# gst: symmetry breaking in time-dependent billiards.

AA << investigate symmetry breaking in a time-dependent billiard that undergoes a continuous phase transition when dissipation is introduced. The system presents unlimited velocity, and thus energy growth for the conservative dynamics. When inelastic collisions are introduced between the particle and the boundary, the velocity reaches a plateau after the crossover iteration. The system presents the expected behavior for this type of transition, including scale invariance, critical exponents related by scaling laws, and an order parameter approaching zero in the crossover iteration. >>

AA << analyze the velocity spectrum and its averages for dissipative and conservative dynamics. The transition point in velocity behavior caused by the physical limit of the boundary velocity and by the introduced dissipation coincides with the crossover interaction obtained from the Vrms (root mean sq V) curves. Additionally, (they) examine the velocity distributions, which lose their symmetry once the particle's velocity approaches the lower limit imposed by the boundary's motion and the system's control parameters. This distribution is also characterized analytically by an expression P(V,n), which attains a stationary state, with a well-defined upper bound, only in the dissipative case. >>

Anne Kétri Pasquinelli da Fonseca, Edson Denis Leonel. Symmetry breaking in time-dependent billiards. arXiv: 2505.20488v1 [nlin.CD]. May 26, 2025.

https://arxiv.org/abs/2505.20488

Also: billiard, transition, dissipation,  in https://www.inkgmr.net/kwrds.html 

Keywords: gst, billiard, particles, transitions, dissipation, symmetry breaking, inelastic collisions.

# gst: necklacelike pattern of vortex bound states

<< A vortex is a topological defect in the superconducting condensate when a magnetic field is applied to a type-II superconductor, (..). Because of the confinement of the quasiparticles by a vortex, it exhibits a circular-shaped pattern of bound states with discrete energy levels, (..) >>

 Here, AA << report a completely new type of vortex pattern which is necklacelike in an iron-based superconductor (..). (AA) theoretical analysis shows that this necklacelike vortex pattern arises primarily from selective off-shell interference between vortex bound states of opposite angular momenta in the presence of rotational symmetry breaking due to disorders. >>

<< This fascinating effect can be observed in a system with a small Fermi energy and wave vector, conditions fortuitously met in (Their) samples. (AA) results not only disclose a novel vortex structure, but also unravel a completely new quantum phenomenon in the superconducting condensate. >>️

Zhiyong Hou, Kailun Chen, et al. Necklacelike Pattern of Vortex Bound States. Phys. Rev. X 15, 011027. Feb 7, 2025.   https://journals.aps.org/prx/abstract/10.1103/PhysRevX.15.011027   arXiv: 2407.08547v1 [cond-mat.supr-con]. Jul 11, 2024.    https://arxiv.org/abs/2407.08547

Also: vortex, disorder, disorder & fluctuations, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, vortex, vortex bound states, symmetry breaking, disorder, disorder & fluctuations, necklacelike patterns