Chaotic Cavities Research Articles

Research on scattering in microwave chaotic cavity

The scattering inside the computer box is studied. Some results are found through scattering matrix elements. The ensemble-averaged scattering matrix can be obtained by the measured radiation scattering. With the increase of cavity loss, scattering fluctuations are reduced, and insertion phase shift distribution is becoming more and more uniform. Based on the Dyson’s circular ensemble, the scattering behavior within computer box is found to be chaotic. According to RMT, normalized impedance matrix within the microwave chaotic cavity is universal in their statistical description, depending only upon the value of a single dimensionless cavity loss-parameter.

Transport observables for a FNF mesoscopic system in the extreme quantum limit regime

We study the current-induced torque for electrons on ferromagnet-normal metal-ferromagnet (FNF) trilayer with non-collinear magnetizations. Our system is composed of a chaotic cavity and two junctions, coupled with ideal contacts to ferromagnetic reservatories in local equilibrium by means of a small number of scattering channels. We assume that the normal part is disordered. Each junction is related to the direction of the reservoirs magnetization. The system is taken out of equilibrium causing a spin accumulation. We suppose that all elements have a length smaller than the coherence phase and the spin flip lengths. This consideration lets us neglect decoherence and spin flip processes. The conductance and torque were found numerically by employing the random-matrix theory and scattering matrix formalism for the spin-flux. The observables are presented as a function of the number of propagating channels in the extreme quantum limit regime and of the angle between the magnetizations of the different ferromagnet layers.

Statistics of thermal to shot noise crossover in chaotic cavities

Recently formulated integrable theory of quantum transport (Osipov and Kanzieper, 2008 Phys. Rev. Lett. 101 176804) is extended to describe sample-to-sample fluctuations of the noise power in chaotic cavities with broken time-reversal symmetry. Concentrating on the universal transport regime, we determine dependence of the noise power cumulants on the temperature, applied bias voltage and the number of propagating modes in the leads. Intrinsic connection between statistics of thermal to shot noise crossover and statistics of Landauer conductance is revealed and briefly discussed.

Experimental and Numerical Studies of One-Dimensional and Three-Dimensional Chaotic Open Systems

In this paper we present the results of the experimental and numerical studies of the distribution P(R) of the reflection coecient R and the distributions of the Wigner reaction matrix [26] for microwave networks that correspond to graphs with time reversal symmetry (fl = 1 symmetry class of random matrix theory [38]) in the presence of absorption. Our experimental results are compared with the exact theoretical predictions of Savin et al. [39]. We also present the results of the experimental study of the distribution P(R) of the reflection coecient R for the 3D chaotic microwave cavity in the presence of strong absorption.

Chaotic microcavity laser with high quality factor and unidirectional output

Here we report lasing action in lima\c{c}on-shaped GaAs microdisks with quantum dots (QDs) embedded. Although the intracavity ray dynamics is predominantly chaotic, high-$Q$ modes are concentrated in the region $\chi > \chi_c$ as a result of wave localization. Strong optical confinement by total internal reflection leads to very low lasing threshold. Our measurements show that all the lasing modes have output in the same direction, regardless of their wavelengths and intracavity mode structures. This universal emission direction is determined by directed phase space flow of optical rays in the open chaotic cavity. The divergence angle of output beam is less than 40 degree. The unidirectionality proves to be robust against small deviations of the real cavity shape and size from the designed values.

On the use of a chaotic cavity transducer in nonlinear elastic imaging

We discuss the advantages of “chaotic cavity transducer focusing” to enhance the localization of microdamage in conjunction with nonlinear elastic wave spectroscopy methods. Chaotic cavity transducer focusing is defined as the hardware-software combination of a piezoelectric ceramic glued on a cavity of chaotic shape on the one hand with the reciprocal time reversal (or inverse filter) technique on the other hand. Additional optimization through the use of sweeps and inverse filtering techniques are discussed as well. The technique is applied to image a crack in a steel sample.

Semiclassical approach to the ac conductance of chaotic cavities

We address frequency-dependent quantum transport through mesoscopic conductors in the semiclassical limit. By generalizing the trajectory-based semiclassical theory of dc quantum transport to the ac case, we derive the average screened conductance as well as ac weak-localization corrections for chaotic conductors. Thereby we confirm respective random matrix results and generalize them by accounting for Ehrenfest time effects. We consider the case of a cavity connected through many leads to a macroscopic circuit which contains ac-sources. In addition to the reservoir the cavity itself is capacitively coupled to a gate. By incorporating tunnel barriers between cavity and leads we obtain results for arbitrary tunnel rates. Finally, based on our findings we investigate the effect of dephasing on the charge relaxation resistance of a mesoscopic capacitor in the linear low-frequency regime.

Quasimodes of a chaotic elastic cavity with increasing local losses

We report noninvasive measurements of the complex field of elastic quasimodes of a silicon wafer with chaotic shape. The amplitude and phase spatial distribution of the flexural modes are directly obtained by Fourier transform of time measurements. We investigate the crossover from real mode to complex-valued quasimode, when absorption is progressively increased on one edge of the wafer. The complexness parameter, which characterizes the degree to which a resonance state is complex valued, is measured for nonoverlapping resonances, and is found to be proportional to the nonhomogeneous contribution to the line broadening of the resonance. A simple two-level model based on the effective Hamiltonian formalism supports our experimental results.

Systematic approach to statistics of conductance and shot-noise in chaotic cavities

Applying random matrix theory to quantum transport in chaotic cavities, we develop a powerful method for computing the moments of the conductance and shot-noise (including their joint moments) of arbitrary order and at any number of open channels. Our approach is based on the Selberg integral theory combined with the theory of symmetric functions and is applicable equally well for systems with and without time-reversal symmetry. We also compute higher-order cumulants and perform their detailed analysis. In particular, we establish an explicit form of the leading asymptotic of the cumulants in the limit of the large channel numbers. We derive further a general Pfaffian representation for the corresponding distribution functions. The Edgeworth expansion based on the first four cumulants is found to reproduce fairly accurately the distribution functions in the bulk even for a small number of channels. As the latter increases, the distributions become Gaussian-like in the bulk but are always characterized by a power-law dependence near their edges of support. Such asymptotics are determined exactly up to linear order in distances from the edges, including the corresponding constants.

Microscopic Theory of the Andreev Gap

We present a microscopic theory of the Andreev gap, i.e., the phenomenon that the density of states (DOS) of normal chaotic cavities attached to superconductors displays a hard gap centered around the Fermi energy. Our approach is based on a solution of the quantum Eilenberger equation in the regime tD<<tE, where tD and tE are the classical dwell time and Ehrenfest time, respectively. We show how quantum fluctuations eradicate the DOS at low energies and compute the profile of the gap to leading order in the parameter tD/tE.

Generalized shot noise model for time-reversal in multiple-scattering media allowing for arbitrary inputs and windowing

A theoretical shot noise model to describe the output of a time-reversal experiment in a multiple-scattering medium is developed. This (non-wave equation based) model describes the following process. An arbitrary waveform is transmitted through a high-order multiple-scattering environment and recorded. The recorded signal is arbitrarily windowed and then time-reversed. The processed signal is retransmitted into the environment and the resulting signal recorded. The temporal and spatial signal and noise of this process is predicted statistically. It is found that the time when the noise is largest depends on the arbitrary windowing and this noise peak can occur at times outside the main lobe. To determine further trends, a common set of parameters is applied to the general result. It is seen that as the duration of the input function increases, the signal-to-noise ratio (SNR) decreases (independent of signal bandwidth). It is also seen that longer persisting impulse responses result in increased main lobe amplitudes and SNR. Assumptions underpinning the generalized shot noise model are compared to an experimental realization of a multiple-scattering medium (a time-reversal chaotic cavity). Results from the model are compared to random number numerical simulation.

Computation of the Helmholtz Eigenvalues in a Class of Chaotic Cavities Using the Multipole Expansion Technique

In this paper, we present a numerical computation of the energy levels and the corresponding wave functions in a microwave resonator using the multipole expansion technique. The approach permits closed form, fast, and robust solutions of the Helmholtz equation (and the Schrodinger equation for two-dimensional systems) in an important class of wave chaos problem. In particular, wave functions inside the billiard are expressed in terms of a simple expansion of Hankel functions. The implementation of the approach is described, and the classical bowtie cavity is considered as a case study to demonstrate the versatility and efficiency of the method. To validate the accuracy, the field distribution and the eigenvalues calculated using this approach are compared to the solution obtained by boundary integral method. The case when the cavity contains objects (perfect electric conductors and/or dielectrics) is also presented and discussed.

Distribution of resonances in the quantum open baker map

We study relevant features of the spectrum of the quantum open baker map. The opening consists of a cut along the momentum p direction of the 2-torus phase space, modeling an open chaotic cavity. We study briefly the classical forward trapped set and analyze the corresponding quantum nonunitary evolution operator. The distribution of eigenvalues depends strongly on the location of the escape region with respect to the central discontinuity of this map. This introduces new ingredients to the association among the classical escape and quantum decay rates. Finally, we could verify that the validity of the fractal Weyl law holds in all cases.

Scattering a pulse from a chaotic cavity: Transitioning from algebraic to exponential decay

The ensemble averaged power scattered in and out of lossless chaotic cavities decays as a power law in time for large times. In the case of a pulse with a finite duration, the power scattered from a single realization of a cavity closely tracks the power-law ensemble decay initially, but eventually transitions to an exponential decay. In this paper, we explore the nature of this transition in the case of coupling to a single port. We find that for a given pulse shape, the properties of the transition are universal if time is properly normalized. We define the crossover time to be the time at which the deviations from the mean of the reflected power in individual realizations become comparable to the mean reflected power. We demonstrate numerically that, for randomly chosen cavity realizations and given pulse shapes, the probability distribution function of reflected power depends only on time, normalized to this crossover time.

Quantum interference correction to the shot-noise power in nonideal chaotic cavities

We present analytical results for the leading (weak-localization) quantum interference correction to the shot-noise power in a ballistic chaotic cavity coupled nonideally to two electron reservoirs via leads with an arbitrary number of open scattering channels. The calculations were performed using two independent methods: $S$-matrix diagrammatic perturbation theory and quantum circuit theory. We obtained an unexpected amplification-suppression transition as a function of both the number of open channels and the barriers' transparencies. The effect results from a subtle combination of temporal and spatial quantum coherence in the electron propagation through the system.

Semiclassical Theory of Time-Reversal Focusing

Time-reversal mirrors have been successfully implemented for various kinds of waves propagating in complex media. In particular, acoustic waves in chaotic cavities exhibit a refocalization that is extremely robust against external perturbations or the partial use of the available information. We develop a semiclassical approach in order to quantitatively describe the refocusing signal resulting from an initially localized wave packet. The time-dependent reconstructed signal grows linearly with the temporal window of injection, in agreement with the acoustic experiments, and reaches the same spatial extension of the original wave packet. We explain the crucial role played by the chaotic dynamics for the reconstruction of the signal and its stability against external perturbations.

Distributions of Conductance and Shot Noise and Associated Phase Transitions

For a chaotic cavity with two identical leads each supporting N channels, we compute analytically, for large N, the full distribution of the conductance and the shot noise power and show that in both cases there is a central Gaussian region flanked on both sides by non-Gaussian tails. The distribution is weakly singular at the junction of Gaussian and non-Gaussian regimes, a direct consequence of two phase transitions in an associated Coulomb gas problem.

Disorder effects in the quantum Hall effect of graphenep−njunctions

The quantum Hall effect in graphene $p\text{\ensuremath{-}}n$ junctions is studied numerically with emphasis on the effect of disorder at the interface of two adjacent regions. Conductance plateaus are found to be attached to the intensity of the disorder and are accompanied by universal conductance fluctuations in the bipolar regime, which is in good agreement with theoretical predictions of the random matrix theory on quantum chaotic cavities. The calculated Fano factors can be used in an experimental identification of the underlying transport character.

Resonance distribution in open quantum chaotic systems

In order to study the resonance spectra of chaotic cavities subject to some damping (which can be due to absorption or partial reflection at the boundaries), we use a model of damped quantum maps. In the high-frequency limit, the distribution of (quantum) decay rates is shown to cluster near a "typical" value, which is larger than the classical decay rate of the corresponding damped ray dynamics. The speed of this clustering may be quite slow, which could explain why it has not been detected in previous numerical data.

Integrable Theory of Quantum Transport in Chaotic Cavities

The problem of quantum transport in chaotic cavities with broken time-reversal symmetry is shown to be completely integrable in the universal limit. This observation is utilized to determine the cumulants and the distribution function of conductance for a cavity with ideal leads supporting an arbitrary number n of propagating modes. Expressed in terms of solutions to the fifth Painlevé transcendent and/or the Toda lattice equation, the conductance distribution is further analyzed in the large-n limit that reveals long exponential tails in the otherwise Gaussian curve.