Quantum Backlund transformation for the integrable DST model
Quantum Backlund transformation for the integrable DST model
复制标题
可积 DST 模型的量子 Backlund 变换
DOI：
10.1088/0305-4470/33/1/311
复制
发表时间：
1999
期刊：
影响因子：
--
通讯作者：
E.K.Sklyanin
中科院分区：
文献类型：
--
作者：
V.B.Kuznetsov;M.Salerno;E.K.Sklyanin
对于离散自陷 (DST) 模型的可积情况，我们构造了一个贝克伦德变换。还发现并研究了对偶Lax矩阵和相应的对偶B´acklund变换。贝克伦德变换（Q 算子）的量子模拟被构造为具有无限维辅助空间的单性矩阵的迹。我们将 Q 算子表示为显式积分算子，并在单项式基础上描述其作用。结果，我们获得了量子可积 DST 模型的多元多项式本征函数的一系列积分方程。这些特征函数是 Heun 类的特殊函数，超出了超几何类。所发现的积分方程是新的，它们将为此类复杂函数的有效分析和数值研究提供基础。
For the integrable case of the discrete self-trapping (DST) model we construct a B¨acklund transformation. The dual Lax matrix and the corresponding dual B¨acklund transformation are also found and studied. The quantum analog of the B¨acklund transformation ( Q -operator) is constructed as the trace of a monodromy matrix with an infinite-dimensional auxiliary space. We present the Q -operator as an explicit integral operator as well as describe its action on the monomial basis. As a result we obtain a family of integral equations for multivariable polynomial eigenfunctions of the quantum integrable DST model. These eigenfunctions are special functions of the Heun class which is beyond the hypergeometric class. The found integral equations are new and they shall provide a basis for efficient analytical and numerical studies of such complicated functions.