Quantum Scars in Quantum Field Theory

TL;DR

This paper extends the concept of quantum scars from quantum mechanics to quantum field theories, showing how unstable classical solutions influence quantum eigenstates and affect thermalization, with applications to scalar field solitons.

Contribution

It introduces a formalism for quantum scars in quantum field theories, generalizing existing methods and analyzing their impact on energy eigenstates and thermalization.

Findings

Unstable classical solutions imprint on quantum eigenstates.

Quantum scars can cause breakdown of thermalization.

Q-clouds induce quantum scars in scalar field theories.

Abstract

We develop the theory of quantum scars for quantum fields. By generalizing the formalisms of Heller and Bogomolny from few-body quantum mechanics to quantum fields, we find that unstable periodic classical solutions of the field equations imprint themselves in a precise manner on bands of energy eigenfunctions. This indicates a breakdown of thermalization at certain energy scales, in a manner that can be characterized via semiclassics. As an explicit example, we consider time-periodic non-topological solitons in complex scalar field theories. We find that an unstable variant of Q-balls, called Q-clouds, induce quantum scars. Some technical contributions of our work include methods for characterizing moduli spaces of periodic orbits in field theories, which are essential for formulating our quantum scar formula. We further discuss potential connections with quantum many-body scars in Rydberg atom arrays.