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Ph. Jacquod

Publications and source records attributed to Ph. Jacquod.

35 records · Page 2Linked to original sources
arXiv2005

Lyapunov Generation of Entanglement and the Correspondence Principle

We show how a classically vanishing interaction generates entanglement between two initially nonentangled particles, without affecting their classical dynamics. For chaotic dynamics, the rate of entanglement is shown to saturate at the Lyapunov exponent of the classical dynamics as the interaction strength increases. In the saturation regime, the one-particle Wigner function follows classical dynamics better and better as one goes deeper and deeper in the semiclassical limit. This demonstrates that quantum-classical correspondence at the microscopic level requires neither high temperatures, nor coupling to a large number of external degrees of freedom.

quant-ph↗
arXiv2005

Quantum-to-classical crossover for Andreev billiards in a magnetic field

We extend the existing quasiclassical theory for the superconducting proximity effect in a chaotic quantum dot, to include a time-reversal-symmetry breaking magnetic field. Random-matrix theory (RMT) breaks down once the Ehrenfest time $τ_E$ becomes longer than the mean time $τ_D$ between Andreev reflections. As a consequence, the critical field at which the excitation gap closes drops below the RMT prediction as $τ_E/τ_D$ is increased. Our quasiclassical results are supported by comparison with a fully quantum mechanical simulation of a stroboscopic model (the Andreev kicked rotator).

cond-mat.mes-hall↗
arXiv2005

Microscopic Theory for the Quantum to Classical Crossover in Chaotic Transport

We present a semiclassical theory for the scattering matrix ${\cal S}$ of a chaotic ballistic cavity at finite Ehrenfest time. Using a phase-space representation coupled with a multi-bounce expansion, we show how the Liouville conservation of phase-space volume decomposes ${\cal S}$ as ${\cal S}={\cal S}^{\rm cl} \oplus {\cal S}^{\rm qm}$. The short-time, classical contribution ${\cal S}^{\rm cl}$ generates deterministic transmission eigenvalues T=0 or 1, while quantum ergodicity is recovered within the subspace corresponding to the long-time, stochastic contribution ${\cal S}^{\rm qm}$. 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.

cond-mat.mes-hall↗
arXiv2004

Breakdown of Universality in Quantum Chaotic Transport: the Two-Phase Dynamical Fluid Model

We investigate the transport properties of open quantum chaotic systems in the semiclassical limit. We show how the transmission spectrum, the conductance fluctuations, and their correlations are influenced by the underlying chaotic classical dynamics, and result from the separation of the quantum phase space into a stochastic and a deterministic phase. Consequently, sample-to-sample conductance fluctuations lose their universality, while the persistence of a finite stochastic phase protects the universality of conductance fluctuations under variation of a quantum parameter.

cond-mat.mes-hall↗
arXiv2004

Quasiclassical fluctuations of the superconductor proximity gap in a chaotic system

We calculate the sample-to-sample fluctuations in the excitation gap of a chaotic dynamical system coupled by a narrow lead to a superconductor. Quantum fluctuations on the order of magnitude of the level spacing, predicted by random-matrix theory, apply if $τ_E\ll\hbar/E_T$ (with $τ_E$ the Ehrenfest time and $E_T$ the Thouless energy). For $τ_E\agt\hbar/ E_T$ the fluctuations are much greater than the level spacing. We demonstrate the quasiclassical nature of the gap fluctuations in the large-$τ_E$ regime by correlating them to an integral over the classical dwell-time distribution.

cond-mat.mes-hall↗
arXiv2003

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 large Lyapunov exponent and the logarithmic reduction of the gap when the Ehrenfest time becomes comparable to the quasiparticle dwell time.

cond-mat.mes-hall↗
arXiv2002

Anomalous power law of quantum reversibility for classically regular dynamics

The Loschmidt Echo M(t) (defined as the squared overlap of wave packets evolving with two slightly different Hamiltonians) is a measure of quantum reversibility. We investigate its behavior for classically quasi-integrable systems. A dominant regime emerges where M(t) ~ t^{-alpha} with alpha=3d/2 depending solely on the dimension d of the system. This power law decay is faster than the result ~ t^{-d} for the decay of classical phase space densities.

quant-ph↗
arXiv2002

Decay of the Loschmidt Echo for quantum states with sub-Planck scale structures

Quantum states extended over a large volume in phase space have oscillations from quantum interferences in their Wigner distribution on scales smaller than $\hbar$ [W.H. Zurek, Nature {\bf 412}, 712 (2001)]. We investigate the influence of those sub-Planck scale structures on the sensitivity to an external perturbation of the state's time evolution. While we do find an accelerated decay of the Loschmidt Echo for an extended state in comparison to a localized wavepacket, the acceleration is described entirely by the classical Lyapunov exponent and hence cannot originate from quantum interference.

nlin.CD↗
arXiv2002

Ground State Properties of Many-Body Systems in the Two-Body Random Ensemble and Random Matrix Theory

We explore generic ground-state and low-energy statistical properties of many-body bosonic and fermionic one- and two-body random ensembles (TBRE) in the dense limit, and contrast them with Random Matrix Theory (RMT). Weak differences in distribution tails can be attributed to the regularity or chaoticity of the corresponding Hamiltonians rather than the particle statistics. We finally show the universality of the distribution of the angular momentum gap between the lowest energy levels in consecutive J-sectors for the four models considered.

nucl-th↗
arXiv2001

Golden rule decay versus Lyapunov decay of the quantum Loschmidt echo

The overlap of two wave functions evolving in time with slightly different Hamiltonians decays exponentially, for perturbation strengths greater than the level spacing. We present numerical evidence for a dynamical system that the decay rate is given by the smallest of the Lyapunov exponent of the classical chaotic dynamics and the level broadening that follows from the golden rule of quantum mechanics. This limits the range of validity for the perturbation-strength independent decay rate discovered by Jalabert and Pastawski [Phys. Rev. Lett. 86, 2490 (2001)].

nlin.CD↗
arXiv2001

Can mesoscopic fluctuations reverse the supercurrent through a disordered Josephson junction?

We calculate the Josephson coupling energy $U_J(ϕ)$ (related to the supercurrent $I=(2e/\hbar) dU_J/dϕ$) for a disordered normal metal between two superconductors with a phase difference $ϕ$. We demonstrate that the symmetry of the scattering matrix of non-interacting quasiparticles in zero magnetic field implies that $U_J(ϕ)$ has a minimum at $ϕ=0$. A maximum (that would lead to a $π$-junction or negative superfluid density) is excluded for any realization of the disorder.

cond-mat.mes-hall↗
arXiv2000

Random matrix model for quantum dots with interactions and the conductance peak spacing distribution

We introduce a random interaction matrix model (RIMM) for finite-size strongly interacting fermionic systems whose single-particle dynamics is chaotic. The model is applied to Coulomb blockade quantum dots with irregular shape to describe the crossover of the peak spacing distribution from a Wigner-Dyson to a Gaussian-like distribution. The crossover is universal within the random matrix model and is shown to depend on a single parameter: a scaled fluctuation width of the interaction matrix elements. The crossover observed in the RIMM is compared with the results of an Anderson model with Coulomb interactions.

cond-mat.mes-hall↗
arXiv1997

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.

cond-mat↗
arXiv1996

Two interacting quasiparticles above the Fermi sea

We study numerically the interaction and disorder effects for two quasiparticles in two and three dimensions. The dependence of the interaction-induced Breit-Wigner width on the excitation energy above the Fermi level, the disorder strength and the system size is determined. A regime is found where the width is practically independent of the excitation energy. The results allow to estimate the two quasiparticle mobility edge.

cond-mat↗
arXiv1996

On the Convergence to Ergodic Behaviour of Quantum Wave Functions

We study the decrease of fluctuations of diagonal matrix elements of observables and of Husimi densities of quantum mechanical wave functions around their mean value upon approaching the semi-classical regime ($\hbar \rightarrow 0$). The model studied is a spin (SU(2)) one in a classically strongly chaotic regime. We show that the fluctuations are Gaussian distributed, with a width $σ^2$ decreasing as the square root of Planck's constant. This is consistent with Random Matrix Theory (RMT) predictions, and previous studies on these fluctuations. We further study the width of the probability distribution of $\hbar$-dependent fluctuations and compare it to the Gaussian Orthogonal Ensemble (GOE) of RMT.

chao-dyn↗
arXiv1995

Hidden Breit-Wigner distribution and other properties of random matrices with preferential basis

We study statistical properties of a class of band random matrices which naturally appears in systems of interacting particles. The local spectral density is shown to follow the Breit-Wigner distribution in both localized and delocalized regimes with width independent on the band/system size. We analyse the implications of this distribution to the inverse participation ratio, level spacing statistics and the problem of two interacting particles in a random potential.

cond-mat↗