81 research outputs found
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 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 , we establish a duality transformation mapping the behavior at weak onto the behavior at strong . For intermediate , the mixing of the one body states and the interaction induced delocalization effect are maximum. Furthermore, if (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 necessary to propagate over , de-favors the propagation. On the contrary, favors a very slow delocalization after , characterized by a 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 for . 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 . ----- 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 beaucoup plus grande que la longueur de localisation d'une particule sans interaction. L'effet de délocalisation maximale se manifeste pour une valeur de l'interaction intermédiaire entre les deux limites et 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 et et empêche la transition, engendrée par l'interaction, à un régime complètement chaotique. En changeant 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 est plus petite que la taille du système et au contraire est défavorable quand . 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 (isolant d'Anderson) et (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 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 the Lyapunov
exponent and a typical classical action.Comment: 4 page
Electronic transport through ballistic chaotic cavities: reflection symmetry, direct processes, and symmetry breaking
We extend previous studies on transport through ballistic chaotic cavities
with spatial left-right (LR) reflection symmetry to include the presence of
direct processes. We first analyze fully LR-symmetric systems in the presence
of direct processes and compare the distribution w(T) of the transmission
coefficient T with that for an asymmetric cavity with the same "optical" S
matrix. We then study the problem of "external mixing" of the symmetry caused
by an asymmetric coupling of the cavity to the outside. We first consider the
case where symmetry breaking arises because two symmetrically positioned
waveguides are coupled to the cavity by means of asymmetric tunnel barriers.
Although this system is asymmetric with respect to the LR operation, it has a
striking memory of the symmetry of the cavity it was constructed from.
Secondly, we break LR symmetry in the absence of direct proceses by
asymmetrically positioning the two waveguides and compare the results with
those for the completely asymmetric case.Comment: 15 pages, 8 Postscript figures, submitted to Phys. Rev.
Statistics of Wave Functions in Coupled Chaotic Systems
Using the supersymmetry technique, we calculate the joint distribution of
local densities of electron wavefunctions in two coupled disordered or chaotic
quantum billiards. We find novel spatial correlations that are absent in a
single chaotic system. Our exact result can be interpreted for small coupling
in terms of the hybridization of eigenstates of the isolated billiards. We show
that the presented picture is universal, independent of microscopic details of
the coupling.Comment: 4 pages, 2 figures; acknowledgements and references adde
- …