Analytic expression of the DOS for a new model of 1d-potential and its random perturbation
arxiv(2024)
摘要
In this article we present comparisons between the spectrum of a
one-dimensional Schrödinger operator for a particular periodic potential and
for its restriction to a finite number of sites. We deduce from this finite,
but large, number of sites, the Integrated Density of States (IDS) associated
to the Hamiltonian operator whose derivate is the DOS. The exact formula for
the IDS is given and the expression of the DOS is analytical. All our
calculations are done on the particular periodic Airy-potential, which is a new
case for which one has an analytical expression of the DOS. It is a continuous,
periodic potential, piecewise affine. As a periodic operator, the spectrum is a
band spectrum.
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