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Updated: Feb 22, 2026

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
Published on: December 4, 2017
Anomalous dynamics in complex quantum systems with nonlocal interactions
P Trajanovski1,2, E K Lenzi3, I Petreska1
1Institute of Physics, Faculty of Natural Sciences and Mathematics-Skopje, Ss. Cyril and Methodius University in Skopje, Skopje, Macedonia.
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.
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