Wang Guang-Lei, Ying Lei, Lai Ying-Cheng, Grebogi Celso
School of Electrical, Computer, and Energy Engineering, Arizona State University, Tempe, Arizona 85287, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2013 May;87(5):052908. doi: 10.1103/PhysRevE.87.052908. Epub 2013 May 15.
Quantum chaotic scattering is referred to as the study of quantum behaviors of open Hamiltonian systems that exhibit transient chaos in the classical limit. Traditionally a central issue in this field is how the elements of the scattering matrix or their functions fluctuate as a system parameter, e.g., the electron Fermi energy, is changed. A tacit hypothesis underlying previous works was that the underlying classical phase-space structure remains invariant as the parameter varies, so semiclassical theory can be used to explain various phenomena in quantum chaotic scattering. There are, however, experimental situations where the corresponding classical chaotic dynamics can change characteristically with some physical parameter. Multiple-terminal quantum dots are one such example where, when a magnetic field is present, the classical chaotic-scattering dynamics can change between being nonhyperbolic and being hyperbolic as the Fermi energy is changed continuously. For such systems semiclassical theory is inadequate to account for the characteristics of conductance fluctuations with the Fermi energy. To develop a general framework for quantum chaotic scattering associated with variable classical dynamics, we use multi-terminal graphene quantum-dot systems as a prototypical model. We find that significant conductance fluctuations occur with the Fermi energy even for fixed magnetic field strength, and the characteristics of the fluctuation patterns depend on the energy. We propose and validate that the statistical behaviors of the conductance-fluctuation patterns can be understood by the complex eigenvalue spectrum of the generalized, complex Hamiltonian of the system which includes self-energies resulted from the interactions between the device and the semi-infinite leads. As the Fermi energy is increased, complex eigenvalues with extremely smaller imaginary parts emerge, leading to sharp resonances in the conductance.
量子混沌散射是指对开放哈密顿系统量子行为的研究，这类系统在经典极限下表现出瞬态混沌。传统上，该领域的一个核心问题是散射矩阵的元素或其函数如何随系统参数（例如电子费米能）的变化而波动。先前工作背后隐含的一个假设是，随着参数变化，潜在的经典相空间结构保持不变，因此可以使用半经典理论来解释量子混沌散射中的各种现象。然而，在一些实验情形中，相应的经典混沌动力学可能会随着某些物理参数发生特征性变化。多端量子点就是这样一个例子，当存在磁场时，随着费米能连续变化，经典混沌散射动力学可以在非双曲和双曲之间转变。对于这类系统，半经典理论不足以解释电导随费米能的涨落特性。为了建立与可变经典动力学相关的量子混沌散射的通用框架，我们将多端石墨烯量子点系统用作典型模型。我们发现，即使在固定磁场强度下，电导也会随着费米能发生显著涨落，并且涨落模式的特征取决于能量。我们提出并验证，电导涨落模式的统计行为可以通过系统广义复哈密顿量的复本征值谱来理解，该哈密顿量包括由器件与半无限引线之间的相互作用产生的自能。随着费米能增加，会出现虚部极小的复本征值，从而导致电导出现尖锐共振。
