Exponential Sensitivity to Dephasing of Electrical Conduction Through a Quantum Dot

Tworzydło, J.; Tajic, A.; Schomerus, Henning; Brouwer, Piet W.; Beenakker, C. W. J.

doi:10.1103/physrevlett.93.186806

Cited by 16 publications

(27 citation statements)

References 24 publications

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“…For an open version of the quantum kicked rotator map, numerical simulations were reported for shot noise, 8,9,10 weak localization, 11,21 and universal conductance fluctuations. 9,18,22 Simulation results for shot noise were in good agreement with the predictions of the semiclassical theory. 6 However, for conductance fluctuations, no dependence on τ E was found, despite the fact that Ehrenfest times larger than the dwell time were considered.…”

supporting

confidence: 74%

“…However, semiclassical theories for weak localization and universal conductance fluctuations for the limit τ D ≫ τ E are essentially equal, 14,15,16,17 as are diagrammatic perturbation theories for the same phenomena in diffusive cavities, supporting the expectation that the Ehrenfest-time dependencies of weak localization and universal conductance fluctuations will be equal as well. 18 Direct numerical simulation of the effect of a large Ehrenfest time on quantum transport through twodimensional chaotic cavities has been problematic because of the prohibitively high computational cost of the simulations. The reason is that τ E depends only logarithmically on the product of the electron wavenumber k and the cavity size L, τ E = λ −1 ln kL.…”

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confidence: 99%

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Classical limit of transport in quantum kicked maps

Rahav

Brouwer

2006

Phys. Rev. B

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We investigate the behavior of weak localization, conductance fluctuations, and shot noise of a chaotic scatterer in the semiclassical limit. Time resolved numerical results, obtained by truncating the time-evolution of a kicked quantum map after a certain number of iterations, are compared to semiclassical theory. Considering how the appearance of quantum effects is delayed as a function of the Ehrenfest time gives a new method to compare theory and numerical simulations. We find that both weak localization and shot noise agree with semiclassical theory, which predicts exponential suppression with increasing Ehrenfest time. However, conductance fluctuations exhibit different behavior, with only a slight dependence on the Ehrenfest time.

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confidence: 74%

mentioning

confidence: 99%

Classical limit of transport in quantum kicked maps

Rahav

Brouwer

2006

Phys. Rev. B

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“…5, has received much theoretical support in the context of transport. 18,27,[30][31][32][33][34] The present work shows that it can be successfully used to describe the consequences of time-reversal-symmetry breaking on the superconducting proximity effect.…”

Section: Discussionmentioning

confidence: 99%

Quantum-to-classical crossover for Andreev billiards in a magnetic field

2005

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We extend the existing quasiclassical theory for the superconducting proximity effect in a chaotic quantum dot, to include a time-reversal-symmetry breaking magnetic field. Random-matrix theory ͑RMT͒ breaks down once the Ehrenfest time E becomes longer than the mean time D between Andreev reflections. As a consequence, the critical field at which the excitation gap closes drops below the RMT prediction as E / D is increased. Our quasiclassical results are supported by comparison with a fully quantum mechanical simulation of a stroboscopic model ͑the Andreev kicked rotator͒.

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“…(7), with τ φ,ball replaced by τ φ , for a quantum dot in which dephasing arises from a voltage probe ballistically coupled to the dot [22]. Tworzydlo et al, who considered a tunnel-coupled voltage probe, reported δG ∝ exp(−τ E /τ φ ) based on an 'effective random matrix theory' which neglects the second passage through the Lyapunov region [23]. The correct result for dephasing from a tunnel-coupled voltage probe is δG ∝ exp(−2τ E /τ φ ) [16,22].…”

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confidence: 99%

Interplay of Ehrenfest and Dephasing Times in Ballistic Conductors

Altland¹,

Brouwer²,

Tian³

2007

Phys. Rev. Lett.

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Quantum interference corrections in ballistic conductors require a minimal time: the Ehrenfest time. In this letter, we investigate the fate of the interference corrections to quantum transport in bulk ballistic conductors if the Ehrenfest time and the dephasing time are comparable.PACS numbers: 05.45.Mt, 73.20.Fz Introduction. In recent years, the Ehrenfest time τ E has been recognized as a time scale of profound relevance to the physics of systems interfacial between the mesoscopic and the nanoscopic regime [1]. Loosely speaking, τ E is the time it takes before a minimal wave packet propagating in a chaotic background looses its integrity and spreads over scales of classical proportions [2, 3]. Therefore (i) the Ehrenfest time defines a time threshold before the wave nature of electrons begins to modify the classical behavior of observable system properties. Accordingly, (ii) there is a general expectation that quantum effects are multiplied by exponential weighting factors exp(−ατ E /t 0 ), where t 0 is the (smallest) characteristic time scale of the quantum effect. This expectation has been confirmed for the Ehrenfest-time related suppression of weak localization [1,4,5,6] and shot noise [7,8] in chaotic quantum dots, with t 0 taken to be the dot's mean dwell time τ D , or Ehrenfest-oscillations of the weak localization corrections to the ac conductivity of a random collection of antidots [1] and time-dependent diffusion in periodically kicked atomic gases [9], with t 0 = iω −1 taken to be the inverse angular frequency .In this letter, we consider the competition between the Ehrenfest time and the dephasing time τ φ . Whereas τ E is the minimal time needed for quantum interference, τ φ sets the long-time cut-off for interference processes. The competition between τ E and τ φ is particularly relevant for quantum corrections in bulk conductors, for which the dwell time τ D has no significance. In particular, we'll address the question whether one may expect a suppression of quantum corrections proportional to exp(−ατ E /τ φ ), according to the general expectation (ii) mentioned above. In a subtle manner, the answer depends on whether the dephasing originates from electronelectron interactions or from an external source (such as applied microwave radiation). Conceptually, the observation of an Ehrenfest-time dependence of quantum interference corrections to the conductance has exponential sensitivity to the microscopic mechanism of dephasing.To date, there are only a few experimental signatures of the Ehrenfest time. Oberholzer et al. found a τ Erelated suppression of the shot noise of a chaotic cavity upon decreasing τ D [10]. Shot noise, however, is insensitive to the presence of dephasing. Yevtushenko et al.

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Exponential Sensitivity to Dephasing of Electrical Conduction Through a Quantum Dot

Cited by 16 publications

References 24 publications

Classical limit of transport in quantum kicked maps

Classical limit of transport in quantum kicked maps

Quantum-to-classical crossover for Andreev billiards in a magnetic field

Interplay of Ehrenfest and Dephasing Times in Ballistic Conductors

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