Semi-classical inelastic \(S\)-matrix for one-dimensional \(N\)-states systems. (English) Zbl 0835.34098

Martin, Ph. A.; Nenciu, G.

Rev. Math. Phys. 7, No. 2, 193-242 (1995).

Summary: A mathematically fully controlled study of the semi-classical \(S\)-matrix associated with one-dimensional \(N\)-states systems is presented for energies above the barriers. The transmission coefficients are described by an “effective evolution” model which at high energies approaches the usual “common trajectory” model. In the two-states case a refined Landau-Zener formula describing the cross-over regime between avoided and real crossings is obtained.

MSC:

34L40	Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.)
81U20	\(S\)-matrix theory, etc. in quantum theory

Keywords:

semi-classical \(S\)-matrix; one-dimensional \(N\)-states systems; refined Landau-Zener formula