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Anomalous dynamics in complex quantum systems with nonlocal interactions.

P Trajanovski1,2, E K Lenzi3, I Petreska1

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This summary is machine-generated.

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.

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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.