Algebraic localization-delocalization phase transition in moving potential wells on a lattice

Abstract

The localization and scattering properties of potential wells or barriers uniformly moving on a lattice are strongly dependent on the drift velocity owing to violation of the Galilean invariance of the discrete Schrödinger equation. Here a type of localization-delocalization phase transition of algebraic type is unravelled, which does not require any kind of disorder and arises when a power-law potential well drifts fast on a lattice. While for an algebraic exponent $\alpha$ lower than the critical value ${\alpha }_c=1$ dynamical delocalization is observed, for $\alpha >{\alpha }_c$ asymptotic localization, corresponding to an asymptotic frozen dynamics, is instead realized. At the critical phase transition point ${\alpha }_{=}{\alpha }_c=1$ an oscillatory dynamics is found, corresponding to Bloch oscillations. An experimentally-accessible photonic platform for the observation of the predicted algebraic phase transition, based on light dynamics in synthetic mesh lattices, is suggested.

9 pages, 7 figures, to appear in Annalen der Physik (Wiley)

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