Abstract
We consider a reduced two-channel model of an atom consisting of a quantum dot coupled to an open scattering channel described by a three-dimensional Laplacian. We are interested in the survival probability of a bound state when the dot energy varies smoothly and adiabatically in time. The initial state corresponds to a discrete eigenvalue which dives into the continuous spectrum and re-emerges from it as the dot energy is varied in time and finally returns to its initial value. Our main result is that for a large class of couplings, the survival probability of this bound state vanishes in the adiabatic limit. At the end of the paper, we present a short outlook on how our method may be extended to cover other classes of Hamiltonians; details will be given elsewhere.
Original language | English |
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Article number | 1850011 |
Journal | Reviews in Mathematical Physics |
Volume | 30 |
Issue number | 5 |
Number of pages | 25 |
ISSN | 0129-055X |
DOIs | |
Publication status | Published - 2018 |
Keywords
- gapless adiabatic theorem
- adiabatic limit
- adiabatic pair creation
- mesoscopic transport
- resolvent expansion
- Feshbach method
- propagation estimates