TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.18.6.212
TI  - Knizhnik-Zamolodchikov equations and integrable hyperbolic Landau-Zener models
PY  - 2025/06/27
UR  - https://scipost.org/SciPostPhys.18.6.212
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 18
IS  - 6
SP  - 212
A1  - Barik, Suvendu
AU  - Bakker, Lieuwe
AU  - Gritsev, Vladimir
AU  - Yuzbashyan, Emil
AB  - We study the relationship between integrable Landau-Zener (LZ) models and Knizhnik-Zamolodchikov (KZ) equations. The latter are originally equations for the correlation functions of two-dimensional conformal field theories, but can also be interpreted as multi-time Schrödinger equations. The general LZ problem is to find probabilities of tunneling from eigenstates at $t=t_\text{in}$ to eigenstates at $t\to+∞$ for an $N× N$ time-dependent Hamiltonian $\hat H(t)$. A number of such problems are exactly solvable in the sense that their tunneling probabilities are elementary functions of Hamiltonian parameters. Recently, it has been proposed that exactly solvable LZ models of this type map to KZ equations. Here we use this connection to identify and solve a class of integrable LZ models with hyperbolic time dependence, $\hat H(t)=\hat A+\hat B/t$, for $N=2, 3$, and $4$, where $\hat A$ and $\hat B$ are time-independent matrices.
ER  -

@Article{10.21468/SciPostPhys.18.6.212,
	title={{Knizhnik-Zamolodchikov equations and integrable hyperbolic Landau-Zener models}},
	author={Suvendu Barik and Lieuwe Bakker and Vladimir Gritsev and Emil A. Yuzbashyan},
	journal={SciPost Phys.},
	volume={18},
	pages={212},
	year={2025},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.18.6.212},
	url={https://scipost.org/10.21468/SciPostPhys.18.6.212},
}