The KAM Approach to the Spectral Analysis of Markov Generators and Nonlocal Hamiltonians
V. Chulaevsky, Yu.M. Suhov
2026, v.32, Issue 1, 45-62
ABSTRACT
We study inverse and direct spectral problems for a class of operators H = D + K acting in ℓ^2(ℤ^d), d ≥ 1. Here D is a multiplication operator, and K generalizes a lattice Laplacian and is given by a matrix (K_xy)_(x,y∈ℤ^d) with K_xx ≡ 0 and |K_x,y| ≤ ε e^(-c|x-y|^γ), where γ ∈ (0; 1), c > 0, 0 < ε ≪ 1. We streamline the existing KAM (Kolmogorov-Arnold-Moser) techniques and extend prior results, obtained for a simpler case γ = 1, to the case of a subexponential decay of the off-diagonal entries K_xy.
doi:10.61102/1024-2953-mprf.2026.32.1.002
Keywords: Anderson localization, limit-periodic potentials, long-range hopping
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