Quantum boomerang effect in time-crystalline structures
Phys. Rev. B 114, 014316 – Published 23 July, 2026
DOI: https://doi.org/10.1103/gj3d-qpjf
Abstract
The quantum boomerang effect (QBE) is a unique dynamical signature of Anderson localization, characterized by a launched wave packet that initially drifts but ultimately returns to its initial position due to fundamental quantum interference. In this work, we theoretically establish and quantitatively characterize the QBE in a time-crystalline structure using a periodically driven quantum particle in a one-dimensional potential well. By constructing maximally localized Floquet-Wannier states and introducing temporal disorder, we rigorously map the continuous Floquet dynamics onto a discrete disordered tight-binding lattice. By positioning a detector at a fixed spatial coordinate, we monitor the temporal evolution of the wave packet to extract the mean temporal center of mass of the probability density in a time-crystalline structure. This mean temporal center of mass exhibits an initial ballistic expansion, followed by a pronounced U-turn, and ultimately returns to its initial temporal position after long-time evolution. These results confirm the existence of the complete QBE in the time domain. They also demonstrate that nontrivial dynamics can be explored within time-crystalline systems, even though these structures already possess an inherent temporal periodicity.
