2025/04/07 by Victor Gurarie, Gurarie, V.
Biochemistry, Genetics and Molecular Biology · Physics and Astronomy · #Diffusion and Search Dynamics #Disordered Systems and Neural Networks (cond-mat.dis-nn) #FOS: Physical sciences #Quantum Physics (quant-ph) #Quantum chaos and dynamical systems #stochastic dynamics and bifurcation
paper · pdf · doi:10.48550/arxiv.2504.05479
openalex publication_date 2025/04/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the motion of a quantum particle whose position is measured in random places at random moments in time. We show that a freely moving particle measured in this way undergoes superdiffusion, while a charged particle moving in a magnetic field confined to the lowest Landau level undergoes conventional diffusion. We also look at a particle moving in one dimensional space in a random time-independent potential, so that it is Anderson localized, which is also measured at random points in space and randomly in time. We find that random measurements break localization and this particle also undergoes diffusion. To address these questions, we develop formalism similar to that employed when studying classical and quantum problems with time-dependent noise.