Three signatures of phase-coherent Andreev reflection

Wetensch. publicatieFaculteit der Wiskunde en Natuurwetenschappe

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

Coin Tossing as a Billiard Problem

We demonstrate that the free motion of any two-dimensional rigid body colliding elastically with two parallel, flat walls is equivalent to a billiard system. Using this equivalence, we analyze the integrable and chaotic properties of this new class of billiards. This provides a demonstration that coin tossing, the prototypical example of an independent random process, is a completely chaotic (Bernoulli) problem. The related question of which billiard geometries can be represented as rigid body systems is examined.Comment: 16 pages, LaTe

The embedding method beyond the single-channel case: Two-mode and Hubbard chains

We investigate the relationship between persistent currents in multi-channel rings containing an embedded scatterer and the conductance through the same scatterer attached to leads. The case of two uncoupled channels corresponds to a Hubbard chain, for which the one-dimensional embedding method is readily generalized. Various tests are carried out to validate this new procedure, and the conductance of short one-dimensional Hubbard chains attached to perfect leads is computed for different system sizes and interaction strengths. In the case of two coupled channels the conductance can be obtained from a statistical analysis of the persistent current or by reducing the multi-channel scattering problem to several single-channel setups.Comment: 14 pages, 13 figures, submitted for publicatio

Interplay disorder-interaction in one dimensional quantum models

URL: http://www-spht.cea.fr/articles/S98/116 Compétition entre le désordre et les interactions dans des modèles quantiques unidimensionnels 210th WE-Heraeus Seminar (PILS'98), Berlin, Germany, October 6-9, 1998We show that the crossover from the weak interaction limit towards the strong interaction limit may be accompanied by a delocalization effect in one dimensional disordered quantum models. The spin degrees of freedom are frozen and the spatial wave functions remain symmetric or antisymmetric when the strength $U$ of a short range interaction is varied. The study concerns the excited states for two interacting particles and the ground state for a finite density of carriers. First, for two particles in a chain of length $L$, we establish a duality transformation mapping the behavior at weak $U$ onto the behavior at strong $U$. For intermediate $U$, the mixing of the one body states and the interaction induced delocalization effect are maximum. Furthermore, if $L \approx L_1$ (the one particle localization length), the system becomes weakly chaotic with critical spectral statistics. This weak chaos is related to the multifractality of the interaction matrix. For two particles starting close to each other, localization is reached in two steps. Before the time $t_1$ necessary to propagate over $L_1$, $U$ de-favors the propagation. On the contrary, $U$ favors a very slow delocalization after $t_1$, characterized by a $\log(t)$ spreading of the center of mass. Similarly, the curvatures of the energy levels with respect to an enclosed magnetic flux decrease as a function of $U$ for $LL_1$. The changes of the curvatures can be described by a conductance-like single scaling parameter. Second, using the density renormalization group algorithm, we have studied the ground state energy of a finite density of spinless fermions and its change under twisted boundary conditions. For a large disorder, a charge reorganization is induced by the interaction: When the system becomes instable between the inhomogeneous configuration driven by the random potential (Anderson insulator) and the homogeneous one driven by repulsive interactions (Mott insulator), the ground state sensitivity can be enhanced by orders of magnitude. In contrast, no enhancement occurs at weaker disorder, when there are many particles on a scale $L_1$. ----- Cet article est une revue des résultats obtenus récemment par les auteurs sur le rôle joué par l'interaction dans des systèmes unidimensionnels désordonnés. La première partie de l'article traite le problème de deux particules en interaction dans un potentiel aléatoire. On montre que les deux particules peuvent se propager de façon cohérente sur une distance $L_2$ beaucoup plus grande que la longueur de localisation $L_1$ d'une particule sans interaction. L'effet de délocalisation maximale se manifeste pour une valeur de l'interaction $U$ intermédiaire entre les deux limites $U=0$ et $U\to\infty$ et une transformation de dualité permet de passer d'une limite à l'autre. La structure multifractale des termes d'interaction de l'hamiltonien dans la base des états sans interaction influence la relation entre $L_2$ et $L_1$ et empêche la transition, engendrée par l'interaction, à un régime complètement chaotique. En changeant $U$ on parvient à un régime de ``chaos faible'', caractérisé par une statistique spectrale critique intermédiaire entre la statistique de Poisson (systèmes intégrables) et de Wigner (systèmes ergodiques). On montre que l'interaction est favorable au transport quand la longueur de localisation $L_1$ est plus petite que la taille $L$ du système et au contraire est défavorable quand $L_1>L$. Ceci est montré dans l'étude de la dynamique d'une paire de particules et de la courbure des niveaux énergétiques pour une boucle traversée par un flux d'Aharonov--Bohm. La deuxième partie de l'article étudie les propriétés de l'état fondamental d'un système de fermions sans spin. Des effets importants de délocalisation se manifestent quand le système devient instable entre les configurations limites $U=0$ (isolant d'Anderson) et $U\to\infty$ (isolant de Mott). La réorganisation des charges d'une limite à l'autre s'accompagne d'une grande sensibilité de l'énergie de l'état fondamental quand les conditions de bord de périodiques deviennent antipériodiques. L'article montre que l'effet de délocalisation semble persister à la limite thermodynamique. \hfill{G. Benenti

Recurrence of fidelity in near integrable systems

Within the framework of simple perturbation theory, recurrence time of quantum fidelity is related to the period of the classical motion. This indicates the possibility of recurrence in near integrable systems. We have studied such possibility in detail with the kicked rotor as an example. In accordance with the correspondence principle, recurrence is observed when the underlying classical dynamics is well approximated by the harmonic oscillator. Quantum revivals of fidelity is noted in the interior of resonances, while classical-quantum correspondence of fidelity is seen to be very short for states initially in the rotational KAM region.Comment: 13 pages, 6 figure

Signatures of Inelastic Scattering in Coulomb-Blockade Quantum Dots

We calculate the finite-temperature conductance peak-height distributions in Coublomb-blockade quantum dots in the limit where the inelastic scattering rate in the dot is large compared with the mean elastic tunneling rate. The relative reduction of the standard deviation of the peak-height distribution by a time-reversal symmetry-breaking magnetic field, which is essentially temperature-independent in the elastic limit, is enhanced by the inclusion of inelastic scattering at finite temperature. We suggest this quantity as an independent experimental probe for inelastic scattering in closed dots.Comment: 4 pages, 3 eps figures, revtex

Weak-Localization in Chaotic Versus Non-Chaotic Cavities: A Striking Difference in the Line Shape

We report experimental evidence that chaotic and non-chaotic scattering through ballistic cavities display distinct signatures in quantum transport. In the case of non-chaotic cavities, we observe a linear decrease in the average resistance with magnetic field which contrasts markedly with a Lorentzian behavior for a chaotic cavity. This difference in line-shape of the weak-localization peak is related to the differing distribution of areas enclosed by electron trajectories. In addition, periodic oscillations are observed which are probably associated with the Aharonov-Bohm effect through a periodic orbit within the cavities.Comment: 4 pages revtex + 4 figures on request; amc.hub.94.

Orbital effect of in-plane magnetic field on quantum transport in chaotic lateral dots

We show how the in-plane magnetic field, which breaks time-reversal and rotational symmetries of the orbital motion of electrons in a heterostructure due to the momentum-dependent inter-subband mixing, affects weak localisation correction to conductance of a large-area chaotic lateral quantum dot and parameteric dependences of universal conductance fluctuations in it.Comment: 4 pages with a figur

Ehrenfest times for classically chaotic systems

We describe the quantum mechanical spreading of a Gaussian wave packet by means of the semiclassical WKB approximation of Berry and Balazs. We find that the time scale $\tau$ on which this approximation breaks down in a chaotic system is larger than the Ehrenfest times considered previously. In one dimension \tau=\fr{7}{6}\lambda^{-1}\ln(A/\hbar), with $\lambda$ the Lyapunov exponent and $A$ a typical classical action.Comment: 4 page