Floquet Formalism of Quantum Pumps

Kim, Sang Wook

doi:10.1142/s0217979204026317

Cited by 20 publications

(15 citation statements)

References 56 publications

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“…The theory of magnetic field symmetry of pumped currents is the subject of Refs. 23–26. The magnetic field symmetry of an adiabatic two‐parameter pump in the presence of a dc voltage is discussed by Moskalets and Büttiker 27.…”

Section: Introductionmentioning

confidence: 99%

Interaction‐induced magnetic field asymmetry of nonlinear mesoscopic electrical transport

Büttiker

Sánchez

2005

Int J of Quantum Chemistry

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We demonstrate that the nonlinear I-V characteristics of a two-probe conductor are not an even function of a magnetic field. While the conductance of a two-probe conductor is even in a magnetic field, we find that alreadythe contributions to the current that are second order in voltage, are in general not even. This implies a departure from the Onsager microreversibility principle in the weakly nonlinear regime. Interestingly, the effect that we find is due to the Coulomb interaction. A measurement of magnetic-field asymmetry can be used to determine the effective interaction strength. As a generic example, we discuss the I-V characteristics of a chaotic quantum dot. The ensemble averaged I-V of such a cavity is linear: nonlinearities are due to quantum interference. Consequently, phase-breaking reduces the asymmetry. We support this statement with a calculation that treats inelastic scattering with the help of a voltage probe

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Section: Introductionmentioning

confidence: 99%

Interaction‐induced magnetic field asymmetry of nonlinear mesoscopic electrical transport

Büttiker

Sánchez

2005

Int J of Quantum Chemistry

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“…However an important simplification comes from considering the structure of the time-dependent kernel A(k, k ′ ; t) in Eqs. (10,12). Indeed one can see that the first two terms in A(k, k ′ ; 0) always contain singularities at k = ±k ′ (the delta-like singularity and a simple pole) so that the main contribution of these terms in the r.h.s.…”

Section: The Asymptotic Berry Phasementioning

confidence: 99%

“…Of particular importance to the problem of the non-stationary quantum transport are the so-called scattering states χ k 0 [10,28]. These are defined as the solutions of time dependent equation (1) that at t = 0 coincide with the static eigenfunctions ψ k 0 (x).…”

Section: Problem Statement and The Modelmentioning

confidence: 99%

Non-adiabatic quantum pumping by a randomly moving quantum dot

Derevyanko

Waltner

2015

J. Phys. A: Math. Theor.

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We look at the time dependent fluctuations of the electrical charge in an open 1D quantum system represented by a quantum dot experiencing random lateral motion. In essentially non-adiabatic settings we study both diffusive and ballistic (Levy) regimes of the barrier motion where the electric current as well as the net pumped electric charge experience random fluctuations over the static background. We show that in the large-time limit, t → ∞, the wavefunction is naturally separated into the Berry-phase component (resulting from the singular part of the wave amplitude in the co-moving frame) and the non-adiabatic correction (arising from fast oscillating, slow decaying tails of the same amplitude). Based on this separation we report two key results: Firstly, the disorder averaged wave function and current are asymptotically mainly determined by the same Berry phase contribution that applies in the case of adiabatic motion. Secondly, after a short transition period the pumped electric charge exhibits fluctuations that grow much faster than predicted by the adiabatic theory. We also derive the exact expressions for the average propagator (in the co-moving basis representation) for the diffusive and ballistic types of motion considered.

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“…[21][22][23] The reflection and transmission coefficients (r, r and t, t corresponding to b α n ) can be obtained by a series of the recursive equations in every propagating mode. 3,24 As referred in the scattering theory of the quantum pump, 25 in the adiabatic approximation currents flowing in the lead α of the system can be easily derived by the adiabatic Floquet scattering matrix involving to any lead α. More exactly, the variation of the system can be measured by the number of the atoms in every period of one lead, i.e.…”

Section: Quantum Pumps Simulationsmentioning

confidence: 99%

One-dimensional quantum pump simulated by cold atoms

2015

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Quantum pump set up in one-dimensional (1D) channel was proposed by the cold atom simulation. The target pumping system is driven by the double time-dependent potentials. We investigated that the system can be achieved via the study of the cold atoms simulation. And by using the Floquet scattering method and the related transport theories in the mesoscopic systems, simulations of the pumping processes were presented in detail.

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Floquet Formalism of Quantum Pumps

Cited by 20 publications

References 56 publications

Interaction‐induced magnetic field asymmetry of nonlinear mesoscopic electrical transport

Interaction‐induced magnetic field asymmetry of nonlinear mesoscopic electrical transport

Non-adiabatic quantum pumping by a randomly moving quantum dot

One-dimensional quantum pump simulated by cold atoms

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