Linear response theory for arbitrary periodic signals

TL;DR

This paper generalizes Kubo's Linear Response Theory to arbitrary periodic signals, providing exact formulas for energy dissipation and demonstrating how signal shape influences heating efficiency, with applications in magnetic hyperthermia.

Contribution

The authors extend LRT to arbitrary periodic signals and derive exact formulas for energy dissipation, enabling optimized signal design for applications like hyperthermia.

Findings

Different signal shapes can significantly increase energy dissipation for the same input energy.

Exact analytical formulas are obtained for various waveforms including square, sawtooth, and pulsed signals.

Application demonstrated in magnetic hyperthermia for improved heating efficiency.

Abstract

We extend Kubo's Linear Response Theory (LRT) to periodic input signals with arbitrary shapes and obtain exact analytical formulas for the energy dissipated by the system for a variety of signals. These include the square and sawtooth waves, or pulsed signals such as the rectangular, sine and $\delta$-pulses. It is shown that for a given input energy, the dissipation may be substantially augmented by exploiting different signal shapes. We also apply our results in the context of magnetic hyperthermia, where small magnetic particles are used as local heating centers in oncological treatments.