Related papers: The Structure of Langevin's Memory Kernel From Lag…
We study numerical methods for the generalized Langevin equation (GLE) with a positive Prony series memory kernel, in which case the GLE can be written in an extended variable Markovian formalism. We propose a new splitting method that is…
It has been become standard practice to describe steady-state non-equilibrium phenomena by Langevin equations with colored noise and time-dependent friction kernels that do not obey the fluctuation-dissipation theorem, but since these…
Generalized Langevin equations (GLEs) provide a powerful framework for describing slow dynamics in soft-matter systems, but deriving an exact homogeneous GLE (hGLE) for a reaction coordinate from an underlying many-body system remains…
Coarse-graining complex molecular systems to lower-dimensional reaction coordinates is a powerful approach for capturing their effective dynamics. The generalized Langevin equation (GLE) provides an exact framework for modeling…
We consider the problem of inferring the interaction kernel of stochastic interacting particle systems from observations of a single particle. We adopt a semi-parametric approach and represent the interaction kernel in terms of a…
Recent rapid advances in single particle tracking and supercomputing techniques resulted in an unprecedented abundance of diffusion data exhibiting complex behaviours, such the presence of power law tails of the msd and memory functions,…
We consider the stochastic dynamics of a system linearly coupled to a hierarchical thermal bath with two well-separated inherent timescales: one slow, and one fast. The slow part of the bath is modeled as a set of harmonic oscillators and…
We derive generalized Langevin equations (GLEs) for single beads in linear elastic networks. In particular, the derivations of the GLEs are conducted without employing normal modes, resulting in two distinct representations in terms of…
Agent-based models typically treat systems in isolation, discarding environmental coupling as either computationally prohibitive or dynamically irrelevant. We demonstrate that this neglect misses essential physics: environmental degrees of…
The Langevin dynamics of a $d$-dimensional mean spherical model with competing interactions along $m\leq d$ directions of a hypercubic lattice is analysed. After a quench at high temperatures, the dynamical behaviour is characterized by two…
The effective dynamics of a colloidal particle immersed in a complex medium is often described in terms of an overdamped linear Langevin equation for its velocity with a memory kernel which determines the effective (time-dependent) friction…
Local diffusivity of a protein depends crucially on the conformation, and the conformational fluctuations are often non-Markovian. Here, we investigate the Langevin equation with non-Markovian fluctuating diffusivity, where the fluctuating…
This work presents a systematic methodology for describing the transient dynamics of coarse-grained molecular systems inferred from all-atom simulated data. We suggest Langevin-type dynamics where the coarse-grained interaction potential…
Realistic models of physical world rely on differentiable symmetries that, in turn, correspond to conservation laws. Recent works on Lagrangian and Hamiltonian neural networks show that the underlying symmetries of a system can be easily…
Current Lagrangian (particle-tracking) algorithms used to simulate diffusion-reaction equations must employ a certain number of particles to properly emulate the system dynamics---particularly for imperfectly-mixed systems. The number of…
We provide a general construction of quantum generalized master equations with memory kernel leading to well defined, that is completely positive and trace preserving, time evolutions. The approach builds on an operator generalization of…
Memory effects in the dynamics of open systems have been the subject of significant interest in the last decades. The methods involved in quantifying this effect, however, are often difficult to compute and may lack analytical insight. With…
The time-dependent transmission coefficient for the Kramers problem exhibits different behaviors in different parameter regimes. In the high friction regime it decays monotonically ("non-adiabatic"), and in the low friction regime it decays…
We introduce a theory of local kernels, which generalize the kernels used in the standard diffusion maps construction of nonparametric modeling. We prove that evaluating a local kernel on a data set gives a discrete representation of the…
Molecular dynamics (MD) simulation based on Langevin equation has been widely used in the study of structural, thermal properties of matters in difference phases. Normally, the atomic dynamics are described by classical equations of motion…