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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2506.05458 |
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| _version_ | 1866909762219671552 |
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| author | Aguilar-Gutierrez, Sergio E. Fu, Yichao Pal, Kuntal Parmentier, Klaas |
| author_facet | Aguilar-Gutierrez, Sergio E. Fu, Yichao Pal, Kuntal Parmentier, Klaas |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_05458 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quasinormal modes and complexity in saddle-dominated SU(N) spin systems Aguilar-Gutierrez, Sergio E. Fu, Yichao Pal, Kuntal Parmentier, Klaas High Energy Physics - Theory Quantum Physics 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. |
| title | Quasinormal modes and complexity in saddle-dominated SU(N) spin systems |
| topic | High Energy Physics - Theory Quantum Physics |
| url | https://arxiv.org/abs/2506.05458 |