dimension between 1 and 2. The implications to quantum chaos are discussed, and a connection to conservative classical chaos is introduced.Comment: Low-resolution figure is included here. Full resolution image available (upon request) from the author

Semiclassical form factor for spectral and matrix element fluctuations of multi-dimensional chaotic systems

We present a semiclassical calculation of the generalized form factor which characterizes the fluctuations of matrix elements of the quantum operators in the eigenbasis of the Hamiltonian of a chaotic system. Our approach is based on some recently developed techniques for the spectral form factor of systems with hyperbolic and ergodic underlying classical dynamics and f=2 degrees of freedom, that allow us to go beyond the diagonal approximation. First we extend these techniques to systems with f>2. Then we use these results to calculate the generalized form factor. We show that the dependence on the rescaled time in units of the Heisenberg time is universal for both the spectral and the generalized form factor. Furthermore, we derive a relation between the generalized form factor and the classical time-correlation function of the Weyl symbols of the quantum operators.Comment: some typos corrected and few minor changes made; final version in PR