Quantum disorder and quantum chaos in Andreev billiards

Vavilov, Maxim; Larkin, A. I.

doi:10.1103/physrevb.67.115335

Cited by 54 publications

(98 citation statements)

References 47 publications

(138 reference statements)

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“…[47] is based on the quasiclassical theory [27] which models mode-mixing by residual diffraction, and equates the Ehrenfest time with the closed-system Ehrenfest time τ E . The discussion of the formation of the deterministic transport channels suggests that this has to be replaced by the transport Ehrenfest time τ (2) E [33]. Subsequent numerical investigations have tested this prediction for the open kicked rotator [30].…”

Section: Suppression Of Shot Noisementioning

confidence: 99%

“…The same Ehrenfest time also affects the excitation spectrum of normal-metallic cavities which are coupled by the openings to an s-wave superconductor, for which the relevant physical process is the consecutive Andreev reflection of the two quasi-particle species at the superconducting terminal (τ (2) E was actually first derived in that context [33]). In the escape problem, the electron is no longer required to originate from an opening.…”

Section: Classification Of Ehrenfest Timesmentioning

confidence: 99%

“…In the same way, the final extent of the wave packet has to be compared to W or L depending on whether the physical process requires the particle to leave the system or not. For sufficiently ergodic chaotic dynamics (λ −1 , τ B ≪ τ D , which implies W ≪ L) and in the absence of sharp geometrical features (besides the presence of the openings), the resulting Ehrenfest time can be expressed by the three classical time scales and the Heisenberg time τ H [28,33,34]:…”

Section: Classification Of Ehrenfest Timesmentioning

confidence: 99%

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Quantum-to-classical correspondence in open chaotic systems

Schomerus¹,

Jacquod²

2005

J. Phys. A: Math. Gen.

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Abstract. We review properties of open chaotic mesoscopic systems with a finite Ehrenfest time τ E . The Ehrenfest time separates a short-time regime of the quantum dynamics, where wave packets closely follow the deterministic classical motion, from a long-time regime of fully-developed wave chaos. For a vanishing Ehrenfest time the quantum systems display a degree of universality which is well described by randommatrix theory. In the semiclassical limit, τ E becomes parametrically larger than the scattering time off the boundaries and the dwell time in the system. This results in the emergence of an increasing number of deterministic transport and escape modes, which induce strong deviations from random-matrix universality. We discuss these deviations for a variety of physical phenomena, including shot noise, conductance fluctuations, decay of quasibound states, and the mesoscopic proximity effect in Andreev billiards.

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Section: Suppression Of Shot Noisementioning

confidence: 99%

Section: Classification Of Ehrenfest Timesmentioning

confidence: 99%

Section: Classification Of Ehrenfest Timesmentioning

confidence: 99%

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Quantum-to-classical correspondence in open chaotic systems

Schomerus¹,

Jacquod²

2005

J. Phys. A: Math. Gen.

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“…The kicking strength K = 7.5 determines the Lyapunov exponent λ = ln(K/2) = 1.32. The Ehrenfest time is given by [16,17] …”

mentioning

confidence: 99%

Exponential Sensitivity to Dephasing of Electrical Conduction Through a Quantum Dot

et al. 2004

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According to random-matrix theory, interference effects in the conductance of a ballistic chaotic quantum dot should vanish ∝ (τ φ /τD) p when the dephasing time τ φ becomes small compared to the mean dwell time τD. Aleiner and Larkin have predicted that the power law crosses over to an exponential suppression ∝ exp(−τE/τ φ ) when τ φ drops below the Ehrenfest time τE. We report the first observation of this crossover in a computer simulation of universal conductance fluctuations. Their theory also predicts an exponential suppression ∝ exp(−τE/τD) in the absence of dephasing -which is not observed. We show that the effective random-matrix theory proposed previously for quantum dots without dephasing explains both observations. PACS numbers: 73.63.Kv, 03.65.Yz, 05.45.Mt An instructive way to classify quantum interference effects in mesoscopic conductors is to ask whether they depend exponentially or algebraically on the dephasing time τ φ . The Aharonov-Bohm effect is of the former class, while weak localization (WL) and universal conductance fluctuations (UCF) are of the latter class [1,2]. It is easy enough to understand the difference: On the one hand, Aharonov-Bohm oscillations in the magnetoconductance of a ring require phase coherence for a certain minimal time t min (the time it takes to circulate once along the ring), which becomes exponentially improbable if τ φ < t min . On the other hand, WL and UCF in a disordered quantum dot originate from multiple scattering on a broad range of time scales, not limited from below, and the superposition of exponents with a range of decay rates amounts to a power law decay.In a seminal paper [3], Aleiner and Larkin have argued that ballistic chaotic quantum dots are in a class of their own. In these systems the Ehrenfest time τ E introduces a lower limiting time scale for the interference effects, which are exponentially suppressed if τ φ < τ E . The physical picture is that electron wave packets in a chaotic system can be described by a single classical trajectory for a time up to τ E [4]. Both WL and UCF, however, require that a wave packet splits into partial waves which follow different trajectories before interfering. Only the fraction exp(−τ E /τ φ ) of electrons which have not yet dephased at time τ E can therefore contribute to WL and UCF.The WL correction ∆G = G − G cl is the deviation of the ensemble averaged conductance G (in zero magnetic field) from the classical value G cl = N/2. (We measure conductances in units of 2e 2 /h and assume an equal number of modes N ≫ 1 in the two leads that connect the quantum dot to electron reservoirs.) The WL correction according to random-matrix theory (RMT),has a power law suppression ∝ τ φ /τ D when τ φ becomes smaller than the mean dwell time τ D in the quantum dot [5]. Similarly, RMT predicts for the UCF a power law suppression ∝ (τ φ /τ D ) 2 of the mean-squared sample-tosample conductance fluctuations [5,6],with β = 2 (1) in the presence (absence) of a timereversal-symmetry-breaking magnetic field. Aleiner and ...

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“…23 However, some difficulties have emerged: for example, the excitation gap in the DOS for billiards with a chaotic N cavity cannot be properly accounted for. 24,25,26 A direct inspection of the electron-and hole-components of the wave functions 23,27 revealed markedly different patterns, clearly signaling a breakdown of the retracing approximation.…”

Section: Introductionmentioning

confidence: 99%

Non-retracing orbits in Andreev billiards

2006

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The validity of the retracing approximation in the semiclassical quantization of Andreev billiards is investigated. The exact energy spectrum and the eigenstates of normal-conducting, ballistic quantum dots in contact with a superconductor are calculated by solving the Bogoliubov-de Gennes equation and compared with the semiclassical Bohr-Sommerfeld quantization for periodic orbits which result from Andreev reflections. We find deviations that are due to the assumption of exact retracing electron-hole orbits rather than the semiclassical approximation, as a concurrently performed Einstein-Brillouin-Keller quantization demonstrates. We identify three different mechanisms producing non-retracing orbits which are directly identified through differences between electron and hole wave functions.

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Quantum disorder and quantum chaos in Andreev billiards

Cited by 54 publications

References 47 publications

Quantum-to-classical correspondence in open chaotic systems

Quantum-to-classical correspondence in open chaotic systems

Exponential Sensitivity to Dephasing of Electrical Conduction Through a Quantum Dot

Non-retracing orbits in Andreev billiards

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