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arXiv · 2209.09307

Eigenvalue crossing as a phase transition in relaxation dynamics

Gianluca Teza·Ran Yaacoby·Oren Raz
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Abstract

When a system's parameter is abruptly changed, a relaxation towards the new equilibrium of the system follows. We show that a crossing between the second and third eigenvalues of the relaxation matrix results in a relaxation trajectory singularity, which is analogous to a first-order equilibrium phase transition. We demonstrate this in a minimal 4-state system and in the thermodynamic limit of the 1D Ising model.

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Gianluca Teza, Ran Yaacoby, Oren Raz. 2022-09-19. Eigenvalue crossing as a phase transition in relaxation dynamics. https://doi.org/10.1103/physrevlett.130.207103

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