Generalized Langevin dynamics for single beads in linear elastic networks.

Area of Science:

• Statistical Mechanics
• Polymer Physics
• Soft Matter Physics

Background:

• Generalized Langevin equations (GLEs) are crucial for describing complex systems with memory effects.
• Traditional methods for deriving GLEs in elastic networks often rely on normal mode analysis.
• Understanding bead dynamics in elastic networks is fundamental to polymer science.

Purpose of the Study:

• To derive generalized Langevin equations (GLEs) for single beads in linear elastic networks.
• To present two distinct GLE representations using resistance and mobility kernels, avoiding normal modes.
• To validate the derived GLEs using established polymer models and explore hydrodynamic interactions.

Main Methods:

• Derivation of GLEs without employing normal modes.
• Utilizing projection operator methods for an alternative GLE derivation.
• Application of the general theory to the Rouse model and ring polymer.
• Analysis of elastic networks with hydrodynamic interactions under the pre-averaging approximation.

Main Results:

• Two distinct GLE representations (resistance and mobility kernels) were derived without normal modes.
• Fluctuation-dissipation relations were confirmed for both GLE representations.
• The projection operator method yielded a GLE consistent with the resistance kernel representation.
• Explicit GLEs were derived for Rouse and ring polymer models, and for elastic networks with hydrodynamic interactions.

Conclusions:

• The study provides a novel, mode-independent framework for deriving GLEs in elastic networks.
• The interconnectedness of resistance and mobility kernels via Laplace transforms is demonstrated.
• The derived GLEs offer a versatile tool for analyzing polymer dynamics in various network configurations.