Divergence of classical trajectories and weak localization

Aleǐner, I. L.; Larkin, A. I.

doi:10.1103/physrevb.54.14423

Cited by 214 publications

(436 citation statements)

References 29 publications

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“…In contrast to the non-interacting problem, the currents to the left and right are now completely correlated. Equations (137) and (138) can be used to eliminate the voltage fluctuations. The result is conveniently expressed in the frequency representation,…”

Section: Noise Of a Capacitormentioning

confidence: 99%

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Shot noise in mesoscopic conductors

2000

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Theoretical and experimental work concerned with dynamic fluctuations has developed into a very active and fascinating subfield of mesoscopic physics. We present a review of this development focusing on shot noise in small electric conductors. Shot noise is a consequence of the quantization of charge. It can be used to obtain information on a system which is not available through conductance measurements. In particular, shot noise experiments can determine the charge and statistics of the quasiparticles relevant for transport, and reveal information on the potential profile and internal energy scales of mesoscopic systems. Shot noise is generally more sensitive to the effects of electron-electron interactions than the average conductance. We present a discussion based on the conceptually transparent scattering approach and on the classical Langevin and BoltzmannLangevin methods; in addition a discussion of results which cannot be obtained by these methods is provided. We conclude the review by pointing out a number of unsolved problems and an outlook on the likely future development of the field.

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Section: Noise Of a Capacitormentioning

confidence: 99%

“…These developments are described in Section VI. 34 Exceptions are frequency dependent weak localization corrections [137] which depend in addition to the RC-time also on the dwell time [138], and perfect ballistic wires which have a charge neutral mode determined by the transit time as the lowest collective mode [139].…”

Section: Scattering Theory Of Frequencymentioning

confidence: 99%

Shot noise in mesoscopic conductors

2000

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“…. imp ) of a product of a retarded and advanced Green's functions, Following the standard route of the quasiclassical formalism 35,36,37 , we perform the Wigner transformation, 6) where R 1 = (r 4 + r 1 )/2, R 2 = (r 2 + r 3 )/2, r = r 4 − r 1 , and r ′ = r 2 − r 3 . Note that the factors depending on the vector potential make the ballistic diffuson (2.6) gaugeinvariant.…”

Section: General Formalism a Smooth Disordermentioning

confidence: 99%

Interaction-induced magnetoresistance in a two-dimensional electron gas

2004

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We study the interaction-induced quantum correction δσ αβ to the conductivity tensor of electrons in two dimensions for arbitrary T τ (where T is the temperature and τ the transport scattering time), magnetic field, and type of disorder. A general theory is developed, allowing us to express δσ αβ in terms of classical propagators ("ballistic diffusons"). The formalism is used to calculate the interaction contribution to the longitudinal and the Hall resistivities in a transverse magnetic field in the whole range of temperature from the diffusive (T τ ≪ 1) to the ballistic (T τ 1) regime, both in smooth disorder and in the presence of short-range scatterers. Further, we apply the formalism to anisotropic systems and demonstrate that the interaction induces novel quantum oscillations in the resistivity of lateral superlattices.

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“…This counter-intuitive feature, usually referred to as dynamical localization [7], was fully understood [8] after mapping the kicked rotor problem onto a short range one-dimensional disordered system where localization is well established. Deviations from the BGS conjecture are also expected [9] for eigenvalue separations δE ∼ /t E due to weak localization effects. The typical scale t E = λ −1 | log | is the Ehrenfest time with λ the classical Lyapunov exponent.…”

Section: Introductionmentioning

confidence: 84%

Anderson Localization in Quantum Chaos: Scaling and Universality

García-García

Wang

2007

Acta Phys. Pol. A

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The one-parameter scaling theory is a powerful tool to investigate Anderson localization effects in disordered systems. In this paper we show that this theory can be adapted to the context of quantum chaos provided that the classical phase space is homogeneous, not mixed. The localization problem in this case is defined in momentum, not in real space. We then employ the one-parameter scaling theory to: (a) propose a precise characterization of the type of classical dynamics related to the Wigner-Dyson and Poisson statistics which also predicts in which situations Anderson localization corrections invalidate the relation between classical chaos and random matrix theory encoded in the Bohigas-Giannoni-Schmit conjecture, (b) to identify the universality class associated with the metal-insulator transition in quantum chaos. In low dimensions it is characterized by classical superdiffusion, in higher dimensions it has in general a quantum origin as in the case of disordered systems. We illustrate these two cases by studying 1d kicked rotors with non-analytical potentials and a 3d kicked rotor with a smooth potential.

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Divergence of classical trajectories and weak localization

Cited by 214 publications

References 29 publications

Shot noise in mesoscopic conductors

Shot noise in mesoscopic conductors

Interaction-induced magnetoresistance in a two-dimensional electron gas

Anderson Localization in Quantum Chaos: Scaling and Universality

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