Vincenzo Grecchi, Andrea Sacchetti
Wannier-Bloch oscillators
(207K, Postscript)
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.
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