ADIABATIC EVOLUTION OF 1D SHAPE RESONANCES: AN ARTIFICIAL INTERFACE CONDITIONS APPROACH

作者：Faraj Ali^*; Mantile Andrea; Nier Francis

来源：Mathematical Models and Methods in Applied Sciences, 2011, 21(3): 541-618.

DOI：10.1142/S0218202511005143

• Shape resonances
• spectral theory
• asymptotic analysis
• adiabatic theorem

Artificial interface conditions parametrized by a complex number theta(0) are introduced for 1D-Schrodinger operators. When this complex parameter equals the parameter theta is an element of iR 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 erect 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 is an element of N) as h -> 0, according to theta(0).

• 出版日期2011-3