Bulletin of the American Physical Society
2007 APS March Meeting
Volume 52, Number 1
Monday–Friday, March 5–9, 2007; Denver, Colorado
Session U3: Quantum Chaos in Condensed Matter Physics |
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Sponsoring Units: DCMP Chair: Wentao Lu, Northeastern University Room: Colorado Convention Center Korbel 2A-3A |
Thursday, March 8, 2007 8:00AM - 8:36AM |
U3.00001: Single-Channel Scattering from Disordered Samples: a sensitive probe of the eigenfunctions behavior Invited Speaker: Yan Fyodorov The goal of the talk is to demonstrate that that statistics of waves reflected from a disordered sample via a single open channel can serve as a sensitive probe of the eigenfunctions behaviour inside the sample in all regimes: localized, extended, and critical (multifractal). In particular, it allows one to understand the anomalous scaling exponents governing the multifractal behavior of the moments of the Wigner time delay at the point of the Anderson localization transition. The method also reveals some nontrivial exact symmetry relations which must be satisfied by the anomalous exponents and multifractality spectra. These predictions were recently verified in accurate numerical simulations. [Preview Abstract] |
Thursday, March 8, 2007 8:36AM - 9:12AM |
U3.00002: Scattering fidelity in random matrix elastodynamics, the effect of temperature on diffuse ultrasound Invited Speaker: Richard L. Weaver Temperature variations in a high Q elastic body provide access to a slowly and reversibly tuned wave chaotic random ultrasound ``Hamiltonian.'' This allows benchtop measurements of scattering fidelity in quantum chaotic, and other, systems. To a first approximation, temperature changes merely rescale time, as the wave speeds and specimen size change. But inasmuch as the shear and longitudinal wave speeds change by different amounts, the wave fields are distorted as well. The degree of distortion is a measure of how rapidly the shear and longitudinal waves mix. We show how that distortion varies with temperature, with the age of a transient waveform, with frequency, and with specimen size and geometry. Measured scattering fidelities are found to be in accord with predictions from random matrix theory for both irregular and regular bodies, up to a scaling parameter that is related to the rate of mixing of the rays. That rate is very different depending on the regularity of the specimen. Fidelity is greater in ray-chaotic bodies than in regular bodies. [Preview Abstract] |
Thursday, March 8, 2007 9:12AM - 9:48AM |
U3.00003: Analog Experiments on Quantum Chaotic Scattering and Transport Invited Speaker: Steven Anlage The transport properties of mesoscopic and nanoscopic materials are dominated by quantum interference effects. Nevertheless it is challenging to delineate these effects through conventional transport experiments on real materials. Complications arise from finite temperatures (thermal smearing, inelastic scattering), and the excitation of two-level systems that can cause the electrons to ``decohere'' and drop out of the quantum-coherent transport process. We approach this problem from the perspective of nonlinear dynamics and utilize a unique experimental technique that directly simulates the quantum scattering properties of complicated (ray-chaotic) systems. A microwave cavity is used to simulate solutions to the time-independent Schr\"{o}dinger equation for a two-dimensional ray-chaotic infinite square-well potential. The classically chaotic ray trajectories within a suitably shaped microwave cavity play a role analogous to that of the chaotic dynamics of noninteracting electron transport through a ballistic quantum dot in the absence of thermal fluctuations. In wave chaotic scattering, statistical fluctuations of the scattering matrix $S$ and the impedance (`reaction') matrix $Z$ depend both on universal properties and on nonuniversal details of how the scatterer is coupled to external channels. We remove the non-universal effects of the coupling from the experimental $S $data using the radiation impedance obtained directly from the experiments, thus eliminating one of the most significant complications in conventional transport measurements. The Landauer-B\"{u}ttiker formalism is applied to obtain the conductance of a corresponding mesoscopic quantum-dot device. We find good agreement for the probability density functions of the experimentally derived surrogate conductance, as well as its mean and variance, with the theoretical predictions based on random matrix theory [1]. We also observe a linear relation between the quantum dephasing parameter and the cavity ohmic loss parameter. The results apply to scattering measurements on any wave chaotic system. We also discuss future directions for this work. \newline \underline {[1]} S. Hemmady, \textit{et al.},(http://dx.doi.org/10.1103/PhysRevB.74.195326) Phys. Rev. B 74, 195326 (2006). [Preview Abstract] |
Thursday, March 8, 2007 9:48AM - 10:24AM |
U3.00004: Quantum Networks as Models of Mesoscopic Systems Invited Speaker: Tsampikos Kottos We review our work on quantum networks. These are one-dimensional systems consisting of vertices connected by bonds that have incommensurate lengths L. Particles with a fixed wave-number k can propagate freely on the bonds and scatter at the vertices. Combining the free propagation and the vertex scattering we have ended up with a quantum ``evolution'' operator on the graph. The corresponding classical dynamics was defined as follows: we have constructed a Liouville description by considering the evolution of a phase-space density over the space of directed bonds. The classical evolution operator consists of transition probabilities between connected bonds taken from the corresponding quantum evolution operator. Due to the multiple connectivity (stretching) and the compactness of the system (folding), the classical dynamics is chaotic. This analogy enables us to study the connection between statistical properties of eigenvalues and eigenfunctions and the classical dynamics. Finally, connecting them with leads to infinity we have also shown that quantum networks are excellent paradigms for the study of mesoscopic transport. [Preview Abstract] |
Thursday, March 8, 2007 10:24AM - 11:00AM |
U3.00005: The classical limit of quantum transport Invited Speaker: Saar Rahav Weak localization and conductance fluctuations are manifestations of quantum interference on transport. These quantum effects take a finite time, the Ehrenfest time, to appear. We present a semiclassical calculation of the Ehrenfest time dependence of weak localization and conductance fluctuations for ballistic quantum dots. Weak localization is found to be suppressed when the Ehrenfest time is larger than the typical dwell time in the dot. In contrast, the conductance fluctuations are found to be Ehrenfest time independent. The calculated Ehrenfest time dependences are consistent with numerical results. [Preview Abstract] |
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