2025/06/05 by Sergio E. Aguilar-Gutierrez, Aguilar-Gutierrez, Sergio E., Y. W. Fu +4 · 2 citations
Physics and Astronomy · #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Quantum Mechanics and Non-Hermitian Physics #Quantum Physics (quant-ph) #Quantum chaos and dynamical systems #Quantum many-body systems
paper · pdf · doi:10.48550/arxiv.2506.05458
openalex publication_date 2025/06/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study SU(N) spin systems that mimic the behavior of particles in N-dimensional de Sitter space for N=2,3. Their Hamiltonians describe a dynamical system with hyperbolic fixed points, leading to emergent quasinormal modes at the quantum level. These manifest as quasiparticle peaks in the density of states. For a particle in 2-dimensional de Sitter, we find both principal and complementary series densities of states from a PT-symmetric version of the Lipkin-Meshkov-Glick model, having two hyperbolic fixed points in the classical phase space. We then study different spectral and dynamical properties of this class of models, including level spacing statistics, two-point functions, squared commutators, spectral form factor, Krylov operator and state complexity. We find that, even though the early-time properties of these quantities are governed by the saddle points -- thereby in some cases mimicking corresponding properties of chaotic systems, a close look at the late-time behavior reveals the integrable nature of the system.