97-411 Vincenzo Grecchi, Andrea Sacchetti

Wannier-Bloch oscillators (207K, Postscript) Jul 21, 97

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Abstract. We consider a Wannier-Stark problem for small field $f$ in the one-ladder case. We prove that a generical first band state is a metastable state (Wannier-Bloch oscillator) with the lifetime determined by the imaginary part of the Wannier-Stark ladder. The infinite resonances of the ladder cause Bloch oscillations as a global beating effect. For an adiabatic time $\tau =ft$ large enough, but much smaller than the resonance lifetime, we have a new version of the acceleration theorem and well specified Bloch oscillators. In the $x$ representation and in the adiabatic scale: $x\to x(f)=\xi /f+y$ the state vanishes externally to a pulsating region of $|\xi |$ defined by $|\xi |<\xi^+(\tau )$ where $\xi^+(n)=0$ and $\xi^+ (n+1/2)$ is the maximum value equal to the first band width. For $\xi$ and $\tau$ such that $|\xi |$ is in this region and for $y$ in a fixed domain, the state approaches a finite combination of oscillating Bloch states. --=====================_869519544==_ Content-Type: text/plain; charset="us-ascii"

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