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arXiv · 2111.07681

Finite-time dynamical phase transition in non-equilibrium relaxation

Jan Meibohm·Massimiliano Esposito
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Abstract

We uncover a finite-time dynamical phase transition in the thermal relaxation of a mean-field magnetic model. The phase transition manifests itself as a cusp singularity in the probability distribution of the magnetisation that forms at a critical time. The transition is due to a sudden switch in the dynamics, characterised by a dynamical order parameter. We derive a dynamical Landau theory for the transition that applies to a range of systems with scalar, parity-invariant order parameters. Close to criticalilty, our theory reveals an exact mapping between the dynamical and equilibrium phase transitions of the magnetic model, and implies critical exponents of mean-field type. We argue that interactions between nearby saddle points, neglected at the mean-field level, may lead to critical, spatiotemporal fluctuations of the order parameter, and thus give rise to novel, dynamical critical phenomena.

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Jan Meibohm, Massimiliano Esposito. 2021-11-15. Finite-time dynamical phase transition in non-equilibrium relaxation. https://doi.org/10.1103/physrevlett.128.110603

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