Linear Continuum Mechanics for Quantum Many-Body Systems

TL;DR

This paper develops a continuum mechanics framework for quantum many-body systems in the linear response regime, deriving an exact equation of motion for the displacement field and demonstrating its accuracy for single-particle and high-frequency systems.

Contribution

It introduces a novel continuum mechanics approach for quantum systems using a displacement field, with exact results for certain regimes and applications to simple models.

Findings

Exact equation of motion for displacement field in quantum systems

Accurate excitation spectrum with correct integrated strength

Validated approach on one- and two-electron models

Abstract

We develop the continuum mechanics of quantum many-body systems in the linear response regime. The basic variable of the theory is the displacement field, for which we derive a closed equation of motion under the assumption that the time-dependent wave function in a locally co-moving reference frame can be described as a geometric deformation of the ground-state wave function. We show that this equation of motion is exact for systems consisting of a single particle, and for all systems at sufficiently high frequency, and that it leads to an excitation spectrum that has the correct integrated strength. The theory is illustrated by simple model applications to one- and two-electron systems.