A Small-Scale Density of States Formula (original) (raw)
2003, Communications in Mathematical Physics
Let (M,g) be a C ∞ compact Riemann manifold with classical Hamiltonian, HC ∞ (T * M). Assume that the corresponding -quantization P 1 :=Op (H) is quantum completely integrable. We establish an -microlocal Weyl law on short spectral intervals of size 2−ε;∀ε>0 for various families of operators P 1 u ;uI containing P 1 , both in the mean and pointwise a.e. for uI. The -microlocalization refers to a small tubular neighbourhood of a non-degenerate, stable periodic bicharacteristic γ⊂T * M−0.
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