双梯形势垒中的量子透射与隧穿

doi:10.3969/j.issn.1007-5461.2026.03.007

量子电子学报 ›› 2026, Vol. 43 ›› Issue (3): 394-411.doi: 10.3969/j.issn.1007-5461.2026.03.007

双梯形势垒中的量子透射与隧穿

赖检辉 , 吕俊毅 , 张瑞 ,张奕亮 , 平梦超 , 刘超飞*

江西理工大学理学院, 江西赣州　341000

收稿日期:2025-08-27 修回日期:2025-12-25 出版日期:2026-05-28 发布日期:2026-05-28
通讯作者: E-mail: liuchaofei@jxust.edu.cn E-mail:E-mail: liuchaofei@jxust.edu.cn
作者简介:赖检辉 ( 2001 - ), 江西赣州人, 研究生, 主要从事量子隧穿方面的研究。E-mail: 2974556115@qq.com
基金资助:
国家自然科学基金 (12375014), 江西省青年井冈学者计划以及江西理工大学清江拔尖人才计划

Quantum transmission and tunneling in double ladder barriers

LAI Jianhui, LÜ Junyi, ZHANG Rui, ZHANG Yiliang, PING Mengchao, LIU Chaofei

School of Science, Jiangxi University of Science and Technology, Ganzhou 341000, China

Received:2025-08-27 Revised:2025-12-25 Published:2026-05-28 Online:2026-05-28

摘要/Abstract

摘要： 为探究双梯形势垒中的量子隧穿特性, 本研究通过严格的理论分析, 系统研究了双梯形势垒的量子透射行为。推导获得梯形势垒结构透射系数的精确解析解, 并揭示其与方势垒的差异: 首先, 梯形势垒结构的透射峰源于梯度势垒结构内形成的准束缚态共振, 该态的形成与特性由势垒斜率、宽度、间距及粒子能量共同决定, 其独特的非线性相位关系使得共振干涉难以完全相消反射波, 从而显著区别于传统矩形势垒的共振机制; 其次, 梯形势垒结构的透射系数呈现独特斜率依赖性, 即正斜率降低透射率, 负斜率提升透射率。研究还发现: 对于梯形势垒结构, 当入射能量低于初始势垒高度时透射受抑制, 当能量远高于初始势垒时, 透射系数与势垒排列顺序无关; 此外, 梯形势垒结构的透射系数随势垒间距呈周期性振荡, 随势垒宽度呈周期性衰减。本研究阐明了梯形势垒中量子透射的多维调控机制。

关键词: 量子力学, 透射系数, 传输矩阵法, 双梯形势垒, Airy函数

Abstract: To investigate the quantum tunneling properties in double trapezoidal barriers, this study systematically examines the quantum transmission behavior in double trapezoidal barriers via rigorous theoretical analysis. The exact analytical solutions for the transmission coefficients of trapezoidal barrier structures are derived, and their essential distinctions from those of rectangular barriers are revealed. Firstly, the transmission peaks of trapezoidal barrier structures originate from the resonances of quasi-bound states formed within the gradient barrier structures, and the formation and characteristics of these quasi-bound states are governed by the slope, width, separation, and particle energy of the barriers. Crucially, the nonlinear phase accumulation inherent to the gradient profile prevents the complete destructive interference of reflected waves during resonance, leading to a mechanism fundamentally different from that in conventional rectangular barriers. Secondly, the transmission coefficients of trapezoidal barrier structures exhibit a distinct slope dependence, where positive slopes suppress transmission and negative slopes enhance it. The study also find that for trapezoidal barrier structures, transmission is suppressed when the incident energy lies below the initial barrier height, the transmission coefficient becomes independent of the barrier sequence when the energy significantly exceeds the initial barrier height, and the transmission coefficient of the trapezoidal barrier structure oscillates periodically with barrier spacing while decaying periodically with the increasing barrier width. This work elucidates the multidimensional tuning mechanisms governing quantum transmission in double trapezoidal barriers.

Key words: quantum mechanics, transmission coefficient, transfer matrix method, double trapezoidal barriers, Airy function

中图分类号:

O413.1

赖检辉 , 吕俊毅 , 张瑞 , 张奕亮 , 平梦超 , 刘超飞. 双梯形势垒中的量子透射与隧穿[J]. 量子电子学报, 2026, 43(3): 394-411.

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双梯形势垒中的量子透射与隧穿

Quantum transmission and tunneling in double ladder barriers

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