Journal
PHYSICAL REVIEW B
Volume 104, Issue 9, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevB.104.094203
Keywords
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Funding
- Simons Foundation [454949]
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The article discusses computating the exponentially small probability of a system jumping from one metastable state to another, focusing on the evaluation of path integrals using mean-field models and saddle-point methods, and solving the resulting dynamical equations with numerical algorithms.
The complex dynamics of an increasing number of systems is attributed to the emergence of a rugged energy landscape with an exponential number of metastable states. To develop this picture into a predictive dynamical theory, I discuss how to compute the exponentially small probability of a jump from one metastable state to another. This is expressed as a path integral that can be evaluated by saddle-point methods in mean-field models, leading to a boundary value problem. The resulting dynamical equations are solved numerically by means of a Newton-Krylov algorithm in the paradigmatic spherical p-spin glass model that is invoked in diverse contexts from supercooled liquids to machine-learning algorithms. I discuss the solutions in the asymptotic regime of large times and the physical implications on the nature of the ergodicity-restoring processes.
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