Properties of certain matrices related to the equilibrium configuration of the one-dimensional many-body problems with the pair potentialsV1(x)=−log ∣sinx∣ andV2(x)=1/sin2x
Properties of certain matrices related to the equilibrium configuration of the one-dimensional many-body problems with the pair potentialsV1(x)=−log ∣sinx∣ andV2(x)=1/sin2x
复制标题
与具有势对 V1(x)=−log ∣sinx∣ 且 V2(x)=1/sin2x 的一维多体问题的平衡配置相关的某些矩阵的性质
DOI：
10.1007/bf01614245
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发表时间：
1978
影响因子：
2.4
通讯作者：
A. Perelomov
中科院分区：
文献类型：
--
作者：
F. Calogero;A. Perelomov
本文证明了在平衡状态下，具有对电位sv1 (x)= - log∣sinx∣和v2 (x)=1/sin2x的一维多体问题的某些矩阵具有非常简单的结构。这些矩阵表征了这些系统在其平衡构型周围的小振荡，对于第二个系统，Lax矩阵证明了它的可积性。
It is shown that at equilibrium certain matrices associated to the one-dimensional many-body problems with the pair potentialsV1(x)=−log∣sinx∣ andV2(x)=1/sin2xhave a very simple structure. These matrices are those that characterize the small oscillations of these systems around their equilibrium configurations, and, for the second system, the Lax matrices that demonstrate its integrability.