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Article Dans Une Revue Mathematical Models and Methods in Applied Sciences Année : 2011

Adiabatic evolution of 1D shape resonances: an artificial interface conditions approach.

Résumé

Artificial interface conditions parametrized by a complex number $\theta_{0}$ are introduced for 1D-Schr{ö}dinger operators. When this complex parameter equals the parameter $\theta\in i\R$ of the complex deformation which unveils the shape resonances, the Hamiltonian becomes dissipative. This makes possible an adiabatic theory for the time evolution of resonant states for arbitrarily large time scales. The effect of the artificial interface conditions on the important stationary quantities involved in quantum transport models is also checked to be as small as wanted, in the polynomial scale $(h^N)_{N\in \N}$ as $h\to 0$, according to $\theta_{0}$.
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Dates et versions

hal-00448868 , version 1 (20-01-2010)
hal-00448868 , version 2 (11-02-2010)
hal-00448868 , version 3 (22-02-2010)
hal-00448868 , version 4 (29-03-2010)

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Ali Faraj, Andrea Mantile, Francis Nier. Adiabatic evolution of 1D shape resonances: an artificial interface conditions approach.. Mathematical Models and Methods in Applied Sciences, 2011, 21 (3), pp.541-618. ⟨10.1142/S0218202511005143⟩. ⟨hal-00448868v4⟩
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