Majorana approach to the stochastic theory of lineshapes

TL;DR

This paper introduces a novel field-theoretic approach using Majorana representation to analyze spectral lineshapes, enabling systematic inclusion of corrections and model-independent extraction of charge fluctuation spectra from experimental data.

Contribution

It recasts the stochastic lineshape theory in a diagrammatic framework and provides methods to predict and invert lineshapes for charge fluctuation analysis.

Findings

Reproduces observed lineshape features including splitting and narrowing.

Allows systematic inclusion of higher-order corrections.

Provides a model-independent way to extract charge fluctuation spectra.

Abstract

Motivated by recent Mossbauer experiments on strongly correlated mixed-valence systems, we revisit the Kubo-Anderson stochastic theory of spectral lineshapes. Using a Majorana representation for the nuclear spin we demonstrate how to recast the classic lineshape theory in a field-theoretic and diagrammatic language. We show that the leading contribution to the self-energy can reproduce most of the observed lineshape features including splitting and lineshape narrowing, while the vertex and the self-consistency corrections can be systematically included in the calculation. This new approach permits us to predict the line-shape produced by an arbitrary bulk charge fluctuation spectrum providing a model-independent way to extract the local charge fluctuation spectrum of the surrounding medium. We also derive an inverse formula to extract the charge fluctuation from the measured lineshape.