Effective mass approach to memory in non-Markovian systems

Abstract: Recent pioneering experiments on non-Markovian dynamics done e.g. for active matter have demonstrated that our theoretical understanding of this challenging yet hot topic is rather incomplete and there is a wealth of phenomena still awaiting discovery. It is related to the fact that typically for simplification the Markovian approximation is employed and as a consequence the memory is neglected. Therefore methods allowing to study memory effects are extremely valuable. We demonstrate that a non-Markovian system described by the Generalized Langevin Equation (GLE) for a Brownian particle of mass $M$ can be approximated by the memoryless Langevin equation in which the memory effects are correctly reproduced solely via the effective mass $M^*$ of the Brownian particle which is determined only by the form of the memory kernel. Our work lays the foundation for an impactful approach which allows to readily study memory-related corrections to Markovian dynamics.