174 research outputs found
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
- …