Ph. Jacquod

EMERGENCE OF QUANTUM CHAOS IN FINITE INTERACTING FERMI SYSTEMS

We study the level spacing statistics P(s) in many-body Fermi systems and determine a critical two-body interaction strength Uc at which a crossover from Poisson to Wigner-Dyson statistics takes place. Near the Fermi level the results allow to find a critical temperature Tch above which quantum chaos and thermalization set in.

Decoherence, entanglement and irreversibility in quantum dynamical systems with few degrees of freedom

In this review we summarize and amplify recent investigations of coupled quantum dynamical systems with few degrees of freedom in the short-wavelength, semiclassical limit. Focusing on the correspondence between quantum and classical physics, we mathematically formulate and attempt to answer three fundamental questions. (i) How can one drive a small dynamical quantum system to behave classically? (ii) What determines the rate at which two single-particle quantum-mechanical subsystems become entangled when they interact? (iii) How does irreversibility occur in quantum systems with few degrees of freedom? These three questions are posed in the context of the quantum-classical correspondence for dynamical systems with few degrees of freedom, and we accordingly rely on two short-wavelength approximations to quantum mechanics to answer them: the trajectory-based semiclassical approach on the one hand, and random matrix theory on the other hand. We construct novel investigative procedures towards decoherence and the emergence of classicality out of quantumness in dynamical systems coupled to external degrees of freedom. In particular, we show how dynamical properties of chaotic classical systems, such as local exponential instability in phase space, also affects their quantum counterparts. For instance, it is often the case that the fidelity with which a quantum state is reconstructed after an imperfect time-reversal operation decays with the Lyapunov exponent of the corresponding classical dynamics. For related reasons, but perhaps more surprisingly, the rate at which two interacting quantum subsystems become entangled can also be governed by the subsystems Lyapunov exponents. Our method allows us to differentiate quantum coherent effects (those related to phase interferences) from classical ones (those related to the necessarily extended envelope of quantal wavefunctions) at each stage in our investigations. This makes it clear that all occurrences of Lyapunov exponents we witness have a classical origin, although they require rather strong decoherence effects to be observed. We extensively rely on numerical experiments to illustrate our findings and briefly comment on possible extensions to more complex problems involving environments with many interacting dynamical systems, going beyond the uncoupled harmonic oscillators model of Caldeira and Leggett.

Quantum Andreev Map: A Paradigm of Quantum Chaos in Superconductivity. .

We introduce quantum maps with particle-hole conversion (Andreev reflection) and particle-hole symmetry, which exhibit the same excitation gap as quantum dots in the proximity to a superconductor. Computationally, the Andreev maps are much more efficient than billiard models of quantum dots. This makes it possible to test analytical predictions of random-matrix theory and semiclassical chaos that were previously out of reach of computer simulations. We have observed the universal distribution of the excitation gap for a large Lyapunov exponent and the logarithmic reduction of the gap when the Ehrenfest time becomes comparable to the quasiparticle dwell time.

Mesoscopic spin Hall effect.

We investigate the spin Hall effect in ballistic chaotic quantum dots with spin-orbit coupling. We show that a longitudinal charge current can generate a pure transverse spin current. While this transverse spin current is generically nonzero for a fixed sample, we show that when the spin-orbit coupling time is short compared to the mean dwell time inside the dot, it fluctuates universally from sample to sample or upon variation of the chemical potential with a vanishing average.

Coherent destruction of Coulomb blockade peaks in molecular junctions

Coherent electronic transport in single-molecule junctions is investigated in the Coulomb blockade regime. Both the transmission phase and probability are calculated for junctions with various contact symmetries. A dramatic suppression of the Coulomb blockade peaks is predicted for junctions where multiple atomic orbitals of the molecule couple to a single electrode although the charging steps are unaffected.

Coherent thermoelectric effects in mesoscopic Andreev interferometers

We investigate thermoelectric transport through quantum chaotic, ballistic mesoscopic Andreev interferometers. We show that the ratio of the thermal and the charge conductances exhibits large oscillations with the phase difference φ between the two superconducting contacts, and that the Wiedemann-Franz law holds only when φ = π. A rather large average thermopower emerges whenever there is an asymmetry in the dwell times to reach the superconducting contacts. When this is the case, the thermopower is odd in φ. In contrast, when the average times to reach either superconducting contact are the same, the average thermopower is zero, in agreement with earlier works on diffusive Andreev interferometers. We show however that mesoscopic effects (analogous to universal conductance fluctuations) lead to a sample-dependent thermopower which is systematically even in φ.

Controlling the sign of magnetoconductance in Andreev quantum dots.

We construct a theory of coherent transport through a ballistic quantum dot coupled to a superconductor. We show that the leading-order quantum correction to the two-terminal conductance of these Andreev quantum dots may change sign depending on (i) the number of channels carried by the normal leads or (ii) the magnetic flux threading the dot. In contrast, spin-orbit interaction may affect the magnitude of the correction, but not always its sign. Experimental signatures of the effect include a nonmonotonic magnetoconductance curve and a transition from an insulator-like to a metal-like temperature dependence of the conductance. Our results are applicable to ballistic or disordered dots.

Microscopic theory for the quantum to classical crossover in chaotic transport.

We present a semiclassical theory for the scattering matrix S of a chaotic ballistic cavity at finite Ehrenfest time. Using a phase-space representation coupled with a multibounce expansion, we show how the Liouville conservation of phase-space volume decomposes S as S=S(cl) plus sign in circle S(qm). The short-time, classical contribution S(cl) generates deterministic transmission eigenvalues T=0 or 1, while quantum ergodicity is recovered within the subspace corresponding to the long-time, stochastic contribution S(qm). This provides a microscopic foundation for the two-phase fluid model, in which the cavity acts like a classical and a quantum cavity in parallel, and explains recent numerical data showing the breakdown of universality in quantum chaotic transport in the deep semiclassical limit. We show that the Fano factor of the shot-noise power vanishes in this limit, while weak localization remains universal.

BREIT-WIGNER WIDTH FOR TWO INTERACTING PARTICLES IN A ONE-DIMENSIONAL RANDOM POTENTIAL

For two interacting particles (TIP) in one-dimensional random potential the dependence of the Breit-Wigner width

Superconductivity-induced macroscopic resonant tunneling.

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