Anomalous Polymer Dynamics Is Non-Markovian: Memory Effects and The Generalized Langevin Equation Formulation
Debabrata Panja
备注：
19 pages, 13 figures, 14 figure files; abstract + introduction + Tables I and II provide a good synopsis of this long paper; minor errors corrected at proofreading, published version
Any first course on polymer physics teaches that the dynamics of a tagged monomer of a polymer is anomalously subdiffusive, i.e., the mean-square displacement of a tagged monomer increases as $t^α$ for some $α<1$ until the terminal relaxation time $τ$ of the polymer. Beyond time $τ$ the motion of the tagged monomer becomes diffusive. Classical examples of anomalous dynamics in polymer physics are single polymeric systems, such as phantom Rouse, self-avoiding Rouse, self-avoiding Zimm, reptation, translocation through a narrow pore in a membrane, and many-polymeric systems such as polymer melts. In this pedagogical paper I report that all these instances of anomalous dynamics in polymeric systems are robustly characterized by power-law memory kernels within a {\it unified} Generalized Langevin Equation (GLE) scheme, and therefore, are non-Markovian. The exponents of the power-law memory kernels are related to the relaxation response of the polymers to local strains, and are derived from the equilibrium statistical physics of polymers. The anomalous dynamics of a tagged monomer of a polymer in these systems is then reproduced from the power-law memory kernels of the GLE via the fluctuation-dissipation theorem (FDT). Using this GLE formulation I further show that the characteristics of the drifts caused by a (weak) applied field on these polymeric systems are also obtained from the corresponding memory kernels.
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DiffGLE: Differentiable Coarse-Grained Dynamics using Generalized Langevin Equation
Department of Mechanical Science and Engineering, The University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校机械科学与工程系）；Walker Department of Mechanical Engineering and Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin（德克萨斯大学奥斯汀分校沃克机械工程系及奥登计算工程与科学研究所）
We investigated the elongational flows of the weakly entangled linear polymer melt using a coarse-grained molecular dynamics simulation. We extended the uniform extensional flow (UEF) method developed by Nicholson and Rutledge (D. A. Nicholson and G. C. Rutledge, J. Chem. Phys., 145, 244903 (2016)) for application to Langevin dynamics. We succeeded in observing the elongational viscosity of the weakly entangled linear polymer melt from the equilibrium state to the steady state using the extended UEF method, whereas the conventional rectangular parallelepiped shape technique for extensional flo…
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The spreading of polymer droplets is studied using molecular dynamics simulations. To study the dynamics of both the precursor foot and the bulk droplet, large drops of ~200,000 monomers are simulated using a bead-spring model for polymers of chain length 10, 20, and 40 monomers per chain. We compare spreading on flat and atomistic surfaces, chain length effects, and different applications of the Langevin and dissipative particle dynamics thermostats. We find diffusive behavior for the precursor foot and good agreement with the molecular kinetic model of droplet spreading using both flat and a…
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We show how a relativistic Langevin equation can be derived from a Lorentz-covariant version of the Caldeira-Leggett particle-bath Lagrangian. In one of its limits, we identify the obtained equation with the Langevin equation used in contemporary extensions of statistical mechanics to the near-light-speed motion of a Brownian particle in non-relativistic dissipative fluids. The proposed framework provides a more rigorous and first-principles form of the Langevin equation often quoted or postulated as ansatz in previous works. We then refine the aforementioned results by considering more terms …
Aalto University School of Science and Technology（阿尔托大学理工学院）；The University of Western Ontario（韦仕敦大学）；University of Waterloo（滑铁卢大学）；Brown University（布朗大学）
Based on a Hamiltonian that incorporates the elastic coupling between a tracer and active particles, we derive a generalized Langevin model for the non-equilibrium mechanical response of active viscoelastic biomatter. Our model accounts for the power-law viscoelastic response of the embedding polymeric network as well as for the non-equilibrium energy transfer between active and tracer particles. Our analytical expressions for the frequency-dependent response function and the positional autocorrelation function agree nicely with experimental data for red blood cells and actomyosin networks wit…
