From Photothermal Transients to Effective Transport Operators: An Operator-Based Interpretation of TTG Dynamics

Abstract

Transient thermal grating (TTG) measurements probe thermal transport on submicrometer spatial and subnanosecond temporal scales, where departures from purely diffusive behavior have been reported in a variety of solid-state systems. Within the Mori-Zwanzig projection framework, such effects can be interpreted as manifestations of memory arising from microscopic degrees of freedom that remain unresolved at the observational scale. Motivated by this perspective, we formulate a forward model for TTG response in which heat transport is described by a linear evolution operator with memory. Microscopic transport processes are systematically coarse-grained into a non-Markovian transport operator, whose finite-memory form provides a general description of TTG dynamics, while diffusive and long-memory behaviors emerge as asymptotic limits of the same underlying framework. Within this formulation, the experimentally observed TTG transient is interpreted as the response of an effective transport operator rather than as a direct signature of a particular microscopic transport mechanism. The primary outcome of the inversion procedure is the determination of effective operator parameters, while microscopic transport mechanisms are inferred only through a subsequent, material-specific modeling step. The proposed Mori-Zwanzig inspired framework therefore establishes a systematic route from TTG measurements to effective transport operators and, subsequently, to coarse-grained descriptions of microscopic transport dynamics.