PT-symmetric knotting of coordinates: a new, topological mechanism of quantum confinement

Breakdown of separability due to confinement, submitted to Report on mathematical physics

A simple system of two particles in a bidimensional configurational space $S$ is studied. The possibility of breaking in $S$ the time independent Schrödinger equation of the system into two separated one-dimensional one-body Schrödinger equations is assumed. In this paper, we focus on how the latter property is countered by imposing such boundary conditions as confinement in a limited region of $S$ and/or restrictions on the joint coordinate probability density stemming from the sign-invariance condition of the relative coordinate (an impenetrability condition). Our investigation demonstrates …

Two-electron resonances in quasi-one dimensional quantum dots with Gaussian confinement

We consider a quasi one-dimensional quantum dot composed of two Coulombically interacting electrons confined in a Gaussian trap. Apart from bound states, the system exhibits resonances that are related to the autoionization process. Employing the complex-coordinate rotation method, we determine the resonance widths and energies and discuss their dependence on the longitudinal confinement potential and the lateral radius of the quantum dot. The stability properties of the system are discussed.

N identical particles under quantum confinement: A many-body dimensional perturbation theory approach II, the lowest-order wave function II

In this paper, the second in a series of two, we complete the derivation of the lowest-order wave function of a dimensional perturbation theory (DPT) treatment for the N-body quantum-confined system. Taking advantage of the symmetry of the zeroth-order configuration, we use group theoretic techniques and the FG matrix method from quantum chemistry to obtain analytic results for frequencies and normal modes. This method directly accounts for each two-body interaction, rather than an average interaction so that even lowest-order results include beyond-mean-field effects. It is thus appropriate f…

Ladder Operators for Quantum Systems Confined by Dihedral Angles

We report the identification and construction of raising and lowering operators for the complete eigenfunctions of isotropic harmonic oscillators confined by dihedral angles, in circular cylindrical and spherical coordinates; as well as for the hydrogen atom in the same situation of confinement, in spherical, parabolic and prolate spheroidal coordinates. The actions of such operators on any eigenfunction are examined in the respective coordinates, illustrating the possibility of generating the complete bases of eigenfunctions in the respective coordinates for both physical systems. The relatio…

对偶-$q$ 量子力学中的有效几何和位置相关质量

Effective Geometry and Position-Dependent Mass in Dual-$q$ Quantum Mechanics

通过坐标和波函数变换，将Borges对偶-$q$框架中的非线性薛定谔方程转化为具有位置相关质量的线性方程，揭示了有效几何结构，并分析了参数$q$对束缚态谱和隧穿的影响。

氧化亚铜量子阱中的连续谱束缚态

Bound states in the continuum in cuprous oxide quantum wells

本文提出在氧化亚铜量子阱中通过调节激子约束强度实现连续谱束缚态，并用数值精确解验证了少通道耦合薛定谔方程计算线宽的准确性，表明该体系是实验识别BICs的便捷平台。