18 Nov 2025 Tue 4 pm

In quantum chaotic systems the Hamiltonian’s symmetries determine which of three classes the statistical correlations between the energy eigenvalues fall into. A symplectic symmetry is associated with the strongest degree of level repulsion, and it also implies a Kramers degeneracy. We analyse the spectral statistics of three contact-interacting particles in a spherical harmonic trap and find numerical evidence of strong level repulsion for weak interactions. Notably, we observe multiple statistical signatures of a symplectic symmetry despite Kramers degeneracy not being present. For strong interactions the statistics are consistent with regular behaviour with either Poissonian or "stick" statistics depending on relative particle mass. The transition between these two regimes as a function of interaction strength is well described by the Rosenzweig-Porter model. Further, this system is currently realisable with current experimental techniques.

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