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Ergodicity and slow relaxation in the one-dimensional self-gravitating system
1Centro de Ciências Exatas e das Tecnologias, Universidade Federal do Oeste da Bahia and Instituto de Física, Universidade de Brasília, UnB - Brasília, Distrito Federal 70297-400, Brazil.
Physical Review. E
|February 17, 2023
Summary
Homogeneous states in self-gravitating sheets models are nonergodic and do not reach equilibrium. Nonhomogeneous states, however, exhibit ergodic properties within a specific time frame, similar to other long-range interacting systems.
Area of Science:
- Statistical mechanics
- Astrophysics
- Dynamical systems
Background:
- Self-gravitating systems exhibit complex behaviors due to long-range interactions.
- Ergodic properties are crucial for understanding system relaxation and approach to equilibrium.
- One-dimensional self-gravitating sheets provide a simplified yet relevant model for studying these phenomena.
Purpose of the Study:
- To investigate and differentiate the ergodic properties of homogeneous and nonhomogeneous states in one-dimensional self-gravitating sheets models.
- To determine the relaxation dynamics and equilibrium-seeking behavior of these distinct states.
- To compare the findings with other systems characterized by long-range interactions.
Main Methods:
- Analysis of homogeneous and nonhomogeneous states within the one-dimensional self-gravitating sheets model.
- Examination of the one-particle distribution function and its collision term under specific limiting conditions (periodic boundary conditions).
- Comparison of observed ergodic behaviors with theoretical predictions and empirical data from similar systems.
Main Results:
- Homogeneous states were found to be nonergodic, with a zero collision term in the one-particle distribution function under specific limits.
- Nonhomogeneous states demonstrated ergodic behavior within a time window related to the system's relaxation time.
- These findings highlight a divergence in dynamical behavior based on the system's spatial configuration.
Conclusions:
- The ergodic properties of self-gravitating sheets models are state-dependent, distinguishing between homogeneous and nonhomogeneous configurations.
- Homogeneous states do not relax to equilibrium, indicating a lack of ergodicity.
- Nonhomogeneous states exhibit ergodicity over relevant timescales, aligning with observations in other long-range interacting systems.
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