Universal Predictions for Statistical Nuclear Correlations

Abstract

We explore the behavior of collective nuclear excitations under a multi-parameter deformation of the Hamiltonian. The Hamiltonian matrix elements have the form $P(|H_{ij}|)\propto 1/\sqrt{|H_{ij}|}\exp (-|H_{ij}|/V)$, with a parametric correlation of the type $\log ⟨H(x)H(y)⟩\propto -|x-y|$. The studies are done in both the regular and chaotic regimes of the Hamiltonian. Model independent predictions for a wide variety of correlation functions and distributions which depend on wavefunctions and energies are found from parametric random matrix theory and are compared to the nuclear excitations. We find that our universal predictions are observed in the nuclear states. Being a multi-parameter theory, we consider general paths in parameter space and find that universality can be effected by the topology of the parameter space. Specifically, Berry's phase can modify short distance correlations, breaking certain universal predictions.

Latex file + 12 postscript figures

References in corpus (4)

• Chaos {\sl vs} Thermalization in the Nuclear Shell Model
• Universal Parametric Correlations of Eigenfunctions in Chaotic and Disordered Systems
• Phase-Space Exploration in Nuclear Giant Resonance Decay
• Levy Diffusion and Classes of Universal Parametric Correlations

Cited by in corpus (7)

• Random Matrix Theories in Quantum Physics: Common Concepts
• A Uniform Approximation for the Fidelity in Chaotic Systems
• Entanglement and localization transitions in eigenstates of interacting chaotic systems
• Eigenstate entanglement between quantum chaotic subsystems: universal transitions and power laws in the entanglement spectrum
• Quantum Diffusion and Tunneling with Parametric Banded Random Matrix Hamiltonians
• Topological Dependence of Universal Correlations in Multi-Parameter Hamiltonians
• Relating computational complexity and quantum spectral complexity