$\mathcal{PT}$-Supersymmetric Square Well and Barrier

Taha Koohrokhi

英文摘要：

The Parity-Time ($\mathcal{PT}$) symmetric potentials are derived by non-Hermitian supersymmetric quantum mechanics for square well and barrier. These $\mathcal{PT}$-supersymmetric square well and barrier. The partners have complex partners. The partners are isospectral with real energies. $\mathcal{PT}$-symmetry is only unbroken for the bound states.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

阅读原文

阅读 PDF ↗

arXiv 页面 ↗HTML 原文 ↗

本文内容

英文摘要相关论文

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

继续探索

相关论文

Supersymmetric partners of the harmonic oscillator with an infinite potential barrier

Supersymmetry transformations of first and second order are used to generate Hamiltonians with known spectra departing from the harmonic oscillator with an infinite potential barrier. It is studied also the way in which the eigenfunctions of the initial Hamiltonian are transformed. The first and certain second order supersymmetric partners of the initial Hamiltonian possess third-order differential ladder operators. Since systems with this kind of operators are linked with the Painlevé IV equation, several solutions of this non-linear second-order differential equation will be simply found.

2013-12-09hep-thmath-phmath.MP

Barrier Penetration for Supersymmetric Shape-Invariant Potentials

Exact reflection and transmission coefficients for supersymmetric shape-invariant potentials barriers are calculated by an analytical continuation of the asymptotic wave functions obtained via the introduction of new generalized ladder operators. The general form of the wave function is obtained by the use of the F-matrix formalism of Froman and Froman which is related to the evolution of asymptotic wave function coefficients.

1999-10-13nucl-thquant-ph

Extended WKB method, resonances and supersymmetric radial barriers

Semiclassical approximations are implemented in the calculation of position and width of low energy resonances for radial barriers. The numerical integrations are delimited by t/T<<8, with t the period of a classical particle in the barrier trap and T the resonance lifetime. These energies are used in the construction of `haired' short range potentials as the supersymmetric partners of a given radial barrier. The new potentials could be useful in the study of the transient phenomena which give rise to the Moshinsky's diffraction in time.

2011-03-18hep-thnucl-thquant-ph

Electronic transport in two-dimensional strained Dirac materials under multi-step Fermi velocity barrier: transfer matrix method for supersymmetric systems

In recent years, graphene and other two-dimensional Dirac materials like silicene, germanene, etc. have been studied from different points of view: from mathematical physics, condensed matter physics to high energy physics. In this study, we utilize both supersymmetric quantum mechanics (SUSY-QM) and transfer matrix method (TTM) to examine electronic transport in two-dimensional Dirac materials under the influences of multi-step deformation as well as multi-step Fermi velocity barrier. The effects of multi-step effective mass and multi-step applied fields are also taken into account in our inv…

2021-10-15cond-mat.mes-hallquant-ph

$\mathcal{N}=2$ supersymmetry and anisotropic scale invariance

We find a class of scale-anomaly-free $\mathcal{N}=2$ supersymmetric quantum systems with non-vanishing potential terms where space and time scale with distinct exponents. Our results generalise the known case of the supersymmetric inverse square potential to a larger class of scaling symmetries.

2018-05-21hep-thmath-phmath.MP

Supersymmetric model of a Bose-Einstein condensate in a $\mathcal{PT}$-symmetric double-delta trap

The most important properties of a Bose-Einstein condensate subject to balanced gain and loss can be modelled by a Gross-Pitaevskii equation with an external $\mathcal{PT}$-symmetric double-delta potential. We study its linear variant with a supersymmetric extension. It is shown that both in the $\mathcal{PT}$-symmetric as well as in the $\mathcal{PT}$-broken phase arbitrary stationary states can be removed in a supersymmetric partner potential without changing the energy eigenvalues of the other state. The characteristic structure of the singular delta potential in the supersymmetry formalism…

2014-12-24cond-mat.quant-gasquant-ph

更多相关论文收起更多论文

Conformal bridge transformation, $\mathcal{PT}$- and super- symmetry

Supersymmetric extensions of the 1D and 2D Swanson models are investigated by applying the conformal bridge transformation (CBT) to the first order Berry-Keating Hamiltonian multiplied by $i$ and its conformally neutral enlargements. The CBT plays the role of the Dyson map that transforms the models into supersymmetric generalizations of the 1D and 2D harmonic oscillator systems, allowing us to define pseudo-Hermitian conjugation and a suitable inner product. In the 1D case, we construct a $\mathcal{PT}$-invariant supersymmetric model with $N$ subsystems by using the conformal generators of su…

2022-08-24hep-thmath-phmath.MP

Supersymmetric approach to exact solutions of $(1+1)$-dimensional time-independent Klein-Gordon equation : Application to a position-dependent mass and a $\mathcal{PT}$-symmetric vector potential

Rigorous use of SUSYQM approach applied for Klein-Gordon equation with scalar and vector potentials is discussed. The method is applied to solve exactly, for bound states, two models with position-dependent masses and $\mathcal{PT}$-symmetric vector potentials, depending on some parameters. The necessary conditions on the parameters to get physical solutions are described. Some special cases are also derived by adjusting the parameters of the models.

2019-11-25quant-ph

On Quantum Semipermeable Barriers: Investigating Maxwell's Demon Toolbox

We study quantum Maxwell's demon in a discrete space-time setup. We consider a collection of particles hopping on a one-dimensional chain and a semipermeable barrier that allows the particles to hop in only one direction. Our main result is a formulation of a local unitary dynamics describing the action of this barrier. Such dynamics utilises an auxiliary system $\mathcal{A}$ and we study how properties of $\mathcal{A}$ influence the behaviour of particles. An immediate consequence of unitarity is the fact that particles cannot be trapped on one side of the barrier forever, unless $\mathcal{A}…

2021-05-25quant-ph

源自超对称哈密顿量平方根的类$\u0001PT$相变

$\mathcal{PT}$-like phase transitions from square roots of supersymmetric Hamiltonians

Basque Center for Applied Mathematics（巴斯克应用数学中心）；Department of Electrical and Computer Engineering, Saint Louis University（圣路易斯大学电气与计算机工程系）

本研究提出一种基于超对称伙伴哈密顿量平方根构造的通用框架，可在无显式宇称-时间对称性的非厄米系统中实现类$\u0001PT$相变，揭示了非厄米物理与超对称的新关联，为光子阵列设计提供新途径。

2025-11-16physics.opticsquant-ph