Related papers: Quasinormal modes and complexity in saddle-dominated SU(N) spin systems

Quasinormal modes and complexity in saddle-dominated SU(N) spin systems

URL: http://arxiv.org/abs/2506.05458v1
Date: Thu, 05 Jun 2025 18:00:00 GMT
Title: Quasinormal modes and complexity in saddle-dominated SU(N) spin systems
Authors: Sergio E. Aguilar-Gutierrez, Yichao Fu, Kuntal Pal, Klaas Parmentier,
Abstract summary: We study spin systems that mimic the behavior of particles in $N$-dimensional de Sitter space for $N=2,3$.<n>We find that, even though the early-time properties of these quantities are governed by the saddle points, a close look at the late-time behavior reveals the integrable nature of the system.
Score: 0.0
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Abstract: 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.

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