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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.
Chaos (Woodbury, N.Y.)
|February 20, 2026
Summary
This study introduces a generalized Schrödinger equation with fractional derivatives and memory effects to model anomalous transport and nonlocal interactions. Findings reveal novel quantum phenomena and distinct localization behaviors in time-space dynamics.
Area of Science:
- Quantum Mechanics
- Mathematical Physics
- Nonlinear Dynamics
Background:
- Anomalous transport phenomena require advanced mathematical models beyond standard differential equations.
- Temporal nonlocality and long-range interactions are crucial in various quantum systems.
Purpose of the Study:
- To propose and investigate a generalized Schrödinger equation incorporating fractional derivatives and memory effects.
- To analyze the impact of nonlocal potentials and memory on quantum dynamics.
- To derive and explore analytical solutions for the proposed model.
Main Methods:
- Introduction of a fractional Riesz derivative for anomalous transport.
- Inclusion of a memory kernel for temporal nonlocality.
- Modeling long-range interactions using an integral operator.
- Application of the Green function approach for deriving analytical solutions.
Main Results:
- Derivation of analytical solutions using the Green function method.
- Identification of novel quantum phenomena resulting from the interplay of fractional dynamics, nonlocal potentials, and memory effects.
- Observation of new local maxima in Green's function evolution.
- Characterization of distinct localization behaviors in the time-space domain.
Conclusions:
- The generalized Schrödinger equation effectively captures anomalous transport and nonlocal effects.
- The interplay of fractional dynamics, memory, and long-range interactions leads to unique quantum behaviors.
- The findings offer new insights into quantum dynamics with complex transport and interaction mechanisms.
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