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.
Highlights
Metastability in stochastic systems is ubiquitous in nature
We have shown that the many-body explosion of eigenmode expansion coefficients is responsible for slow relaxation in many-body stochastic systems
We emphasize that this is a generic phenomenon, and it would occur in nonequilibrium dynamics without detailed balance
Summary
Metastability in stochastic systems is ubiquitous in nature. In particular, it is often associated with first-order phase transitions [1,2,3], (spin) glasses [4,5,6], protein folding [7], and so forth. [13,14,15] for quantum systems) Such a spectral characterization of metastable states is appealing since it is purely dynamical; we do not have to rely on thermodynamic notions such as the (free) energy landscape, which is difficult to define precisely except for mean-field models [16]. By many-body explosion of eigenmode expansion coefficients, which was recently studied in the context of open quantum systems [18,19] Our results provide insights into slow relaxation and metastability in many-body stochastic systems.
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