Canonical form of Hamiltonian matrices

Abstract

On the basis of shell model simulations, it is conjectured that the Lanczos construction at fixed quantum numbers defines---within fluctuations and behaviour very near the origin---smooth canonical matrices whose forms depend on the rank of the Hamiltonian, dimensionality of the vector space, and second and third moments. A framework emerges that amounts to a general Anderson model capable of dealing with ground state properties and strength functions. The smooth forms imply binomial level densities. A simplified approach to canonical thermodynamics is proposed.

4 pages 6 figures

References in corpus (2)

• Generalized seniority from random Hamiltonians
• Binomial level densities

Cited by in corpus (6)

• The Shell Model as Unified View of Nuclear Structure
• Regularities of Many-body Systems Interacting by a Two-body Random Ensemble
• Krylov fractality and complexity in generic random matrix ensembles
• Tridiagonal Hamiltonians modeling the density of states of the Double-Scaled SYK model
• Microscopic calculations of nuclear level densities with the Lanczos method
• Binomial level densities