Diffusive Spin Transport

Abstract

Information to be stored and transported requires physical carriers. The quantum bit of information (qubit) can for instance be realised as the spin 1 2 degree of freedom of a massive particle like an electron or as the spin 1 polarisation of a massless photon. In this lecture, I first use irreducible representations of the rotation group to characterise the spin dynamics in a least redundant manner. Specifically, I describe the decoherence dynamics of an arbitrary spin S coupled to a randomly fluctuating magnetic field in the Liouville space formalism. Secondly, I discuss the diffusive dynamics of the particle's position in space due to the presence of randomly placed impurities. Combining these two dynamics yields a coherent, unified picture of diffusive spin transport, as applicable to mesoscopic electronic devices or photons propagating in cold atomic clouds. * Notes based on a lecture given at the "International School on Quantum Information", Max-Planck-Institut für Physik komplexer Systeme, Dresden, 2005 1. Internal composition: ∀R 1,2 ∈ SO(3) : R 21 = R 2 R 1 ∈ SO(3); 2. Existence of the identity: ∃E : RE = ER = R ∀R ∈ SO(3) with E = ½ 3 ;

Effective Dynamics of Disordered Quantum Systems

“…For example, the master-equation in Lindblad form presented in Section III, which is valid in the limit of short times, has been used in [17] to study homogeneous disorder models. In order to extend its validity beyond short times, one could employ a Born-Markov-type approximation, as done in [63] to derive an evolution equation for diffusive spin-transport in a disordered medium. Another perspective to describe complex disordered system may consist in complementing our master equation approach with techniques from disorder transport theory such as perturbation theory or diagrammatic methods as used, e.g., in the study of weak localization [64].…”

Disorder and interference: localization phenomena

“…where E σ = 2 /mσ 2 is a characteristic correlation energy and I 0 a modified Bessel function. In a one-dimensional speckle potential, we can use (105) and (106) with the speckle potential correlation function (92). In d = 1, the only contributions can come from forward scattering k = k and backward scattering k = −k, such that…”

Open System Model for Quantum Dynamical Maps with Classical Noise and Corresponding Master Equations

“…Hence, it is clear that the Markov approximation cannot be applied to the previous two examples, which are characterized by the time-dependent master equation (21). Finally, we note that when the GKLS master equation arises as a consequence of averaging over random impurities in a disordered sample, one obtains pure momentumdephasing random unitary dynamics [25].…”