非赫密PT對稱漢米爾頓及贋赫密性之探討

The formulation of non-Hermitian PT-symmetric Hamiltonians and pseudo-Hermiticity

孫國洪(Gwo-Hong Suen)

指導教授 ： 李慶德

國立臺灣大學/理學院/物理研究所/博士(2007年)

https://doi.org/10.6342/NTU.2007.02425

摘要

無資料

關鍵字

非赫密PT對稱漢米爾頓及贋赫密性之探討

並列摘要

In recent years there has been much interest in non-Hermitian Hamiltonians with real eigenvalues. In particular, PT-symmetric Hamiltonians H, i.e., , where P is the parity operator and T is the time reversal operator, have been conjectured to have a real spectrum except when the symmetry is spontaneously broken. It is also known that PT symmetry is not a necessary condition for the occurrence of real eigenvalues. Then, -pseudo-Hermiticity, i.e., , was introduced to establish the mathematical relation with PT symmetry and explored the basic structure responsible for the reality of the spectrum of non-Hermitian Hamiltonians. Because of intrinsic interest and their applications in condensed matter, quantum optics and others, we study the pseudo-Hermitian interactions in both non-relativistic and relativistic quantum mechanics by considering several examples about delocalization transition in superconductors and spin-orbit coupling in semiconductors. In addition, the pseudo-supersymmetry and boson sea are studied. Finally, the PT-symmetric quantum field theory, Klein-Gordon-type field and quantum cosmology are discussed, too.

Keywords:
Pseudo unitarity; Pseudo-Hyper-virial theorem; Pseudo-probability current density; Pseudo-supersymmetry; Boson sea; Abnormal pseudo-Hermitian fermion; PT-symmetric quantum field theory; Klein-Gordon-type field.

並列關鍵字

The formulation of non-Hermitian PT-symmetric

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