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Role of initial conditions in one-dimensional diffusive systems: Compressibility, hyperuniformity, and long-term
Tirthankar Banerjee1, Robert L Jack1,2, Michael E Cates1
1DAMTP, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom.
Physical Review. E
|January 21, 2023
Summary
Initial conditions profoundly impact one-dimensional diffusive systems. A generalized compressibility quantifies this memory, revealing new universality classes for dynamical fluctuations.
Area of Science:
- Statistical Mechanics
- Condensed Matter Physics
- Non-equilibrium Systems
Background:
- Dynamical fluctuations in diffusive systems are influenced by initial states.
- Understanding the long-term memory of initial conditions is crucial for predicting system behavior.
Purpose of the Study:
- To analytically investigate the lasting effects of initial conditions on dynamical fluctuations.
- To identify universal properties governing the memory of initial states in diffusive systems.
Main Methods:
- Analytical derivation of mean-squared displacement and current fluctuations.
- Characterization of initial condition memory via generalized compressibility.
- Verification using extensive Monte Carlo simulations.
Main Results:
- The long-term memory of initial conditions is universally mediated by generalized compressibility.
- Identification of a universality class for hyperuniform initial states.
- Demonstration of a continuous family of initial condition classes, including equilibrated states.
Conclusions:
- Generalized compressibility is a key static quantity determining dynamical variances.
- Initial states, not just equilibration, define universality classes in diffusive systems.
- The findings offer a new perspective on memory effects in statistical physics.
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