TY - JOUR
T1 - An Egorov Theorem for Avoided Crossings of Eigenvalue Surfaces
AU - Fermanian Kammerer, Clotilde
AU - Lasser, Caroline
N1 - Publisher Copyright:
© 2017, Springer-Verlag Berlin Heidelberg.
PY - 2017/8/1
Y1 - 2017/8/1
N2 - We study nuclear propagation through avoided crossings of electron energy levels. We construct a surface hopping semigroup, which gives an Egorov-type description of the dynamics. The underlying time-dependent Schrödinger equation has a two-by-two matrix-valued potential, whose eigenvalue surfaces have an avoided crossing. Using microlocal normal forms reminiscent of the Landau–Zener problem, we prove convergence to the true solution in the semi-classical limit.
AB - We study nuclear propagation through avoided crossings of electron energy levels. We construct a surface hopping semigroup, which gives an Egorov-type description of the dynamics. The underlying time-dependent Schrödinger equation has a two-by-two matrix-valued potential, whose eigenvalue surfaces have an avoided crossing. Using microlocal normal forms reminiscent of the Landau–Zener problem, we prove convergence to the true solution in the semi-classical limit.
UR - http://www.scopus.com/inward/record.url?scp=85019259242&partnerID=8YFLogxK
U2 - 10.1007/s00220-017-2890-1
DO - 10.1007/s00220-017-2890-1
M3 - Article
AN - SCOPUS:85019259242
SN - 0010-3616
VL - 353
SP - 1011
EP - 1057
JO - Communications in Mathematical Physics
JF - Communications in Mathematical Physics
IS - 3
ER -