Chaotic Cavities Research Articles

Effect of dephasing on charge-counting statistics in chaotic cavities

We calculate the cumulants of the charge transmitted through a chaotic cavity in the limit that the two openings have a large number of scattering channels. The shot noise, which is the second cumulant, is known to be insensitive to dephasing in this limit. Unexpectedly, the fourth and higher cumulants are found to depend on dephasing: A semiclassical theory and a quantum mechanical model with strong dephasing give a result different from a fully phase-coherent quantum mechanical theory.

Shot noise by quantum scattering in chaotic cavities.

We have experimentally studied shot noise of chaotic cavities defined by two quantum point contacts in series. The cavity noise is determined as (1/4)2e/I/ in agreement with theory and can be well distinguished from other contributions to noise generated at the contacts. Subsequently, we have found that cavity noise decreases if one of the contacts is further opened and reaches nearly zero for a highly asymmetric cavity. Heating inside the cavity due to electron-electron interaction can slightly enhance the noise of large cavities and is also discussed quantitatively.

Average conductance coefficients in multiterminal chaotic cavities

We calculate exactly the average conductance coefficients of a ballistic chaotic cavity coupled via tunnel barriers to an arbitrary number of reservoirs. Explicit formulas are derived for several regimes of interest: ideal contacts, strongly overlapping resonances, locally weakly absorbing limit, equivalent channels, and equivalent terminals.

Rate of energy absorption for a driven chaotic cavity

We consider the response of a chaotic cavity in d dimensions to periodic driving. We are motivated by older studies of one-body dissipation in nuclei, and also by anticipated mesoscopic applications. For calculating the rate of energy absorption due to time-dependent deformation of the confining potential, we introduce an improved version of the wall formula. Our formulation takes into account that a special class of deformations causes no heating in the zero-frequency limit. We also derive a mesoscopic version of the Drude formula, and explain that it can be regarded as a special example of our calculations. Specifically we consider a quantum dot driven by an electro-motive force which is induced by a time-dependent homogeneous magnetic field.

Single-mode delay time statistics for scattering by a chaotic cavity

We investigate the low-frequency dynamics for transmission or reflection of a wave by a cavity with chaotic scattering. We compute the probability distribution of the phase derivative ϕ' = dϕ/dω of the scattered wave amplitude, known as the single-mode delay time. In the case of a cavity connected to two single-mode waveguides we find a marked distinction between detection in transmission and in reflection: The distribution P(ϕ') vanishes for negative ϕ' in the first case but not in the second case.

Chaos and time-reversed acoustics

The objective of this paper is to show that time-reversal invariance can be exploited in acoustics to accurately control wave propagation through random propagating media as well as through chaotic reverberant cavities. To illustrate these concepts, several experiments are presented. They show that chaotic dynamics reduces the number of transducers needed to insure an accurate time-reversal experiment. Multi-pathing in random media and in chaotic cavities enhances resolution in time-reversal acoustics by making the effective size of time reversal mirrors much larger than its physical size. Comparisons with phase conjugated experiments will show that this effect is typical of broadband time-reversed acoustics and is not observed in monochromatic phase conjugation. Self averaging properties of time reversal experiments conducted in chaotic scattering environments will be emphasized.

Electronic transport through ballistic chaotic cavities: reflection symmetry, direct processes, and symmetry breaking.

We extend previous studies on transport through ballistic chaotic cavities with spatial left-right (LR) reflection symmetry to include the presence of direct processes. We first analyze fully LR-symmetric systems in the presence of direct processes and compare the distribution w(T) of the transmission coefficient T with that for an asymmetric cavity with the same "optical" S matrix. We then study the problem of "external mixing" of the symmetry caused by an asymmetric coupling of the cavity to the outside. We first consider the case where symmetry breaking arises because two symmetrically positioned waveguides are coupled to the cavity by means of asymmetric tunnel barriers. Although this system is asymmetric with respect to the LR operation, there is an effect of the symmetry of the cavity it was constructed from. Second, we break LR symmetry in the absence of direct processes by asymmetrically positioning the two waveguides and compare the results with those for the completely asymmetric case.

A comparison between one-channel time reversal and phase conjugation in random media and in reverberant cavities

In this paper, we are interested in time-reversal experiments conducted with only one omnidirectional transducer. Focusing through random media or inside chaotic reverberant cavities is shown to be possible when broadband pulses are used. A comparison with phase-conjugated experiments shows that this result is not obtained for monochromatic waves. It will be shown that the time-reversal focusing quality depends on the pulse bandwidth and on the statistical decorrelation of the wave fields for different frequencies. A set of experiments conducted through multiple scattering media of different thickness and through closed cavities will be presented. Self-averaging properties of time-reversed fields will be discussed for these various configurations.

Relation between stable orbits and quantum transmission resonance in ballistic cavities

Classical and quantum-mechanical transport properties in chaotic cavities are investigated to establish a link between them. Because of the stickiness at the boundary between stochastic seas and islands of regular orbits in phase space, classical trajectories spend a long time in the vicinity of a few regular orbits. The trapping results in an exclusive excitation of these stable orbits even when the cavity is terminated by classical leads. The wave-function pattern at quantum transmission resonances is found to be identical with one of the stable orbits. The correspondence implies that the transmission resonance takes place when the stable orbit satisfies Bohr and Sommerfeld's quantization rule, and hence explains why conductance fluctuations in ballistic cavities contain only several frequency components.

Self-similar magnetoconductance fluctuations in quantum dots

Self-similarity of magnetoconductance fluctuations in quantum dots is investigated by means of a tight binding Hamiltonian on a square lattice. Regular and chaotic dots are modeled by either a perfect $L\ifmmode\times\else\texttimes\fi{}L$ square or introducing diagonal disorder on a number of sites proportional to L. The conductance is calculated by means of an efficient implementation of the Kubo formula. The degree of opening of the cavity is varied by changing the width W of the connected leads. It is shown that the fractal dimension D is controlled by the ratio $W/L.$ The fractal dimension decreases from 2 to 1 when $W/L$ increases from $1/L$ to 1, and is almost independent of other parameters such as Fermi energy, leads configuration, etc. This result is consistent with recent experimental data for soft-wall cavities, which indicate that D decreases with the degree of wall softening (or, alternatively, cavity opening). The results hold for both regular and chaotic cavities.

Quantum limit of the laser line width in chaotic cavities and statistics of residues of scattering matrix poles

The quantum-limited line width of a laser cavity is enhanced above the Schawlow–Townes value by the Petermann factor K, due to the non-orthogonality of the cavity modes. We derive the relation between the Petermann factor and the residues of poles of the scattering matrix and investigate the statistical properties of the Petermann factor for cavities in which the radiation is scattered chaotically. For a single scattering channel we determine the complete probability distribution of K and find that the average Petermann factor 〈 K〉 depends non-analytically on the area of the opening, and greatly exceeds the most probable value. For an arbitrary number N of scattering channels we calculate 〈 K〉 as a function of the decay rate Γ of the lasing mode. We find for N⪢1 that for typical values of Γ the average Petermann factor 〈K〉∝ N ⪢1 is parametrically larger than unity.

Coherent backscattering of an elastic wave in a chaotic cavity

We report the first experimental evidence of coherent backscattering enhancement for transient elastic waves propagating in a two-dimensional chaotic cavity. The time-integrated squared amplitude at the point source is twice as large as at the other points around the source. Contrary to analogous optical experiments, this effect is already clearly observable on a single realization. Especially, the spatial shape of the coherent backscattering enhancement is well predicted by a generalization of the existing theory.

Semiclassical theory of conductance and noise in open chaotic cavities

Conductance and shot noise of an open cavity with diffusive boundary scattering are calculated within the Boltzmann-Langevin approach. In particular, conductance contains a nonuniversal geometric contribution, originating from the presence of open contacts. Subsequently, universal expressions for multiterminal conductance and noise, valid for all chaotic cavities, are obtained classically, based on the fact that the distribution function in the cavity depends only on energy, and using the principle of minimal correlations.

Quantum-limited linewidth of a chaotic laser cavity

A random-matrix theory is presented for the linewidth of a laser cavity in which the radiation is scattered chaotically. The linewidth is enhanced above the Schawlow-Townes value by the Petermann factor K, due to the nonorthogonality of the cavity modes. The factor K is expressed in terms of a non-Hermitian random matrix, and its distribution is calculated exactly for the case in which the cavity is coupled to the outside via a small opening. The average of K is found to depend nonanalytically on the area of the opening, and to greatly exceed the most probable value.

Wave scattering through classically chaotic cavities in the presence of absorption: An information-theoretic model

We propose an information-theoretic model for the transport of waves through a chaotic cavity in the presence of absorption. The entropy of the S-matrix statistical distribution is maximized, with the constraint <Tr SSdagger>=alphan: n is the dimensionality of S, and 0</=alpha</=1, alpha=0(1) meaning complete (no) absorption. For strong absorption our result agrees with a number of analytical calculations already given in the literature. In that limit, the distribution of the individual (angular) transmission and reflection coefficients becomes exponential (Rayleigh statistics), even for n=1. For n>>1 Rayleigh statistics is attained even with no absorption; here, we extend the study to alpha<1. The model is compared with random-matrix-theory numerical simulations: it describes the problem very well for strong absorption, but fails for moderate and weak absorptions. Thus, in the latter regime, some important physical constraint is missing in the construction of the model.

Time-Dependent Transport in Mesoscopic Structures

A discussion of recent work on time-dependent transport inmesoscopic structures is presented. The discussion emphasizesthe use of time-dependent transport to gain information on thecharge distribution and its collective dynamics. We discussthe RC-time of mesoscopic capacitors, the dynamic conductanceof quantum point contacts and dynamic weak localizationeffects in chaotic cavities. We review work on adiabaticquantum pumping and photon-assisted transport, and concludewith a list which demonstrates the wide range of problemswhich are of interest.

Conductance and statistical properties of chaotic and integrable electron waveguides

We show that the S-matrix for electrons propagating in a waveguide has different statistical properties depending on whether the waveguide cavity shape gives rise to chaotic or integrable behavior classically. We obtain distributions of energy level spacings for integrable and chaotic billiards shaped like the waveguide cavity. We also obtain distributions for Wigner delay times and resonance widths for the waveguide, for integrable and chaotic cavity geometries. Our results, obtained by direct numerical calculation of the electron wave function, are consistent with the predictions of random matrix theory.

Distribution of the quantum mechanical time-delay matrix for a chaotic cavity

We calculate the joint probability distribution of the Wigner-Smith time-delay matrix Q=−iℏS −1∂S/∂ε and the scattering matrix S for scattering from a chaotic cavity with ideal point contacts. To this end we prove a conjecture by Wigner about the unitary invariance property of the distribution functional P[S(ε)] of energy-dependent scattering matrices S(ε). The distribution of the inverse of the eigenvalues τ1,…,τ N of Q is found to be the Laguerre ensemble from random-matrix theory. The eigenvalue density ρ(τ) is computed using the method of orthogonal polynomials. This general theory has applications to the thermopower, magnetoconductance, and capacitance of a quantum dot.

Charge Relaxation Resistances and Charge Fluctuations in Mesoscopic Conductors

A brief overview is presented of recent work which investigates the time-dependent relaxation of charge and its spontaneous fluctuations on mesoscopic conductors in the proximity of gates. The leading terms of the low frequency conductance are determined by a capacitive or inductive emittance and a dissipative charge relaxation resistance. The charge relaxation resistance is determined by the ratio of the mean square dwell time of the carriers in the conductor and the square of the mean dwell time. The contribution of each scattering channel is proportional to half a resistance quantum. We discuss the charge relaxation resistance for mesoscopic capacitors, quantum point contacts, chaotic cavities, ballistic wires and for transport along edge channels in the quantized Hall regime. At equilibrium the charge relaxation resistance also determines via the fluctuation-dissipation theorem the spontaneous fluctuations of charge on the conductor. Of particular interest are the charge fluctuations in the presence of transport in a regime where the conductor exhibits shot noise. At low frequencies and voltages charge relaxation is determined by a nonequilibrium charge relaxation resistance.

One-channel time-reversal in chaotic cavities: Theoretical limits

One-channel time-reversal experiments in closed chaotic cavities produce excellent, but not perfect, time-reversed focusing. This paper investigates such experiments by a simple eigenmode analysis of the system. It shows that the process is, even for long reversed signals, subject to an information loss during recording and re-emission which prevents perfect time-reversal. This fact can be expressed by a simple equation, called the cavity equation, which states that the signal of a one-channel time-reversal is equal to the signal of a perfect time-reversal after convolution with the backscattering impulse response of the reversal point (i.e., from this point to this point). The latter convolution describes the introduction of the loss of information. Furthermore, arguments are presented suggesting that one third of the total energy of the time-reversed wave field is actually contained in the refocusing wavefront. The predictions are verified by numerical finite-difference time-domain simulations.