Integrable time-dependent Hamiltonians, solvable Landau-Zener models and Gaudin magnets

Emil A. Yuzbashyan

doi:10.1016/j.aop.2018.01.017

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arXiv · 1802.01571

Integrable time-dependent Hamiltonians, solvable Landau-Zener models and Gaudin magnets

Emil A. Yuzbashyan

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Abstract

We solve the non-stationary Schrodinger 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 Schrodinger equation for the above models has a similar structure and is integrable with a similar technique as Knizhnikov-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.

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cond-mat.stat-mech cond-mat.quant-gas cond-mat.supr-con hep-th math-ph math.MP quant-ph

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Emil A. Yuzbashyan. 2018-02-03. Integrable time-dependent Hamiltonians, solvable Landau-Zener models and Gaudin magnets. https://doi.org/10.1016/j.aop.2018.01.017

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