Microscopic dynamical origin of scale-dependent spectral correlations

Determine how specific dynamical structures in ultracold erbium collision dynamics—particularly hierarchical trapping near regular structures and the associated distribution of dynamical time scales—give rise to the observed scale-dependent spectral correlations, spectral exponents, and intermediate spectral regime.

Background

The paper finds that the Fano–Feshbach resonance spectra of ultracold 166Er and 168Er exhibit intermediate quantum-chaotic statistics: strong local level repulsion coexists with weaker higher-order correlations and reduced long-range spectral rigidity. In particular, the accumulated power spectral density shows an intermediate exponent at full spectral resolution and a tendency toward the integrable random-walk limit at intermediate decimation scales.

The authors interpret these observations as being compatible with hierarchical mixed-phase-space dynamics, in which trapping near regular structures weakens spectral rigidity at mesoscopic scales. However, the resonance spectra alone do not identify a direct mapping between particular collision-dynamical structures and the measured spectral exponents. Resolving this problem requires combining spectral-statistical analysis with a direct characterization of the underlying collision dynamics to establish the microscopic mechanism producing the observed intermediate behavior.