Thermodynamics at zero temperature: inequalities for the ground state of a quantum many-body system

TL;DR

This paper establishes fundamental inequalities relating interaction energy, pressure, and volume in zero-temperature quantum many-body systems, extending to impurity interactions, with broad applicability.

Contribution

It proves a general inequality for the ground state of quantum many-body systems at zero temperature, including impurity effects, using Anderson-type bounds.

Findings

Proves $E_{int} \,\leq\, P V$ inequality for ground states.

Derives bounds on impurity chemical potential and binding energy.

Applies to a wide class of quantum many-body systems.

Abstract

We prove that for a single-component many-body system at zero temperature the inequality $E_{\rm int} \leq\, P\,V$ holds, where $E_{\rm int}$ is the interaction energy, $P$ is pressure and $V$ is volume. This inequality is proven under rather general assumptions with the use of Anderson-type bound relating ground state energies of systems with different numbers of particles. We also consider adding impurity particles to the system and derive inequalities on the chemical potential of the impurity and binding energy of the bound state of two impurities.