Canonical form of Hamiltonian matrices
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.
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