# Validating and Implementing Modified Filinov Phase Filtration in Semiclassical Dynamics

## TL;DR

This paper demonstrates that the modified Filinov filtration significantly improves the efficiency and accuracy of semiclassical correlation function calculations in MQC-IVR, especially by damping noise in oscillatory regions and enabling linear scaling.

## Contribution

It introduces a novel MQC-IVR formulation with linear scaling and validates the effectiveness of MFF in reducing noise and computational effort in semiclassical dynamics.

## Key findings

- MFF reduces noise by damping amplitude in oscillatory phase regions.
- The new MQC-IVR formulation achieves linear computational scaling.
- MFF is highly effective for correlation function calculations, unlike in wavepacket propagation.

## Abstract

The Mixed Quantum-Classical Initial Value Representation (MQC-IVR) is a recently introduced approximate semiclassical (SC) method for the calculation of real-time quantum correlation functions. MQC-IVR employs a modified Filinov filtration (MFF) scheme to control the overall phase of the SC integrand, extending the applicability of SC methods to complex systems while retaining their ability to accurately describe quantum coherence effects. Here, we address questions regarding the effectiveness of the MFF scheme in combination with SC dynamics. Previous work showed that this filtering scheme is of limited utility in the context of semiclassical wavepacket propagation, but we find the MFF is extraordinarily powerful in the context of correlation functions. By examining trajectory phase and amplitude contributions to the real-time SC correlation function in a model system, we clearly demonstrate that the MFF serves to reduce noise by damping amplitude only in regions of highly oscillatory phase leading to a reduction in computational effort while retaining accuracy. Further, we introduce a novel and efficient MQC-IVR formulation that allows for linear scaling in computational cost with the total simulation length, a significant improvement over the more-than quadratic scaling exhibited by the original method.