Metastability associated with many-body explosion of eigenmode expansion coefficients

TL;DR

This paper reveals that in many-body stochastic systems, slow relaxation and metastability can be characterized by a many-body explosion of eigenmode expansion coefficients rather than small eigenvalues, offering new insights into complex dynamics.

Contribution

The study introduces the concept of eigenmode explosion as a novel indicator of metastability in many-body systems, challenging the traditional focus on small eigenvalues.

Findings

Eigenmode explosion correlates with slow relaxation in models.

Demonstrated in double-well potential and kinetically constrained models.

Provides new perspective on metastability in complex systems.

Abstract

Metastable states in stochastic systems are often characterized by the presence of small eigenvalues in the generator of the stochastic dynamics. We here show that metastability in many-body systems is not necessarily associated with small eigenvalues. Instead, many-body explosion of eigenmode expansion coefficients characterizes slow relaxation, which is demonstrated for two models, interacting particles in a double-well potential and the Fredrickson-Andersen model, the latter of which is a prototypical example of kinetically constrained models studied in glass and jamming transitions. Our results provide new insights into slow relaxation and metastability in many-body stochastic systems.