Interference Phenomena in Electronic Transport Through Chaotic Cavities: An Information-Theoretic Approach

We develop a statistical theory describing quantum-mechanical scattering of a particle by a cavity when the geometry is such that the classical dynamics is chaotic. This picture is relevant to a variety of systems, ranging from atomic nuclei to microwave cavities; the main application here is to electronic transport through ballistic microstructures. The theory describes the regime in which there are two distinct time scales, associated with a prompt and an equilibrated response, and is cast in terms of the matrix of scattering amplitudes S. The prompt response is related to the energy average of S which, through ergodicity, is expressed as the average over an ensemble of systems. We use an information-theoretic approach: the ensemble of S-matrices is determined by (1) general physical features-- symmetry, causality, and ergodicity, (2) the specific energy average of S, and (3) the notion of minimum information in the ensemble. This ensemble, known as Poisson's kernel, is meant to describe those situations in which any other information is irrelevant. Thus, one constructs the one-energy statistical distribution of S using only information expressible in terms of S itself without ever invoking the underlying Hamiltonian. This formulation has a remarkable predictive power: from the distribution of S we derive properties of the quantum conductance of cavities, including its average, its fluctuations, and its full distribution in certain cases, both in the absence and presence prompt response. We obtain good agreement with the results of the numerical solution of the Schrodinger equation for cavities in which either prompt response is absent or there are two widely separated time scales. Good agreement with experimental data is obtained once temperature smearing and dephasing effects are taken into account.Comment: 38 pages, 11 ps files included, uses IOP style files and epsf.st

Quantum Monte Carlo Study of Disordered Fermions

We study a strongly correlated fermionic model with attractive interactions in the presence of disorder in two spatial dimensions. Our model has been designed so that it can be solved using the recently discovered meron-cluster approach. Although the model is unconventional it has the same symmetries of the Hubbard model. Since the naive algorithm is inefficient, we develop a new algorithm by combining the meron-cluster technique with the directed-loop update. This combination allows us to compute the pair susceptibility and the winding number susceptibility accurately. We find that the s-wave superconductivity, present in the clean model, does not disappear until the disorder reaches a temperature dependent critical strength. The critical behavior as a function of disorder close to the phase transition belongs to the Berezinsky-Kosterlitz-Thouless universality class as expected. The fermionic degrees of freedom, although present, do not appear to play an important role near the phase transition.Comment: published version, more data added to Fig 5 and clarifications in text, 8 page

On the Inequivalence of Weak-Localization and Coherent Backscattering

We define a current-conserving approximation for the local conductivity tensor of a disordered system which includes the effects of weak localization. Using this approximation we show that the weak localization effect in conductance is not obtained simply from the diagram corresponding to the coherent back-scattering peak observed in optical experiments. Other diagrams contribute to the effect at the same order and decrease its value. These diagrams appear to have no semiclassical analogues, a fact which may have implications for the semiclassical theory of chaotic systems. The effects of discrete symmetries on weak localization in disordered conductors is evaluated and and compared to results from chaotic scatterers.Comment: 24 pages revtex + 12 figures on request; hub.94.

The Enhanced Sensitivity of the Transmission Phase of a Quantum Dot to Kondo Correlations

The strong sensitivity of the transmission phase through a quantum dot embedded into one arm of a two-wave Aharonov-Bohm interferometer to the Kondo effect is explained. The enhancement takes place because of the buildup of the exchange scattering on the dot due to Kondo correlations even much above $T_{K}$. The enhanced exchange competes with the potential scattering, which is always weak. Both cases of the Anderson impurity model and a multilevel quantum dot are considered. In the latter case in addition to the description of peculiar phase behavior a mechanism leading to ferromagnetic Kondo coupling in quantum dots is proposed.Comment: 4 pages, 2 figure

Decoherence by Correlated Noise and Quantum Error Correction

We study the decoherence of a quantum computer in an environment which is inherently correlated in time and space. We first derive the nonunitary time evolution of the computer and environment in the presence of a stabilizer error correction code, providing a general way to quantify decoherence for a quantum computer. The general theory is then applied to the spin-boson model. Our results demonstrate that effects of long-range correlations can be systematically reduced by small changes in the error correction codes.Comment: 4 pages, 1 figure, Phys. Rev. Lett. in pres

Interactions and Broken Time-Reversal Symmetry in Chaotic Quantum Dots

When treating interactions in quantum dots within a RPA-like approach, time-reversal symmetry plays an important role as higher-order terms -- the Cooper series -- need to be included when this symmetry is present. Here we consider model quantum dots in a magnetic field weak enough to leave the dynamics of the dot chaotic, but strong enough to break time-reversal symmetry. The ground state spin and addition energy for dots containing 120 to 200 electrons are found using local spin density functional theory, and we compare the corresponding distributions with those derived from an RPA-like treatment of the interactions. The agreement between the two approaches is very good, significantly better than for analogous calculations in the presence of time-reversal symmetry. This demonstrates that the discrepancies between the two approaches in the time-reversal symmetric case indeed originate from the Cooper channel, indicating that these higher-order terms might not be properly taken into account in the spin density functional calculations.Comment: 4 pages, 3 figure

Mesoscopic Transport Through Ballistic Cavities: A Random S-Matrix Theory Approach

We deduce the effects of quantum interference on the conductance of chaotic cavities by using a statistical ansatz for the S matrix. Assuming that the circular ensembles describe the S matrix of a chaotic cavity, we find that the conductance fluctuation and weak-localization magnitudes are universal: they are independent of the size and shape of the cavity if the number of incoming modes, N, is large. The limit of small N is more relevant experimentally; here we calculate the full distribution of the conductance and find striking differences as N changes or a magnetic field is applied.Comment: 4 pages revtex 3.0 (2-column) plus 2 postscript figures (appended), hub.pam.94.

Signatures of Classical Periodic Orbits on a Smooth Quantum System

Gutzwiller's trace formula and Bogomolny's formula are applied to a non--specific, non--scalable Hamiltonian system, a two--dimensional anharmonic oscillator. These semiclassical theories reproduce well the exact quantal results over a large spatial and energy range.Comment: 12 pages, uuencoded postscript file (1526 kb

Escape from noisy intermittent repellers

Intermittent or marginally-stable repellers are commonly associated with a power law decay in the survival fraction. We show here that the presence of weak additive noise alters the spectrum of the Perron - Frobenius operator significantly giving rise to exponential decays even in systems that are otherwise regular. Implications for ballistic transport in marginally stable miscrostructures are briefly discussed.Comment: 3 ps figures include