Studies on Quantum systems with PT symmetry based on the exact WKB method

我们揭示了保形场论和某些类型的常微分方程式之间的奇怪对应。利用这一点，我们对PT对称量子系统的许多方面进行了定量研究。特别是，对于一个具有六次位势的体系，计算了PT对称相与破缺对称相之间的相分离曲线。还找到了标度极限之前的对应关系。在此基础上，我们利用格子模型(六顶点模型)的知识分析了Heun方程解的解析性质，并研究了激发态在三阶微分方程组中的作用。为了激活研究人员之间的互动，我们于2004年7月在静冈大学组织了一次关于量子力学前沿、PT对称性、准精确可解性、精确WKB的会议。

We unveil curious correspondence between a conformal field theory and certain classed of ordinary differential equations. By utilizing this, many aspects of the PT symmetric Quantum systems are investigated quantitatively. Especially, the phase separation curve between the PT symmetric and the broken symmetry phases are evaluated for a system with the sextic potential. The correspondence before the scaling limit is also found. By this, we analysis the analytic properties of solutions to the Heun equations utilizing the knowledge on the lattice model (the six vertex model).The role of excited states in the 3 rd order differential equations are also studied. To activate the interaction between researchers, we organize a conference on the "Frontier in Quantum Mechanics, PT symmetry, quasi exact solvability, exact WKB" at Shizuoka University, July '04.