Conductance et étalement d'une onde quantique dans un guide unidimensionnel : effet d'une force.

Abstract : A wave can be exponentially localized in a disordered medium, due to interference effects. This Anderson localization phenomenon leads to a cancellation of the conductance of a quantum fluid in 1D. However, theoretical works pointed out that an electric field may reduce or cancel this localization. We study here the effect of a force on the localization of a 1D quantum matter wave. Since both Anderson localization of an expanding wave packet and the effect of disorder on the transport between two reservoirs have been studied in ultracold atom experiments, we focus on two systems, namely the diffusion, or the transmission, of a particle.In order to calculate the transmission, we generalize a transfer matrix formalism to the presence of a, possibly inhomogeneous, force. The case of a speckle disorder as used in ultracold atom experiments is dealt with using two other analytical approaches. Our main is result is that the force can be entirely taken into account by renormalising the length with a local mean free path of the particle. For white-noise disorder, the force leads to a weaker, algebraic localization, whereas full delocalization appears for a correlated disorder. We then focus on the diffusion of a particle, using a numerical approach. A transition of delocalization of the particle for strong forces is shed into light through a power law increase of its position, whose exponent increases with the force. Moreover, we show that localization is systematically destroyed in a correlated disorder.
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Cécile Crosnier de Bellaistre. Conductance et étalement d'une onde quantique dans un guide unidimensionnel : effet d'une force.. Optique [physics.optics]. Université Paris-Saclay, 2017. Français. ⟨NNT : 2017SACLO009⟩. ⟨tel-01686775⟩

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