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Updated: Feb 8, 2026

Stimulated Stokes and Antistokes Raman Scattering in Microspherical Whispering Gallery Mode Resonators
Published on: April 4, 2016
A microscopic model of the Stokes-Einstein relation in arbitrary dimension.
Benoit Charbonneau1, Patrick Charbonneau2, Grzegorz Szamel3
1Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario N2L 3G3, Canada.
Deviations from the Stokes-Einstein relation (SER) in liquids, particularly for self-solvation, are explained by a generalized statistical mechanics model. This work revisits Masters and Madden
Area of Science:
- Physical Chemistry
- Statistical Mechanics
- Liquid State Theory
Background:
- The Stokes-Einstein relation (SER) is a cornerstone in liquid theory, relating diffusion coefficients to viscosity.
- Standard hydrodynamic derivations of SER fail to explain observed deviations, especially in self-solvation dynamics.
- Masters and Madden previously explored a statistical mechanics model for SER using projection operator formalism.
Purpose of the Study:
- To investigate the microscopic origins of deviations from the Stokes-Einstein relation.
- To generalize the statistical mechanics model of SER to various spatial dimensions and solvent structures.
- To explore the validity of SER in idealized fluid systems.
Main Methods:
- Revisiting and generalizing the statistical mechanics model developed by Masters and Madden.
- Applying the projection operator formalism to analyze liquid dynamics.
- Extending the analysis to arbitrary spatial dimensions and partially structured solvents.
- Investigating the exact dynamics of infinite-dimensional fluids.
Main Results:
- Identified a potential microscopic origin for deviations from the Stokes-Einstein relation.
- Successfully generalized the statistical mechanics model to include dimensionality and solvent structure.
- Reproduced SER-like behavior from the exact dynamics of infinite-dimensional fluids.
Conclusions:
- The generalized statistical mechanics model provides insights into the microscopic basis of SER deviations.
- Dimensionality and solvent structure play crucial roles in the validity of the Stokes-Einstein relation.
- Infinite-dimensional fluid dynamics offer a theoretical framework for understanding SER.
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