Lower bounds for the counting function of resonances for a perturbation of a periodic Schrödinger operator by decreasing potential

2002 ◽  
Vol 335 (12) ◽  
pp. 1013-1016 ◽  
Author(s):  
Mouez Dimassi ◽  
Maher Mnif
Keyword(s):  
Lower Bounds ◽  
Schrödinger Operator ◽  
Counting Function ◽  
Schrodinger Operator ◽  
Periodic Schrödinger Operator

scholarly journals Resonances for Perturbed Periodic Schrödinger Operator

2012 ◽  
Vol 2012 ◽  
pp. 1-12
Author(s):  
Mouez Dimassi
Keyword(s):  
Lower Bound ◽  
Schrödinger Operator ◽  
Positive Constant ◽  
Periodic Potential ◽  
Counting Function ◽  
Schrodinger Operator ◽  
Small Positive Constant ◽  
Semiclassical Regime ◽  
Perturbed Periodic ◽  
Periodic Schrödinger Operator

In the semiclassical regime, we obtain a lower bound for the counting function of resonances corresponding to the perturbed periodic Schrödinger operatorPh=-Δ+Vx+W(hx). HereVis a periodic potential,Wa decreasing perturbation andha small positive constant.

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