Asymmetry amplification by a nonadiabatic passage through a critical point

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 Painlev\'e-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 quasiparticles with nearly identical characteristics. The model's integrability also yields exact exponents for the scaling of the density of the nonadiabatically excited quasiparticles.