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Escape of particles in a time-dependent potential well
Diogo Ricardo da Costa1, Carl P Dettmann, Edson D Leonel
1Departamento de Estatística, Matemática Aplicada e Computação, UNESP-Universidade Estadual Paulista, Avenida 24A, 1515 CEP 13506-900, Rio Claro, São Paulo, Brazil.
Summary
Particles escaping a potential box exhibit scaling-invariant escape patterns. Their survival probability shows a crossover from exponential to slower decay due to sticky regions in phase space.
Area of Science:
- Physics
- Statistical Mechanics
- Dynamical Systems
Background:
- Investigating particle dynamics in confined systems is crucial for understanding complex behaviors.
- Time-dependent potentials introduce rich dynamics, including chaos and mixed phase spaces.
- Nonlinear mappings are used to model particle energy and time evolution.
Purpose of the Study:
- To analyze the escape dynamics of noninteracting particles from a potential box with a time-dependent well.
- To characterize the phase space structure and its influence on particle escape.
- To examine the statistical properties of particle escape, such as frequency histograms and survival probabilities.
Main Methods:
- Modeling particle dynamics using a two-dimensional nonlinear area-preserving mapping.
- Analyzing the mixed phase space, identifying chaotic seas, periodic islands, and invariant spanning curves.
- Introducing a 'hole' in the energy axis to study particle escape.
- Calculating and analyzing the histogram of escape frequencies and survival probability over time.
Main Results:
- Observed a scaling-invariant histogram of particle escape frequencies.
- The escape frequency histogram grows, peaks, and then decays towards zero.
- Survival probability exhibits an initial exponential decay followed by a slower decay regime.
- Identified 'sticky regions' in the phase space contributing to the slower decay.
Conclusions:
- The escape dynamics are characterized by scaling invariance and influenced by phase space structures.
- Sticky regions significantly affect particle survival probability at longer times.
- The study provides insights into chaotic transport and escape phenomena in complex systems.
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