• 主题
高级搜索  >
历史搜索 清空历史
首页> 外文学位 >Topics in PT-symmetric Quantum Mechanics and Classical Systems
【24h】

Topics in PT-symmetric Quantum Mechanics and Classical Systems

机译：PT对称量子力学与经典系统中的主题

获取原文
获取原文并翻译 | 示例
页面导航
  • 摘要
  • 著录项
  • 相似文献
  • 相关主题

摘要

Space-time reflection symmetry, or PT symmetry, first proposed in quantum mechanics by Bender and Boettcher in 1998 [2], has become an active research area in fundamental physics. This dissertation contains several research problems which are more or less related to this field of study. After an introduction on complementary topics for the main projects in Chap.1, we discuss about an idea which is originated from the remarkable paper by Chandrasekar et al in Chap.2. They showed that the (second-order constant-coefficient) classical equation of motion for a damped harmonic oscillator can be derived from a Hamiltonian having one degree of freedom. We gives a simple derivation of their result and generalizes it to the case of an nth-order constant-coefficient differential equation.;In Chap.3 we studied the analytical continuation of the coupling constant g of a coupled quantum theory. We get to this conclusion that one can, at least in principle, arrive at a state whose energy is lower than the ground state of the theory. The idea is to begin with the uncoupled g = 0 theory in its ground state, to analytically continue around an exceptional point (square-root singularity) in the complex-coupling-constant plane, and finally to return to the point g = 0. In the course of this analytic continuation, the uncoupled theory ends up in an unconventional state whose energy is lower than the original ground-state energy. However, it is unclear whether one can use this analytic continuation to extract energy from the conventional vacuum state; this process appears to be exothermic but one must do work to vary the coupling constant g.;PT-symmetric quantum mechanics began with a study of the Hamiltonian H=p2+x2(ix) epsilon. When epsilon ≥ 0, this portion of parameter space is known as the region of unbroken PT symmetry. The region of unbroken PT symmetry has been studied but the region of broken PT symmetry which is related to the negative epsilon has thus far been unexplored. In Chap.4 we present a detailed numerical and analytical examination of the behavior of the eigenvalues for 4 < epsilon < 0. In particular, it reports the discovery of an infinite-order exceptional point at epsilon = 1, a transition from a discrete spectrum to a partially continuous spectrum at epsilon = 2, a transition at the Coulomb value epsilon = 3, and the behavior of the eigenvalues as epsilon approaches the conformal limit epsilon = 4.;Finally in Chap.5 we devised a simple and accurate numerical technique for finding eigenvalues, node structure, and expectation values of PT-symmetric potentials. The approach involves expanding the solution to the Schrodinger equation in series involving powers of both the coordinate and the energy. The technique is designed to allow one to impose boundary conditions in PT-symmetric pairs of Stokes sectors. The method is illustrated by using many examples of PT-symmetric potentials in both the unbroken- and broken-PT-symmetric regions.
机译：时空反射对称性或PT对称性最早是由Bender和Boettcher于1998年在量子力学中提出的[2]，现已成为基础物理学中一个活跃的研究领域。本文包含了与该研究领域或多或少相关的几个研究问题。在介绍了第1章中主要项目的补充主题之后，我们讨论了一个想法，该想法源自Chandrasekar等人在第2章中的非凡论文。他们表明，阻尼谐波振荡器的（二阶常系数）经典运动方程可以从具有一个自由度的哈密顿量导出。我们给出它们的结果的简单推导并将其推广到n阶常系数微分方程的情况。在第三章中，我们研究了耦合量子理论的耦合常数g的解析连续性。我们得出的结论是，至少在原理上可以达到一种能量低于理论基态的状态。这个想法是从处于其基态的非耦合g = 0理论开始，以解析方式围绕复数耦合常数平面中的一个例外点（平方根奇点）继续，最后返回到点g = 0。在这种分析的延续过程中，非耦合理论以一种非常规状态结束，其能量低于原始的基态能量。但是，尚不清楚是否可以使用这种解析连续性从常规真空状态中提取能量。这一过程似乎是放热的，但必须做一些工作来改变耦合常数g。； PT对称量子力学始于对哈密顿量H = p2 + x2（ix）ε的研究。当ε≥0时，这部分参数空间称为不间断的PT对称区域。已经研究了PT对称性未破坏的区域，但是到目前为止，还没有探索与负ε相关的PT对称性破坏的区域。在第4章中，我们对4

著录项

  • 作者

    Hassanpour, Nima.;

  • 作者单位

    Washington University in St. Louis.;

  • 授予单位 Washington University in St. Louis.;
  • 学科 Quantum physics.;Physics.;Mathematics.
  • 学位 Ph.D.
  • 年度 2018
  • 页码 163 p.
  • 总页数 163
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

相似文献

  • 外文文献
  • 中文文献
  • 专利
获取原文

客服邮箱：kefu@zhangqiaokeyan.com

京公网安备：11010802029741号 ICP备案号：京ICP备15016152号-6 六维联合信息科技 (北京) 有限公司©版权所有

  • 客服微信

  • 服务号