Displaying similar documents to “Scattering monodromy and the A 1 singularity”

Microlocalization of resonant states and estimates of the residue of the scattering amplitude

Jean-François Bony, Laurent Michel (2003)

Journées équations aux dérivées partielles

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We obtain some microlocal estimates of the resonant states associated to a resonance z 0 of an h -differential operator. More precisely, we show that the normalized resonant states are 𝒪 ( | Im z 0 | / h + h ∞ ) outside the set of trapped trajectories and are 𝒪 ( h ∞ ) in the incoming area of the phase space. As an application, we show that the residue of the scattering amplitude of a Schrödinger operator is small in some directions under an estimate of the norm of the spectral projector. Finally we prove...

Spectral projection, residue of the scattering amplitude and Schrödinger group expansion for barrier-top resonances

Jean-François Bony, Setsuro Fujiié, Thierry Ramond, Maher Zerzeri (2011)

Annales de l’institut Fourier

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We study the spectral projection associated to a barrier-top resonance for the semiclassical Schrödinger operator. First, we prove a resolvent estimate for complex energies close to such a resonance. Using that estimate and an explicit representation of the resonant states, we show that the spectral projection has a semiclassical expansion in integer powers of h , and compute its leading term. We use this result to compute the residue of the scattering amplitude at such a resonance. Eventually,...

A novel approach to the evaluation of interface roughness scattering form factor in intersubband transitions

Nguyen Thanh Tien, Pham Thi Bich Thao, Le Tuan (2014)

Nanoscale Systems: Mathematical Modeling, Theory and Applications

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We propose a modification of the interface roughness (IFR) scattering form factor in intersubband transitions.We properly derived a formula for the form factor for IFR scattering in terms of the integrals of the envelope wave functions. This novel form factor is more global nature than the old one (proposed by Ando) and may be suitable for a wide range of applications. In this paper, we calculate and compare the absorption linewidth with the application of the old form factor and novel...