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arXiv · 2412.01436

Kibble-Zurek mechanism in driven underdamped Brownian motion

Pierre Nazé
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Abstract

Kibble-Zurek mechanism is widely known to appear in the transverse-field quantum Ising chain in the thermodynamic limit at zero temperature, having notorious characteristics, like the divergence of its relaxation time. In this work, I present the same effect in a simple system, the driven underdamped Brownian motion. Using linear response theory, I show the appropriate limits where the Kibble-Zurek mechanism happens. The divergence of the relaxation time, the high-temperature condition in the initial thermal equilibrium state, a new Kibble-Zurek scaling at sudden processes, and the pausing effect in the optimal protocol are presented as consequences.

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Pierre Nazé. 2024-12-02. Kibble-Zurek mechanism in driven underdamped Brownian motion. https://arxiv.org/abs/2412.01436

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