Anomalous dynamics in complex quantum systems with nonlocal interactions
Abstract
We propose and investigate a generalized Schrödinger equation by introducing a fractional Riesz derivative to account for anomalous transport and a memory kernel to describe temporal nonlocal effects. Additionally, we include a long-range interactions term, modeled by an integral operator, which captures spatially extended interactions. Using the Green function approach, we derive analytical solutions and explore their implications in the time-space domain. Our findings reveal novel quantum phenomena arising from the interplay of fractional dynamics, nonlocal potentials, and memory effects, including the emergence of new local maxima in the evolution of Green's functions and distinct localization behaviors.
Fields of Study & Subjects
Fractional Differential Equations Solutions
Quantum Mechanics and Applications
Quantum Mechanics and Non-Hermitian Physics
Publication details
- Journal / source
- Chaos An Interdisciplinary Journal of Nonlinear Science
- Publisher
- AIP Publishing
- Volume
- 36
- Issue
- 2
- Publication date
- 1 February 2026
- Language
- EN