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Non-normalizable quasiequilibrium states under fractional dynamics.
Lucianno Defaveri1, Maike A F Dos Santos2, David A Kessler1
1Department of Physics, Bar-Ilan University, Ramat-Gan 52900, Israel.
Physical Review. E
|September 19, 2023
Summary
Particles in a thermal bath exhibit long-lasting stagnated states, identified as non-normalizable quasiequilibrium (NNQE) states. Their duration depends exponentially on potential depth and temperature, influenced by anomalous diffusion.
Area of Science:
- Physics
- Statistical Mechanics
- Anomalous Diffusion
Background:
- Particles diffusing anomalously in a thermal bath are released from a potential well.
- At low temperatures, system observables remain constant for extended periods.
Purpose of the Study:
- Characterize these long-stagnated states.
- Analyze the factors influencing their duration.
Main Methods:
- Utilized the fractional-time Fokker-Planck equation (FTFPE).
- Employed continuous-time random walk approaches.
- Calculated ensemble averages for dynamical and thermodynamical observables.
Main Results:
- Identified stagnated states as non-normalizable quasiequilibrium (NNQE) states.
- Derived analytical estimates for NNQE state durations.
- Showed timescales depend exponentially on potential depth (in units of temperature) and fractional exponent.
Conclusions:
- NNQE states represent a distinct dynamical regime in anomalous diffusion.
- The duration of transient stagnation is highly sensitive to system parameters like potential depth and temperature.
- Fractional dynamics play a crucial role in governing the persistence of these states.
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