Disappearance of quantum chaos in coupled chaotic quantum dots (original) (raw)
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Signatures of chaos in the statistical distribution of conductance peaks in quantum dots
Physical Review B, 1997
Analytical expressions for the width and conductance peak distributions of irregularly shaped quantum dots in the Coulomb blockade regime are presented in the limits of conserved and broken time-reversal symmetry. The results are obtained using random matrix theory and are valid in general for any number of non-equivalent and correlated channels, assuming that the underlying classical dynamic of the electrons in the dot is chaotic or that the dot is weakly disordered. The results are expressed in terms of the channel correlation matrix which for chaotic systems is given in closed form for both point-like contacts and extended leads. We study the dependence of the distributions on the number of channels and their correlations. The theoretical distributions are in good agreement with those computed in a dynamical model of a chaotic billiard.
Parametric correlation of coulomb blockade conductance peaks in chaotic quantum dots
Physica Scripta, 1997
We investigate the autocorrelator of conductance peak heights for quantum dots in the Coulomb blockade regime. Analytical and numerical results based on Random Matrix Theory are presented and compared to exact numerical calculations based on a simple dynamical model. We consider the case of preserved time-reversal symmetry, which is realized experimentally by varying the shape of the quantum dot in the absence of magnetic fields. Upon a proper rescaling, the correlator becomes independent of the details of the system and its form is solely determined by symmetry properties and the number of channels in the leads. The magnitude of the scaling parameter is estimated by a semiclassical approach.
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We investigate the conductance statistics of a quantum-chaotic dot-a normal-metal grain-with a superconducting lead attached to it. The cases of one and two normal leads additionally attached to the dot are studied. For these two configurations the complete distribution of the conductance is calculated, within the framework of random matrix theory, as a function of the transparency parameter of the Schottky barrier formed at the interface of the normal-metal and superconducting regions. Our predictions are verified by numerical simulations.
Periodic orbit effects on conductance peak heights in a chaotic quantum dot
Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 2000
We study the effects of short-time classical dynamics on the distribution of Coulomb blockade peak heights in a chaotic quantum dot. The location of one or both leads relative to the short unstable orbits, as well as relative to the symmetry lines, can have large effects on the moments and on the head and tail of the conductance distribution. We study these effects analytically as a function of the stability exponent of the orbits involved, and also numerically using the stadium billiard as a model. The predicted behavior is robust, depending only on the short-time behavior of the many-body quantum system, and consequently insensitive to moderate-sized perturbations and interactions.
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Chaos in Quantum Dots: Dynamical Modulation of Coulomb Blockade Peak Heights
Physical Review Letters, 1999
We develop a semiclassical theory of Coulomb blockade peak heights in quantum dots and show that the dynamics in the dot leads to a large modulation of the peak height. The corrections to the standard statistical theory of peak height distributions, power spectra, and correlation functions are nonuniversal and can be expressed in terms of the classical periodic orbits of the dot that are well coupled to the leads. The resulting correlation function oscillates as a function of the peak number in a way defined by such orbits. In addition, the correlation of adjacent conductance peaks is enhanced. Both of these effects are in agreement with recent experiments.
Semiclassical theory of Coulomb blockade peak heights in chaotic quantum dots
Physical Review B, 2001
We develop a semiclassical theory of Coulomb blockade peak heights in chaotic quantum dots. Using Berry's conjecture, we calculate peak height distributions and correlation functions. We demonstrate that corrections to the corresponding results of the standard statistical theory are nonuniversal, and can be expressed in terms of the classical periodic orbits of the dot that are well coupled to the leads. The main effect is an oscillatory dependence of the peak heights on any parameter which is varied; it is substantial for both symmetric and asymmetric lead placement. Surprisingly, these dynamical effects do not influence the full distribution of peak heights, but are clearly seen in the correlation function or power spectrum. For nonzero temperature, the correlation function obtained theoretically is consistent with that measured experimentally.
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We study numerically the production of orbital and spin entangled states in chaotic quantum dots for non-interacting electrons. The introduction of spin-orbit coupling permit us to identify signatures of time-reversal symmetry correlations in the entanglement production previously unnoticed, resembling weak-(anti)localization quantum corrections to the conductance. We find the entanglement to be strongly dependent on spin-orbit coupling, showing universal features for broken time-reversal and spin-rotation symmetries.
Advances in Mathematical Physics
We analyze the phenomenon of semiquantum chaos in two GaAs quantum dots coupled linearly and quadratically by two harmonic potentials. We show how semiquantum dynamics should be derived via the Ehrenfest theorem. The extended Ehrenfest theorem in two dimensions is used to study the system. The numerical simulations reveal that, by varying the interdot distance and coupling parameters, the system can exhibit either periodic or quasi-periodic behavior and chaotic behavior.