Environment-independent decoherence rate in classically chaotic systems

We study the decoherence of a one-particle system, whose classical correpondent is chaotic, when it evolves coupled to a weak quenched environment. This is done by analytical evaluation of the Loschmidt Echo, (i.e. the revival of a localized density excitation upon reversal of its time evolution), in presence of the perturbation. We predict an exponential decay for the Loschmidt Echo with a (decoherence) rate which is asymptotically given by the mean Lyapunov exponent of the classical system, and therefore independent of the perturbation strength, within a given range of strengths. Our results are consistent with recent experiments of Polarization Echoes in nuclear magnetic resonance and preliminary numerical simulations.Comment: No figures. Typos corrected and minor modifications to the text and references. Published versio

Correlations and fluctuations of a confined electron gas

The grand potential $\Omega$ and the response $R = - \partial \Omega /\partial x$ of a phase-coherent confined noninteracting electron gas depend sensitively on chemical potential $\mu$ or external parameter $x$. We compute their autocorrelation as a function of $\mu$, $x$ and temperature. The result is related to the short-time dynamics of the corresponding classical system, implying in general the absence of a universal regime. Chaotic, diffusive and integrable motions are investigated, and illustrated numerically. The autocorrelation of the persistent current of a disordered mesoscopic ring is also computed.Comment: 12 pages, 1 figure, to appear in Phys. Rev.

Effect of deconfinement on resonant transport in quantum wires

The effect of deconfinement due to finite band offsets on transport through quantum wires with two constrictions is investigated. It is shown that the increase in resonance linewidth becomes increasingly important as the size is reduced and ultimately places an upper limit on the energy (temperature) scale for which resonances may be observed.Comment: 6 pages, 6 postscript files with figures; uses REVTe

Universal parametric correlations in the transmission eigenvalue spectra of disordered conductors

We study the response of the transmission eigenvalue spectrum of disordered metallic conductors to an arbitrary external perturbation. For systems without time-reversal symmetry we find an exact non-perturbative solution for the two-point correlation function, which exhibits a new kind of universal behavior characteristic of disordered conductors. Systems with orthogonal and symplectic symmetries are studied in the hydrodynamic regime.Comment: 10 pages, written in plain TeX, Preprint OUTP-93-36S (University of Oxford), to appear in Phys. Rev. B (Rapid Communication

Nonuniversality in level dynamics

Statistical properties of parametric motion in ensembles of Hermitian banded random matrices are studied. We analyze the distribution of level velocities and level curvatures as well as their correlation functions in the crossover regime between three universality classes. It is shown that the statistical properties of level dynamics are in general non-universal and strongly depend on the way in which the parametric dynamics is introduced.Comment: 24 pages + 10 figures (not included, avaliable from the author), submitted to Phys. Rev.

Spectral form factor in a random matrix theory

In the theory of disordered systems the spectral form factor $S(\tau)$, the Fourier transform of the two-level correlation function with respect to the difference of energies, is linear for $\tau<\tau_c$ and constant for $\tau>\tau_c$. Near zero and near $\tau_c$ its exhibits oscillations which have been discussed in several recent papers. In the problems of mesoscopic fluctuations and quantum chaos a comparison is often made with random matrix theory. It turns out that, even in the simplest Gaussian unitary ensemble, these oscilllations have not yet been studied there. For random matrices, the two-level correlation function $\rho(\lambda_1,\lambda_2)$ exhibits several well-known universal properties in the large N limit. Its Fourier transform is linear as a consequence of the short distance universality of $\rho(\lambda_1,\lambda_2)$. However the cross-over near zero and $\tau_c$ requires to study these correlations for finite N. For this purpose we use an exact contour-integral representation of the two-level correlation function which allows us to characterize these cross-over oscillatory properties. The method is also extended to the time-dependent case.Comment: 36P, (+5 figures not included

Quantum transport using the Ford-Kac-Mazur formalism

The Ford-Kac-Mazur formalism is used to study quantum transport in (1) electronic and (2) harmonic oscillator systems connected to general reservoirs. It is shown that for non-interacting systems the method is easy to implement and is used to obtain many exact results on electrical and thermal transport in one-dimensional disordered wires. Some of these have earlier been obtained using nonequilibrium Green function methods. We examine the role that reservoirs and contacts can have on determining the transport properties of a wire and find several interesting effects.Comment: 10 pages, 4 figure

Level Curvature Distribution and the Structure of Eigenfunctions in Disordered Systems

The level curvature distribution function is studied both analytically and numerically for the case of T-breaking perturbations over the orthogonal ensemble. The leading correction to the shape of the curvature distribution beyond the random matrix theory is calculated using the nonlinear supersymmetric sigma-model and compared to numerical simulations on the Anderson model. It is predicted analytically and confirmed numerically that the sign of the correction is different for T-breaking perturbations caused by a constant vector-potential equivalent to a phase twist in the boundary conditions, and those caused by a random magnetic field. In the former case it is shown using a nonperturbative approach that quasi-localized states in weakly disordered systems can cause the curvature distribution to be nonanalytic. In $2d$ systems the distribution function $P(K)$ has a branching point at K=0 that is related to the multifractality of the wave functions and thus should be a generic feature of all critical eigenstates. A relationship between the branching power and the multifractality exponent $d_{2}$ is suggested. Evidence of the branch-cut singularity is found in numerical simulations in $2d$ systems and at the Anderson transition point in $3d$ systems.Comment: 34 pages (RevTeX), 8 figures (postscript

Extreme sensitivity of the spin-splitting and 0.7 anomaly to confining potential in one-dimensional nanoelectronic devices

Quantum point contacts (QPCs) have shown promise as nanoscale spin-selective components for spintronic applications and are of fundamental interest in the study of electron many-body effects such as the 0.7 x 2e^2/h anomaly. We report on the dependence of the 1D Lande g-factor g* and 0.7 anomaly on electron density and confinement in QPCs with two different top-gate architectures. We obtain g* values up to 2.8 for the lowest 1D subband, significantly exceeding previous in-plane g-factor values in AlGaAs/GaAs QPCs, and approaching that in InGaAs/InP QPCs. We show that g* is highly sensitive to confinement potential, particularly for the lowest 1D subband. This suggests careful management of the QPC's confinement potential may enable the high g* desirable for spintronic applications without resorting to narrow-gap materials such as InAs or InSb. The 0.7 anomaly and zero-bias peak are also highly sensitive to confining potential, explaining the conflicting density dependencies of the 0.7 anomaly in the literature.Comment: 23 pages, 7 figure

A Brownian Motion Model of Parametric Correlations in Ballistic Cavities

A Brownian motion model is proposed to study parametric correlations in the transmission eigenvalues of open ballistic cavities. We find interesting universal properties when the eigenvalues are rescaled at the hard edge of the spectrum. We derive a formula for the power spectrum of the fluctuations of transport observables as a response to an external adiabatic perturbation. Our formula correctly recovers the Lorentzian-squared behaviour obtained by semiclassical approaches for the correlation function of conductance fluctuations.Comment: 19 pages, written in RevTe