We prove that the spectrum of the discrete Schrödinger operator on ℓ2(ℤ2)(ψn,m)↦−(ψn+1,m+ψn−1,m+ψn,m+1+ψn,m−1)+Vnψn,m,(n,m)∈ℤ2,Vn∈ℓ∞(ℤ) is absolutely continuous.
Absolute Continuity of the Spectrum of Coupled Identical Systems on 1D Lattices / B. Langella, D. Bambusi. - In: MATHEMATICAL PHYSICS ANALYSIS AND GEOMETRY. - ISSN 1385-0172. - 21:4(2018), pp. 31.1-31.5.
Absolute Continuity of the Spectrum of Coupled Identical Systems on 1D Lattices
B. Langella;D. Bambusi
2018
Abstract
We prove that the spectrum of the discrete Schrödinger operator on ℓ2(ℤ2)(ψn,m)↦−(ψn+1,m+ψn−1,m+ψn,m+1+ψn,m−1)+Vnψn,m,(n,m)∈ℤ2,Vn∈ℓ∞(ℤ) is absolutely continuous.
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