Degenerate LandauZener model: Analytical solution
Abstract
The exact analytical solution of the degenerate LandauZener model, wherein two bands of degenerate energies cross in time, is presented. The solution is derived by using the MorrisShore transformation, which reduces the fully coupled system to a set of independent nondegenerate twostate systems and a set of decoupled states. Due to the divergence of the phase of the offdiagonal element of the propagator in the original LandauZener model, not all transition probabilities exist for infinite time duration. In general, apart from some special cases, only the transition probabilities between states within the same degenerate set exist, but not between states of different sets. An illustration is presented for the transition between the magnetic sublevels of two atomic levels with total angular momenta J=2 and 1.
 Publication:

Physical Review A
 Pub Date:
 January 2007
 DOI:
 10.1103/PhysRevA.75.013417
 arXiv:
 arXiv:0909.5396
 Bibcode:
 2007PhRvA..75a3417V
 Keywords:

 32.80.Bx;
 03.65.Ge;
 34.70.+e;
 Level crossing and optical pumping;
 Solutions of wave equations: bound states;
 Charge transfer;
 Quantum Physics
 EPrint:
 Physical Review A 75, 013417 (2007)