共轭线性对称性及其对PT-对称量子理论的应用

传统量子系统的哈密顿是自伴算子,哈密顿的自伴性不仅保证系统遵循酉演化和保持概率守恒,而且也保证了它自身具有实的能量本征值,这类系统称为自伴量子系统.然而,确实存在一些物理系统(如PT-对称量子系统),其哈密顿不是自伴的,这类系统称为非自伴量子系统.为了深入研究PT-对称量子系统,并考虑到算子PT的共轭线性性,首先讨论了...     

表面等离激元在具有PT对称性的环谐振器中的传输

提出了具有PT对称性的金属-绝缘体-金属波导系统,由两个波导耦合一个环谐振器组成,环谐振器的上臂填充增益介质而下臂填充损耗介质。对表面等离激元在该系统的传输特性进行了研究,结果表明:通过平衡增益介质和损耗介质,PT对称性诱导的透明峰可以被清楚地看到,并且该透明峰具有反相位的特点。     

Supersymmetry, PT-symmetry and spectral bifurcation

We demonstrate that large class of PT-symmetric complex potentials, which can have isospectral real partner potentials, possess two different superpotentials. In the parameter domain, where the superpotential is unique, the spectrum is real and shape-invariant, leading to translational shift in a suitable parameter by real units. The case of two different superpotentials, leading to same potential, yields broken PT-symmetry, the energy spectra in the two phases being separated by a bifurcation. Interestingly, these two superpotentials generate the two disjoint sectors of the Hilbert space. In the broken case, shape invariance produces complex parametric shifts.     

PT-Symmetry, Canonical Decomposition, Perturbation Theory

Let H be any PT-symmetric Schrödinger operator of the type H=- ² +x ² +igW(x), where W is a real polynomial, odd under reflection of all coordinates, gR, acting on L ² ( R ^d ). The proof is outlined of the following statements: PH is self-adjoint and its eigenvalues coincide with the eigenvalues of (H*H). Moreover the eigenvalues of (H*H), known as the singular values of H, can be computed via perturbation theory by Borel summability.     

Is Pseudo-Hermitian Quantum Mechanics an Indefinite-Metric Quantum Theory?

With a view to eliminate an important misconception in some recent publications, we give a brief review of the notion of a pseudo-Hermitian operator, outline pseudo-Hermitian quantum mechanics, and discuss its basic difference with the indefinite-metric quantum mechanics. In particular, we show that the answer to the question posed in the title is a definite No.     

再谈“PT对称的非厄米体系的能谱性质”

本文详细讨论了具有PT对称的一维量子系统虚数势对能谱的影响,补充了《大学物理》2018年第3期《PT对称的非厄米体系的能谱性质》一文在系统维度为奇数情况下的结论.     

基于PT对称高斯势的孤子单向散射的操控

本文运用数值模拟的方法讨论在PT对称高斯势中孤子的散射问题,包括演化动力学,孤子振幅和质心位置的传输动力学以及PT对称高斯势对孤子单向散射特性的影响.结果表明在一定的参数范围内,单个孤子或孤子串的散射都能展现出单向流的特性,并且可以通过适当地调节PT对称高斯势的参数来实现孤子单向散射的操控.     

A non-Hermitian circular billiard

A perturbative form of a circular billiard with an off-centre flux line yields a non-Hermitian Hamiltonian with real spectrum. The spacing among neighbouring levels deviates from Poisson distribution (expected for integrable systems). The eigenfunctions exhibit directional property due to broken parity and time-reversal symmetries.     

Adiabatic approximation in PT-symmetric quantum mechanics

In this paper, we present a quantitative sufficient condition for adiabatic approximation in PT-symmetric quantum mechanics, which yields that a state of the PT-symmetric quantum system at any time will remain approximately in the m-th eigenstate up to a multiplicative phase factor whenever it is initially in the m-th eigenstate of the Hamiltonian. In addition, we estimate the approximation errors by the distance and the fidelity between the exact solution and the adiabatic approximate solution to the time evolution equation, respectively.     

Solution of Schrodinger Equation for Two-Dimensional Complex Ouartic Potentials

We investigate the quasi-exact solutions of the Schrodinger wave equation for two-dimensional non-hermitian complex Hamiltonian systems within the frame work of an extended complex phase space characterized by x = x1 ＋ ip3, y = x2 ＋ ip4, px= p1＋ ix3, py= p2 ＋ ix4. Explicit expressions of the energy eigenvalues and the eigenfunctions for ground and first excited states for a complex quartic potential are obtained. Eigenvalue spectra of some variants of the complex quartic potential, including PT-symmetrie one, are also worked out.