Isosbestic Points: Theory and Applications

TL;DR

This paper investigates the theoretical basis of isosbestic points in various physical measurements, demonstrating how their sharpness can be used to approximate functions and extract parameter dependencies across different systems.

Contribution

It provides a perturbative framework explaining the sharpness of isosbestic points and applies it to analyze experimental data and models in condensed matter physics.

Findings

Narrow crossing regions imply a perturbative approximation of f(x,p).

The method extracts temperature dependence from experimental spectra.

The approach explains sharp isosbestic points in models like Falicov-Kimball and Hubbard.

Abstract

We analyze the sharpness of crossing ("isosbestic") points of a family of curves which are observed in many quantities described by a function f(x,p), where x is a variable (e.g., the frequency) and p a parameter (e.g., the temperature). We show that if a narrow crossing region is observed near x* for a range of parameters p, then f(x,p) can be approximated by a perturbative expression in p for a wide range of x. This allows us, e.g., to extract the temperature dependence of several experimentally obtained quantities, such as the Raman response of HgBa2CuO4+delta, photoemission spectra of thin VO2 films, and the reflectivity of CaCu3Ti4O12, all of which exhibit narrow crossing regions near certain frequencies. We also explain the sharpness of isosbestic points in the optical conductivity of the Falicov-Kimball model and the spectral function of the Hubbard model.