Exact results for models of multichannel quantum nonadiabatic transitions
Abstract
We consider nonadiabatic transitions in explicitly timedependent systems with Hamiltonians of the form H ̂(t ) =A ̂+B ̂t +C ̂/t , where t is time and A ̂,B ̂,C ̂ are Hermitian N ×N matrices. We show that in any model of this type, scattering matrix elements satisfy nontrivial exact constraints that follow from the absence of the Stokes phenomenon for solutions with specific conditions at t →∞ . This allows one to continue such solutions analytically to t →+∞ , and connect their asymptotic behavior at t →∞ and t →+∞ . This property becomes particularly useful when a model shows additional discrete symmetries. In particular, we derive a number of simple exact constraints and explicit expressions for scattering probabilities in such systems.
 Publication:

Physical Review A
 Pub Date:
 December 2014
 DOI:
 10.1103/PhysRevA.90.062509
 arXiv:
 arXiv:1411.4307
 Bibcode:
 2014PhRvA..90f2509S
 Keywords:

 32.70.Cs;
 42.50.Lc;
 03.65.Nk;
 02.30.Hq;
 Oscillator strengths lifetimes transition moments;
 Quantum fluctuations quantum noise and quantum jumps;
 Scattering theory;
 Ordinary differential equations;
 Condensed Matter  Mesoscale and Nanoscale Physics;
 Quantum Physics
 EPrint:
 16 pages, 7 figures