Scattering Expansion for Localization in One Dimension
ORAL
Abstract
We present a perturbative approach to a broad class of disordered systems in one spatial dimension. Considering a long chain of identically disordered scatterers, we expand in the reflection strength of any individual scatterer. This expansion accesses the full range of phase disorder from weak to strong. As an example application, we show analytically that in a discrete-time quantum walk, the localization length can depend non-monotonically on the strength of phase disorder (whereas expanding in weak disorder yields monotonic decrease). Returning to the general case, we obtain to all orders in the expansion a particular non-separable form for the joint probability distribution of the log-transmission and reflection phase. Furthermore, we show that for weak local reflection strength, a version of the scaling theory of localization holds: the joint distribution is determined by just three parameters.
*This work used computational and storage services associated with the Hoffman2 Shared Cluster provided by UCLA Institute for Digital Research and Education's Research Technology Group. A.B.C., P.S., and R.R. acknowledge financial support from the University of California Laboratory Fees Research Program funded by the UC Office of the President (UCOP), grant number LFR-20-653926. A.B.C acknowledges financial support from the Joseph P. Rudnick Prize Postdoctoral Fellowship (UCLA). P.S. acknowledges financial support from the Center for Quantum Science and Engineering Fellowship (UCLA) and the Bhaumik Graduate Fellowship (UCLA).
–
Publication:A. B. Culver, P. Sathe, and R. Roy, arXiv:2210.07999 A. B. Culver, P. Sathe, and R. Roy (in preparation)
