# Quantum Quench and $f$-Sum Rules on Linear and Non-linear Conductivities

## TL;DR

This paper derives the $f$-sum rule for conductivity in quantum many-particle systems under a quench process and extends it to an infinite series applicable to nonlinear conductivities at all orders.

## Contribution

It introduces a generalized framework for $f$-sum rules applicable to both linear and nonlinear conductivities in quantum systems under quench conditions.

## Key findings

- Derived the $f$-sum rule for general quantum systems.
- Extended the sum rule to an infinite series for nonlinear conductivities.
- Applicable to systems subjected to electric field pulses.

## Abstract

Considering a quench process in which an electric field pulse is applied to the system, "$f$-sum rule" for the conductivity for general quantum many-particle systems is derived. It is furthermore extended to an infinite series of sum rules, applicable to the nonlinear conductivity at every order.