Stability of quantum systems at three scales: Passivity, quantum weak energy inequalities and the microlocal spectrum condition

TL;DR

This paper explores the stability of quantum systems across three scales by linking quantum weak energy inequalities, the microlocal spectrum condition, and passivity, showing their equivalence in ensuring dynamical stability.

Contribution

It formulates quantum weak energy inequalities for dynamical systems on static spacetimes and demonstrates their equivalence with the microlocal spectrum condition and passivity.

Findings

Quantum weak energy inequalities relate to thermodynamic stability.

The free scalar field with Hadamard states satisfies these conditions.

The three conditions are essentially equivalent at different length scales.

Abstract

Quantum weak energy inequalities have recently been extensively discussed as a condition on the dynamical stability of quantum field states, particularly on curved spacetimes. We formulate the notion of a quantum weak energy inequality for general dynamical systems on static background spacetimes and establish a connection between quantum weak energy inequalities and thermodynamic stability in the general setting. We show that the free scalar field in representations induced by quasifree Hadamard states provides an example system, and we indicate that (1) the microlocal spectrum condition, (2) quantum weak energy inequalities and (3) the existence of passive states (e.g., mixtures of ground- and thermal equilibrium states) are essentially equivalent, which is significant because each of these conditions becomes effective at a different length scale. [See title page of paper for the full abstract.]