Transient ordering in the Gross-Pitaevskii lattice subject to an energy quench within the disordered phase

TL;DR

This study numerically explores how energy quenches in a 3D disordered Gross-Pitaevskii lattice induce a transient U(1) order, exceeding equilibrium correlation lengths, due to energy localization on slowly relaxing sites.

Contribution

It reveals that transient U(1) ordering occurs during non-equilibrium relaxation after quenches, driven by energy localization on specific lattice sites, a phenomenon potentially common in various physical systems.

Findings

Transient U(1) order exceeds equilibrium correlation length.

Longer heating enhances transient ordering.

Energy accumulates on slowly relaxing sites.

Abstract

We numerically investigate heating-and-cooling quenches taking place entirely in the non-ordered phase of the discrete Gross-Pitaevskii equation on a three-dimensional cubic lattice. In equilibrium, this system exhibits a U(1)-ordering phase transition at an energy density which is significantly lower than the minimum one during the quench. Yet, we observe that the post-quench relaxation is accompanied by a transient U(1) ordering, namely, the correlation length of U(1) fluctuations significantly exceeds its equilibrium pre-quench value. The longer and the stronger the heating stage of the quench, the stronger the U(1) transient ordering. We identify the origin of this ordering with the emergence of a small group of slowly relaxing lattice sites accumulating a large fraction of the total energy of the system. Our findings suggest that the transient ordering may be a robust feature of a broad class of physical systems. This premise is consistent with the growing experimental evidence of the transient U(1) order in rather dissimilar settings.