Kubo-Martin-Schwinger-Gated Imaginary-Time Reconstruction of Time-Resolved Electronic Circular Dichroism in Organic Excitonic Aggregates

Abstract

Time-resolved electronic circular dichroism (TR-ECD) and time-resolved circular dichroism (TRCD) probe pump-prepared chiral exciton dynamics through a weak circular probe. In linear response, the measured signal is a retarded mixed electric--magnetic response of the pump-prepared ensemble, whereas imaginary-time reconstruction is justified only when the relevant state is sufficiently stationary. Here, we introduce a Kubo-Martin-Schwinger-gated criterion for deciding, delay by delay, when a TR-ECD/TRCD response can be reconstructed from an imaginary-time reference and when it requires real-time or Keldysh dynamics. For organic aggregates hosting Frenkel excitons, we define a conditional admissibility diagnostic that combines a state-level distance from a one-exciton Gibbs reference with an observable-level spectral distance for the selected TRCD-like response. The protocol is tested on three established benchmarks: a reconstructed Ress-type squaraine-polymer squeezed helix, a cisoid indolenine squaraine B hexamer, and a helical perylene-bisimide stack. These tests show that early nonthermal exciton distributions are non-admissible, whereas dephased and intramanifold-relaxed states can become Matsubara-admissible before complete excited-state decay. The resulting workflow provides a practical delay-resolved gate for using imaginary-time methods in ultrafast chiroptical spectroscopy without imposing artificial equilibrium on genuinely nonequilibrium signals.