Validity criterion for the Markovian approximation

Determine what degree of separation between the memory time and the characteristic dynamical time scales is required for the Markovian approximation to remain valid for non-Markovian physical systems.

Background

The dissertation studies systems described by generalized Langevin equations, in which temporal correlations in the thermal environment generate non-Markovian dynamics. Its effective mass approach shows that short memory can substantially alter transport and other dynamical properties, even when the memory time is much shorter than the characteristic system time scales.

The authors explicitly identify the quantitative time-scale separation needed to justify neglecting memory as unresolved. Establishing such a criterion would clarify when the conventional Markovian approximation is reliable and when memory corrections, such as the effective mass correction, are necessary.