Chaotic Cavities Research Articles

Delay times in chaotic quantum systems

By an inductive reasoning, and based on recent results of the joint moments of proper delay times of open chaotic systems for ideal coupling to leads, we obtain a general expression for the distribution of the partial delay times for an arbitrary number of channels and any symmetry. This distribution was not completely known for all symmetry classes. Our theoretical distribution is verified by random matrix theory simulations of ballistic chaotic cavities.

Energy Localization Effects Within a Reverberation Chamber and Their Reduction in Chaotic Geometries

A method of studying energy localization effects in a reverberation chamber is proposed and applied to simulation results. Its application to field spatial distributions of a classical reverberation chamber equipped with a mode stirrer shows a strong energy localization phenomenon of damaging effect on the field homogeneity. From the energy distributions, it appears that this phenomenon is principally related to energy localization around the mode stirrer. To avoid the presence of a mode stirrer causing this phenomenon, an alternative shape of the reverberation chamber, inspired from geometries of chaotic cavities, is proposed. The results obtained with this new cavity configuration show that the strong energy localizations are avoided and the resonant modes better contribute to the field uniformity and isotropy within the working volume.

Order, disorder, and tunable gaps in the spectrum of Andreev bound states in a multiterminal superconducting device

We consider the spectrum of Andreev bound states (ABSs) in an exemplary 4-terminal superconducting structure where 4 chaotic cavities are connected by QPCs to the terminals and to each other forming a ring. Such a tunable device can be realized in 2DEG-superconductor structures. We concentrate on the limit of a short structure and large conductance of the QPCs where a quasi-continuous spectrum is formed. The energies can be tuned by the superconducting phases. We observe the opening and closing of gaps in the spectrum. This concerns the usual proximity gap that separates the levels from zero energy as well as less usual "smile" gaps that split the levels of the spectrum. We demonstrate a remarkable crossover in the overall spectrum that occurs upon changing the ratio of conductance of the inner and outer QPCs. At big values of the ratio, the levels exhibit a generic behavior expected for the spectrum of a disordered system manifesting level repulsion and "Brownian motion" upon changing the phases. At small values of the ratio, the levels are squeezed into narrow bunches separated by wide smile gaps. Each bunch consists of almost degenerate ABSs. We study in detail the properties of the spectrum in the limit of a small ratio, paying special attention to the crossings of bunches. We distinguish two types of crossings: i. with a regular phase dependence of the levels and ii. crossings where the Brownian motion of the levels leads to an apparently irregular phase-dependence. We work out a perturbation theory to explain the observations. The unusual properties of the spectrum originate from unobvious topological effects. Topology of the first kind is related to the winding of the semiclassical Green's function. It is responsible for the proximity gaps. Topology of the second kind comes about the discreteness of the number of modes and is responsible for the smile gaps.

Electron backscattering in a cavity: Ballistic and coherent effects

Numerous experimental and theoretical studies have focused on low-dimensional systems locally perturbed by the biased tip of a scanning force microscope. In all cases either open or closed weakly gate-tunable nanostructures have been investigated, such as quantum point contacts, open or closed quantum dots, etc. We study the behaviour of the conductance of a quantum point contact with a gradually forming adjacent cavity in series under the influence of a scanning gate. Here, an initially open quantum point contact system gradually turns into a closed cavity system. We observe branches and interference fringes known from quantum point contacts coexisting with irregular conductance fluctuations. Unlike the branches, the fluctuations cover the entire area of the cavity. In contrast to previous studies, we observe and investigate branches under the influence of the confining stadium potential, which is gradually built up. We find that the branches exist only in the area surrounded by cavity top gates. As the stadium shrinks, regular fringes originate from tip-induced constrictions leading to quantized conduction. In addition, we observe arc-like areas reminiscent of classical electron trajectories in a chaotic cavity. We also argue that electrons emanating from the quantum point contact spread out like a fan leaving branch-like regions of enhanced backscattering.

Large-N expansion for the time-delay matrix of ballistic chaotic cavities

We consider the 1/N-expansion of the moments of the proper delay times for a ballistic chaotic cavity supporting N scattering channels. In the random matrix approach, these moments correspond to traces of negative powers of Wishart matrices. For systems with and without broken time reversal symmetry (Dyson indices β = 1 and β = 2), we obtain a recursion relation, which efficiently generates the coefficients of the 1/N-expansion of the moments. The integrality of these coefficients and their possible diagrammatic interpretation is discussed.

Statistical Analysis of the Figure of Merit of a Two-Level Thermoelectric System: A Random Matrix Approach

Using the tools of random matrix theory we develop a statistical analysis of the transport properties of thermoelectric low-dimensional systems made of two electron reservoirs set at different temperatures and chemical potentials, and connected through a low-density-of-states two-level quantum dot that acts as a conducting chaotic cavity. Our exact treatment of the chaotic behavior in such devices lies on the scattering matrix formalism and yields analytical expressions for the joint probability distribution functions of the Seebeck coefficient and the transmission profile, as well as the marginal distributions, at arbitrary Fermi energy. The scattering matrices belong to circular ensembles which we sample to numerically compute the transmission function, the Seebeck coefficient, and their relationship. The exact transport coefficients probability distributions are found to be highly non-Gaussian for small numbers of conduction modes, and the analytical and numerical results are in excellent agreement. The system performance is also studied, and we find that the optimum performance is obtained for half-transparent quantum dots; further, this optimum may be enhanced for systems with few conduction modes.

Acoustic Scattering in Duct With a Chaotic Cavity

Acoustic Scattering in Duct With a Chaotic Cavity

Nonlinear damage detection and localization via an innovative metamaterial-based sensor

In recent years, acoustic metamaterials have attracted increasing scientific interest for very diverse technological applications ranging from sound abatement to ultrasonic imaging, mainly due to their ability to act as band-stop filters. At the same time, the concept of chaotic cavities has been recently proposed as an efficient tool to enhance the quality of nonlinear signal analysis, particularly in the ultrasonic/acoustic case. The goal of the present work is to merge the two concepts to propose a metamaterial-based device that can be used as a natural and selective linear filter for the detection of signals resulting from the propagation of elastic waves in nonlinear solids, e.g., in the presence of damage, and as a detector for the damage itself in time reversal experiments. Numerical simulations and experimental measurements based on scanning laser Doppler vibrometer demonstrate the feasibility of the approach and the potential of the device in providing improved signal to noise ratios and enhanced focusing on scatterer locations.

Correlators for the Wigner–Smith time-delay matrix of chaotic cavities

We study the Wigner–Smith time-delay matrix Q of a ballistic quantum dot supporting N scattering channels. We compute the v-point correlators of the power traces for arbitrary at leading order for large N using techniques from the random matrix theory approach to quantum chromodynamics. We conjecture that the cumulants of the 's are integer-valued at leading order in N and include a MATHEMATICA code that computes their generating functions recursively.

Multiparticle Correlations in Mesoscopic Scattering: Boson Sampling, Birthday Paradox, and Hong-Ou-Mandel Profiles.

The interplay between single-particle interference and quantum indistinguishability leads to signature correlations in many-body scattering. We uncover these with a semiclassical calculation of the transmission probabilities through mesoscopic cavities for systems of noninteracting particles. For chaotic cavities we provide the universal form of the first two moments of the transmission probabilities over ensembles of random unitary matrices, including weak localization and dephasing effects. If the incoming many-body state consists of two macroscopically occupied wave packets, their time delay drives a quantum-classical transition along a boundary determined by the bosonic birthday paradox. Mesoscopic chaotic scattering of Bose-Einstein condensates is, then, a realistic candidate to build a boson sampler and to observe the macroscopic Hong-Ou-Mandel effect.

Simulation study of a chaotic cavity transducer based virtual phased array used for focusing in the bulk of a solid material

In acoustic and ultrasonic non-destructive testing techniques, it is sometimes beneficial to concentrate sound energy at a chosen location in space and at a specific instance in time, for example to improve the signal-to-noise ratio or activate the nonlinearity of damage features. Time Reversal (TR) techniques, taking advantage of the reversible character of the wave equation, are particularly suited to focus ultrasonic waves in time and space. The characteristics of the energy focusing in solid media using principles of time reversed acoustics are highly influenced by the nature and dimensions of the medium, the number of transducers and the length of the received signals. Usually, a large number of transducers enclosing the domain of interest is needed to improve the quality of the focusing. However, in the case of highly reverberant media, the number of transducers can be reduced to only one (single-channel TR). For focusing in a non-reverberant medium, which is impossible when using only one source, an adaptation of the single-channel reciprocal TR procedure has been recently suggested by means of a Chaotic Cavity Transducer (CCT), a single element transducer glued on a cavity of chaotic shape. In this paper, a CCT is used to focus elastic energy, at different times, in different points along a predefined line on the upper surface of a thick solid sample. Doing so, all focusing points can act as a virtual phased array transducer, allowing to focus in any point along the depth direction of the sample. This is impossible using conventional reciprocal TR, as you need to have access to all points in the bulk of the material for detecting signals to be used in the TR process. To asses and provide a better understanding of this concept, a numerical study has been developed, allowing to verify the basic concepts of the virtual phased array and to illustrate multi-component time reversal focusing in the bulk of a solid material.

The Influences of Boundary Shapes on Polarization Characteristics and Lasing Modes in Broad-Area Vertical-Cavity Surface-Emitting Lasers With Cryogenic Detuning: Regular Versus Chaotic Cavities

The broad-area rectangular-shaped and stadium-shaped VCSELs with nearly the same aspect ratio are designed to explore the influence of lateral boundary shapes on polarization states and lasing spectra with large detuning by cryogenic cooling. For the rectangular-shaped VCSEL, the lasing modes usually exhibit linearly polarized state and their far-field emissions mainly concentrate on four diagonal directions. On the other hand, the lasing modes of the stadium-shaped VCSEL generally display two orthogonally polarized states and their far-field emissions extensively spread on azimuthal directions. More intriguingly, the lasing spectra of the two devices clearly manifest the features of the energy-level distribution in regular and chaotic quantum billiards, respectively.

Metamaterials-based sensor to detect and locate nonlinear elastic sources

In recent years, acoustic metamaterials have attracted increasing scientific interest for very diverse technological applications ranging from sound abatement to ultrasonic imaging, mainly due to their ability to act as band-stop filters. At the same time, the concept of chaotic cavities has been recently proposed as an efficient tool to enhance the quality of nonlinear signal analysis, particularly in the ultrasonic/acoustic case. The goal of the present paper is to merge the two concepts in order to propose a metamaterial-based device that can be used as a natural and selective linear filter for the detection of signals resulting from the propagation of elastic waves in nonlinear materials, e.g., in the presence of damage, and as a detector for the damage itself in time reversal experiments. Numerical simulations demonstrate the feasibility of the approach and the potential of the device in providing improved signal-to-noise ratios and enhanced focusing on the defect locations.

Quantum transport in chaotic ballistic cavity: a Brownian-motion approach

We apply the evolution equation method derived for Brownian-motion ensembles of random matrix theory (Macedo-Junior and Macêdo 2006 Nucl. Phys. B 752 439) to study the universal transport properties of a ballistic chaotic cavity coupled ideally to two electron reservoirs via perfect conducting leads with an arbitrary number of scattering channels. We obtain exact results for all universality classes of circular ensembles associated to the Cartan’s classification of symmetric spaces.

Influence of a Superconducting Lead on Orbital Entanglement Production in Chaotic Cavities

We study orbital entanglement production in a chaotic cavity connected to four single-channel normal-metal leads and one superconducting lead, assuming the presence of time-reversal symmetry and within a random matrix theory approach. The scattered state of two incident electrons is written as the superposition of several two-outgoing quasi-particle components, four of which are orbitally entangled in a left-right bipartition. We calculate numerically the mean value of the squared norm of each entangled component, as functions of the number of channels in the superconducting lead. Its behavior is explained as resulting from the proximity effect. We also study statistically the amount of entanglement carried by each pair of outgoing quasi-particles. When the influence of the superconductor is more intense, the device works as an entangler of electron-hole pairs, and the average entanglement is found to be considerably larger than that obtained without the superconducting lead.

Random coupling model for the radiation of irregular apertures

AbstractIn this work, we extend results on the coupling of radiation through apertures inside wave chaotic electromagnetic cavities to the short‐wavelength limit. The aperture is assumed to have irregular and smooth boundary geometry. A statistical approach is then used to model both fields in the aperture and in the plane of the aperture. Particular emphasis is devoted to the calculation of the free‐space or radiation aperture admittance matrix, whose ensemble averaged element takes a simple closed‐form expression. The radiation admittance matrix is found to be purely diagonal at relatively short wavelength, and it exhibits unusual frequency behavior. The extreme scenario of an irregular aperture radiating inside an irregular cavity is represented through the random coupling model. This mathematical framework uses a limited number of details of both the aperture and the environment in those problems involving the coupling of an external radiation. The universal fluctuation of the effective area of an electrically large aperture is found for a wave chaotic cavity at variable losses. Results are expected to be useful for the physical understanding of scattering in extremely complicated environments, mode‐stirred reverberation chambers, wireless channels, radar traces, and statistical optics.

Statistical distribution of the Wigner-Smith time-delay matrix moments for chaotic cavities.

We derive the joint distribution of the moments TrQ(κ) (κ≥1) of the Wigner-Smith matrix for a chaotic cavity supporting a large number of scattering channels n. This distribution turns out to be asymptotically Gaussian, and we compute explicitly averages and covariances. The results are in a compact form and have been verified numerically. The general methodology of proof and computations has a wide range of applications.

Statistics of time delay and scattering correlation functions in chaotic systems. I. Random matrix theory

We consider the statistics of time delay in a chaotic cavity having M open channels, in the absence of time-reversal invariance. In the random matrix theory approach, we compute the average value of polynomial functions of the time delay matrix Q = − iħS†dS/dE, where S is the scattering matrix. Our results do not assume M to be large. In a companion paper, we develop a semiclassical approximation to S-matrix correlation functions, from which the statistics of Q can also be derived. Together, these papers contribute to establishing the conjectured equivalence between the random matrix and the semiclassical approaches.

Joint statistics of quantum transport in chaotic cavities

We study the joint statistics of conductance G and shot noise P in chaotic cavities supporting a large number N of open electronic channels in the two attached leads. We determine the full phase diagram in the -plane, employing a Coulomb gas technique on the joint density of transmission eigenvalues, as dictated by random matrix theory. We find that in the region of typical fluctuations, conductance and shot noise are uncorrelated and jointly Gaussian, and away from it they fluctuate according to a different joint rate function in each phase of the -plane. Different functional forms of the rate function in different regions emerge as a direct consequence of third-order phase transitions in the associated Coulomb gas problem.

Statistics of time delay and scattering correlation functions in chaotic systems. II. Semiclassical approximation

We consider S-matrix correlation functions for a chaotic cavity having M open channels, in the absence of time-reversal invariance. Relying on a semiclassical approximation, we compute the average over E of the quantities Tr[S†(E − ϵ) S(E + ϵ)]n, for general positive integer n. Our result is an infinite series in ϵ, whose coefficients are rational functions of M. From this, we extract moments of the time delay matrix Q = − iħS†dS/dE and check that the first 8 of them agree with the random matrix theory prediction from our previous paper [M. Novaes, J. Math. Phys. 56, 062110 (2015)].