From the Underdamped Generalized Elastic Model to the Single Particle Langevin Description
Abstract
:1. Introduction
2. Underdamped Generalized Elastic Model
2.1. Generalized FD Relationship
2.2. Limiting Behaviours
- Short time limit: , i.e., , .This situation refer to the case where the fractional interactions among the system components are not yet sufficiently strong to affect the dynamics of the tracer. In this case the solution (12) takes the following form:
- Long time limit: , i.e., , .In this case the Fourier solution of the UGEM in Equation (12) can be written neglecting the inertia of the system:
3. Conclusions
Acknowledgments
Conflicts of Interest
Abbreviations
GEM | Generalized elastic model |
FD | Fluctuation-dissipation |
RHS | Right-hand side |
LHS | Left-hand side |
GLE | Generalized Langevin equation |
FLE | Fractional Langevin equation |
UGEM | Underdamped generalized elastic model |
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Taloni, A. From the Underdamped Generalized Elastic Model to the Single Particle Langevin Description. Mathematics 2017, 5, 3. https://doi.org/10.3390/math5010003
Taloni A. From the Underdamped Generalized Elastic Model to the Single Particle Langevin Description. Mathematics. 2017; 5(1):3. https://doi.org/10.3390/math5010003
Chicago/Turabian StyleTaloni, Alessandro. 2017. "From the Underdamped Generalized Elastic Model to the Single Particle Langevin Description" Mathematics 5, no. 1: 3. https://doi.org/10.3390/math5010003