Asymmetry Amplification by a Nonadiabatic Passage through a Critical Point

• URL: http://arxiv.org/abs/2408.15897v2
• Date: Mon, 17 Feb 2025 02:17:19 GMT
• Title: Asymmetry Amplification by a Nonadiabatic Passage through a Critical Point
• Authors: Bhavay Tyagi, Fumika Suzuki, Vladimir A. Chernyak, Nikolai A. Sinitsyn,
• Abstract summary: We generalize the Hamiltonian dynamics of the Painleve'-2 equation to the case with many degrees of freedom. The evolution eventually leads to a highly asymmetric state, no matter how weak the symmetry breaking parameter of the Hamiltonian is. This suggests a potential mechanism for strong asymmetry in the production of quasi-particles with nearly identical characteristics.
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• Abstract: We propose and solve a minimal model of dynamic passage through a second-order phase transition in the presence of symmetry breaking interactions and no dissipation. Our model generalizes the Hamiltonian dynamics of the Painleve'-2 equation to the case with many degrees of freedom, while maintaining the integrability property. The evolution eventually leads to a highly asymmetric state, no matter how weak the symmetry breaking parameter of the Hamiltonian is. This suggests a potential mechanism for strong asymmetry in the production of quasi-particles with nearly identical characteristics. The model's integrability also yields exact exponents for the scaling of the density of the nonadiabatically excited quasi-particles.

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