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arXiv · 2505.06048

Exact S-matrices for higher dimensional representations of generalized Landau-Zener Hamiltonians

S. Malikis·V. Cheianov
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Abstract

We explore integrable Landau-Zener-type Hamiltonians through the framework of Lie algebraic structures. By reformulating the classic two-level Landau-Zener model as a Lax equation, we show that higher-spin generalizations lead to exactly solvable scattering matrices, which can be computed efficiently for any higher-spin representation. We further extend this approach to generalized bow-tie Landau-Zener Hamiltonians, employing non-Abelian gauge fields that satisfy a zero-curvature condition to derive their scattering matrices algebraically. This method enables the systematic construction of new exactly solvable multi-level models; as a result, we present previously unknown six-dimensional and eight-dimensional Landau-Zener models.

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S. Malikis, V. Cheianov. 2025-05-09. Exact S-matrices for higher dimensional representations of generalized Landau-Zener Hamiltonians. https://arxiv.org/abs/2505.06048

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