 97411 Vincenzo Grecchi, Andrea Sacchetti
 WannierBloch oscillators
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Jul 21, 97

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Abstract. We consider a WannierStark problem for small field $f$ in the oneladder
case. We prove
that a generical first band state is a metastable state (WannierBloch
oscillator) with the
lifetime determined by the imaginary part of the WannierStark 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.
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