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

基于精确WKB方法的PT对称性量子系统研究

• 批准号: 14540376
• 负责人: SUZUKI Junji
• 金额: $ 1.86万
• 依托单位: Shizuoka University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2002
• 资助国家: 日本
• 起止时间: 2002 至 2004
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-14540376/
• 关键词: integrable system; exact WKB; quantum mechanics

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.

我们揭示了共形场论和某些类别的常微分方程之间的奇怪对应关系。通过利用这一点，对 PT 对称量子系统的许多方面进行了定量研究。特别是，针对具有六次势的系统评估 PT 对称相和破缺对称相之间的相分离曲线。还找到了缩放限制之前的对应关系。由此，我们利用晶格模型（六顶点模型）的知识分析了Heun方程解的解析性质。还研究了激发态在三阶微分方程中的作用。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。

项目成果

An application of the Bethe ansatz method to certain classes of ODE

Bethe ansatz 方法在某些 ODE 类中的应用

• 发表时间: 2005
• 期刊: RIMS Kokyuryoku 1424
• 作者: 鈴木淳史;Junji Suzuki;Junji Suzuki
• 通讯作者: Junji Suzuki

Junji Suzuki: "Stokes multipliers, spectral determinants and T-Q relations"京都大学数理解析研講究録. 1221. 21-37 (2001)

铃木顺二：《斯托克斯乘子、谱行列式和T-Q关系》京都大学数学分析研究记录1221. 21-37 (2001)。

Excited state Nonlinear integral equations for an integrable anisotropi spin-1 chain

可积各向异性自旋 1 链的激发态非线性积分方程

• 发表时间: 2004
• 期刊: J.Phys.A Math.Gen 37
• 作者: 鈴木淳史;Junji Suzuki;Junji Suzuki;Junji Suzuki;Junji Suzuki;Junji Suzuki;Junji Suzuki
• 通讯作者: Junji Suzuki

Junji Suzuki: "The dilute AL models and the integrable perturbations of unitary minimal CFTS"Journal of Physics A. 37. 511-520 (2004)

Junji Suzuki：“稀 AL 模型和酉最小 CFTS 的可积扰动”物理学杂志 A. 37. 511-520 (2004)

The dilute A_L models and the Φ_<1,2> perturbation of unitary minimal CFT_s

稀A_L模型和酉最小CFT_s的Φ_<1,2>摄动

• 发表时间: 2005
• 期刊: Journal of Statistical mechanics JANUARY(P01004)
• 作者: 鈴木淳史;Junji Suzuki;Junji Suzuki;Junji Suzuki;Junji Suzuki;Junji Suzuki
• 通讯作者: Junji Suzuki