Floquet operators without absolutely continuous spectrum. (English) Zbl 0795.47032

Nenciu, G.

Ann. Inst. Henri Poincaré, Phys. Théor. 59, No. 1, 91-97 (1993).

Summary: We extend some recent results of J. S. Howland [ibid. 50, No. 3, 309-334 (1989; Zbl 0689.34022 and 689.34023)], concerning the absence of absolutely continuous spectrum of Floquet operators for time periodic perturbations of discrete Hamiltonians with increasing gaps. Our results cover the case of \(n\) coupled pulsed rotors (the case \(n=1\) has been considered by Bellissard): \[ {\mathbf H}(t)= -{d^ 2\over d\theta^ 2} \text{\textbf{1}}_ n+{\mathbf V}(\theta,t) \] on \(0< \theta< 2\pi\) with periodic boundary conditions, and \(V_{i,j}(\theta,t)\in {\mathcal C}^ 2\); \(i,j=1,\dots,n\).

MSC:

47E05	General theory of ordinary differential operators
47A10	Spectrum, resolvent
34B15	Nonlinear boundary value problems for ordinary differential equations

Keywords:

absolutely continuous spectrum of Floquet operators; time periodic perturbations of discrete Hamiltonians with increasing gaps; coupled pulsed rotors; periodic boundary conditions

Citations:

Zbl 0689.34022; Zbl 0689.34023

References:

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