Calogero模型的PT对称形变

Antilinear deformations of Coxeter groups, an application to Calogero models

We construct complex root spaces remaining invariant under antilinear involutions related to all Coxeter groups. We provide two alternative constructions: One is based on deformations of factors of the Coxeter element and the other based on the deformation of the longest element of the Coxeter group. Motivated by the fact that non-Hermitian Hamiltonians admitting an antilinear symmetry may be used to define consistent quantum mechanical systems with real discrete energy spectra, we subsequently employ our constructions to formulate deformations of Coxeter models remaining invariant under these…

Spectral singularity and non-Hermitian PT-symmetric extension of $A_{N-1}$ type Calogero model without confining potential

We consider non-Hermitian PT-symmetric deformation of $A_{N-1}$ type Calogero model without confining potential to investigate the possible existence of spectral singularity. By considering the Wronskian between asymptotic incoming and outgoing scattering state wave functions, we found that there exist no spectral singularity in this model. We further explicitly show that the transmission coefficient vanishes and the reflection coefficient becomes unity for all values of the energy in such a momentum dependent non-Hermitian PT-symmetric model.

无约束相互作用A_{N-1} Calogero模型PT对称非厄米扩展的相移分析

Phase shift analysis of PT-symmetric nonhermitian extension of A_{N-1} Calogero model without confining interaction

本文讨论了一个多粒子量子系统，该系统是在没有限制势的$A_{N-1}$有理Calogero模型中加入非厄米但PT（宇称和时间反演）不变的相互作用而得到的.该模型产生了具有连续实谱的散射态。通过交换统计参数确定散射相移。我们发现，不同于通常的Calogero模型的情况下，排斥和交换统计参数的PT不变的相互作用的存在下，彼此不同。

PT-symmetric deformations of integrable models

We review recent results on new physical models constructed as PT-symmetrical deformations or extensions of different types of integrable models. We present non-Hermitian versions of quantum spin chains, multi-particle systems of Calogero-Moser-Sutherland type and non-linear integrable field equations of Korteweg-de-Vries type. The quantum spin chain discussed is related to the first example in the series of the non-unitary models of minimal conformal field theories. For the Calogero-Moser-Sutherland models we provide three alternative deformations: A complex extension for models related to al…

$C_λ$ -扩张振子代数及其变形和在量子力学中的应用

$C_λ$-extended oscillator algebras and some of their deformations and applications to quantum mechanics

从数学和应用的角度研究了推广Calogero-Vasiliev代数的$C_λ$ -扩张振子代数，其中$C_λ$是$λ$阶循环群.给出了代数的Casimir算子，并在数算子谱为非退化的假设下，给出了它们的酉不可约表示的完全分类.变形代数承认卡西米尔运营商类似于他们的未变形的同行寻找，产生三个新的代数结构。其中之一包括布热津斯基{ \em et al.}变形的Calogero-Vasiliev代数作为一个特殊的情况。在其玻色子Fock空间表示中，$C_λ$ -扩展振子代数作为广义变形振子代数的实现被证明提供了超对称量子力学的几个变体的玻色化：对于任何$λ$，准超对称量子力学为$p = λ-1$阶，以及对于$λ=3$，准超对称和正交超对称量子力学为二阶。

PT-对称变形的可积模型

Integrable models from PT-symmetric deformations

我们解决的问题，可积模型是否允许PT对称变形，保持其integrability。为此，我们进行了Painleve测试PT对称变形的Burgers和Korteweg-De Vries方程。我们发现，前方程允许无限多的变形，通过Painleve测试。对于一个特定的变形，我们证明了Painleve膨胀的收敛性，从而建立了这些模型，因此被认为是可积的Painleve属性。Korteweg-De Vries方程不允许通过Painleve检验的变形，但我们能够构造一个有缺陷的Painleve展开式。