Effect of chaos on relativistic quantum tunneling

X. Ni, Liang Huang, Y. Lai, L. Pecora
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引用次数: 13

Abstract

We solve the Dirac equation in two spatial dimensions in the setting of resonant tunneling, where the system consists of two symmetric cavities connected by a finite potential barrier. The shape of the cavities can be chosen to yield both regular and chaotic dynamics in the classical limit. We find that certain pointer states about classical periodic orbits can exist, which suppress quantum tunneling, and the effect becomes less severe as the underlying classical dynamics in the cavity is chaotic, leading to regularization of tunneling dynamics even in the relativistic quantum regime. Similar phenomena have been observed in graphene. A physical theory is developed to explain the phenomenon based on the spectrum of complex eigenenergies of the non-Hermitian Hamiltonian describing the effectively open cavity system.
混沌对相对论量子隧穿的影响
在共振隧穿的情况下,我们在两个空间维度上求解狄拉克方程,其中系统由两个由有限势垒连接的对称腔组成。可以选择空腔的形状,以在经典极限下产生规则和混沌动力学。我们发现经典周期轨道的某些指针态可以抑制量子隧穿,并且由于腔内底层经典动力学是混沌的,这种影响变得不那么严重,导致即使在相对论量子状态下隧穿动力学也会正则化。在石墨烯中也观察到类似的现象。基于描述有效开腔系统的非厄米哈密顿量的复特征能谱,提出了一种物理理论来解释这一现象。
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