Abstract
We solve the non-stationary Schrödinger equation for several time-dependent Hamiltonians, such as the BCS Hamiltonian with an interaction strength inversely proportional to time, periodically driven BCS and linearly driven inhomogeneous Dicke models as well as various multi-level Landau–Zener tunneling models. The latter are Demkov–Osherov, bow-tie, and generalized bow-tie models. We show that these Landau–Zener problems and their certain interacting many-body generalizations map to Gaudin magnets in a magnetic field. Moreover, we demonstrate that the time-dependent Schrödinger equation for the above models has a similar structure and is integrable with a similar technique as Knizhnik–Zamolodchikov equations. We also discuss applications of our results to the problem of molecular production in an atomic Fermi gas swept through a Feshbach resonance and to the evaluation of the Landau–Zener transition probabilities.
Original language | English (US) |
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Pages (from-to) | 323-339 |
Number of pages | 17 |
Journal | Annals of Physics |
Volume | 392 |
DOIs | |
State | Published - May 2018 |
All Science Journal Classification (ASJC) codes
- Physics and Astronomy(all)
Keywords
- Gaudin magnets
- Integrable time-dependent Hamiltonians
- Knizhnik–Zamolodchikov equations
- Landau–Zener models