Exact results for models of multichannel quantum nonadiabatic transitions
Abstract
We consider nonadiabatic transitions in explicitly time-dependent 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
- E-Print:
- 16 pages, 7 figures