代数几何与Hofstadter型模型
Algebraic Geometry and Hofstadter Type Model
摘要：
本文通过代数Bethe方程研究了Hofstadter型模型的代数几何性质。在一类Hofstadter型Hamilton算子的对角化问题中，利用高亏格谱曲线上的Baxter向量构造了Bethe方程.当谱变量位于有理曲线上时，得到了多项式Bethe方程的完全显式解，并讨论了与多项式根的Bethe不等式的关系.结合物理模型讨论了高亏格代数曲线上Bethe方程的某些代数几何性质。
英文摘要：
In this report, we study the algebraic geometry aspect of Hofstadter type models through the algebraic Bethe equation. In the diagonalization problem of certain Hofstadter type Hamiltonians, the Bethe equation is constructed by using the Baxter vectors on a high genus spectral curve. When the spectral variables lie on rational curves, we obtain the complete and explicit solutions of the polynomial Bethe equation; the relation with the Bethe ansatz of polynomial roots is discussed. Certain algebraic geometry properties of Bethe equation on the high genus algebraic curves are discussed in cooperation with the consideration of the physical model.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
