Integrable time-dependent Hamiltonians, solvable Landau–Zener models and Gaudin magnets
- Department of Physics and Astronomy, Rutgers University, Piscataway, NJ 08854 (United States)
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.
- OSTI ID:
- 22848311
- Journal Information:
- Annals of Physics, Vol. 392; Other Information: © 2018 Elsevier Inc. All rights reserved.; Country of input: International Atomic Energy Agency (IAEA); ISSN 0003-4916
- Country of Publication:
- United States
- Language:
- English
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