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Quantum diffusion of a relativistic particle in a time-dependent random potential
1Department of Physics, University of Tehran, Tehran 14395-547, Iran.
Summary
Quantum diffusion of relativistic particles shows ballistic spreading, unlike nonrelativistic cases which exhibit superballistic diffusion. This study explores relativistic suppression of wave packet diffusion and its link to conservation laws.
Area of Science:
- Quantum mechanics
- Statistical physics
- Relativistic dynamics
Background:
- Understanding particle diffusion in random potentials is crucial in quantum mechanics.
- Investigating the behavior of relativistic particles under quantum effects presents unique challenges.
- Previous studies often focused on nonrelativistic systems, leaving relativistic quantum diffusion less explored.
Purpose of the Study:
- To rigorously study the quantum diffusion of a relativistic particle.
- To analyze the effects of a time-dependent random potential with delta correlation in time.
- To compare the diffusion behavior of relativistic and nonrelativistic particles.
Main Methods:
- Employing theoretical analysis to model quantum diffusion.
- Solving the relevant quantum mechanical equations for a relativistic particle.
- Analyzing the asymptotic time limit of wave packet spreading.
Main Results:
- The relativistic particle wave packet spreads ballistically in the asymptotic time limit.
- In contrast, the nonrelativistic case exhibits superballistic diffusion under identical conditions.
- Relativistic suppression of wave packet diffusion was observed.
Conclusions:
- Relativistic quantum diffusion differs significantly from its nonrelativistic counterpart.
- The observed suppression is linked to statistical conservation laws inherent in relativistic dynamics.
- This research provides insights into fundamental aspects of quantum field theory and statistical mechanics.
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