Continuity of the spectrum of quasi-periodic Schrödinger operators with finitely differentiable potentials
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DOI: 10.1017/etds.2018.48
Abstract: In this paper, we consider the spectrum of discrete quasi-periodic Schrödinger operators on $\ell ^{2}(\mathbb{Z})$ with the potentials $v\in C^{k}(\mathbb{T})$ . For sufficiently large $k$ , we show that the Lebesgue measure of the spectrum… read more here.
Keywords: periodic schr; schr; quasi periodic; schr dinger ... See more keywords
Large coupling asymptotics for the Lyapunov exponent of finitely smooth quasi-periodic Schrödinger operators
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DOI: 10.1088/1361-6544/abc597
Abstract: We quantify the coupling asymptotics for the Lyapunov exponent of the quasi-periodic Schrödinger operator with two classes of finitely smooth potentials, which are well-studied in [23, 26]. We remark that the rate of convergence in… read more here.
Keywords: lyapunov exponent; coupling asymptotics; asymptotics lyapunov; periodic schr ... See more keywords
On a class of nonself-adjoint multidimensional periodic Schrödinger operators
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DOI: 10.3906/mat-1906-69
Abstract: We investigate the multidimensional Schrodinger operator L(q) with complex-valued periodic, with respect to a lattice, potential q when the Fourier coefficients of q with respect to the orthogonal system {exp(i(a,x))}, where a changes in the… read more here.
Keywords: adjoint multidimensional; class; multidimensional periodic; class nonself ... See more keywords