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

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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.