论文标题
双曲双井中波袋动力学的替代定量条件
Alternative quantisation condition for wavepacket dynamics in a hyperbolic double well
论文作者
论文摘要
我们提出了一种分析方法，用于计算特征性高度或宽度的双曲双重井潜力的相应特征状态，这超出了应用于准溶解模型的通常技术。我们将无关的Schrödinger方程映射到HEUN汇合微分方程上，该方程是通过使用无限幂序列求解的。该系列的系数是定量参数中的多项式，其根对应于系统的特征力。这导致了定量条件，使我们能够确定整个光谱，而不是单个特征力。然后，使用此方法对电子波包动力学进行了深入分析，重点是孔内隧道和先前出版物中报道的干扰诱导的量子桥[H. Chomet等人，New J. Phys。 21，123004（2019）]。考虑到不同宽度和峰位置的初始波数据包，我们计算自相关功能和Wigner Quasiprobasity分布。我们的结果与数值计算表现出了极好的一致性，并使我们能够解散控制相位动力学的不同本征频。
We propose an analytical approach for computing the eigenspectrum and corresponding eigenstates of a hyperbolic double well potential of arbitrary height or width, which goes beyond the usual techniques applied to quasi-exactly solvable models. We map the time-independent Schrödinger equation onto the Heun confluent differential equation, which is solved by using an infinite power series. The coefficients of this series are polynomials in the quantisation parameter, whose roots correspond to the system's eigenenergies. This leads to a quantisation condition that allows us to determine a whole spectrum, instead of individual eigenenergies. This method is then employed to perform an in depth analysis of electronic wave-packet dynamics, with emphasis on intra-well tunneling and the interference-induced quantum bridges reported in a previous publication [H. Chomet et al, New J. Phys. 21, 123004 (2019)]. Considering initial wave packets of different widths and peak locations, we compute autocorrelation functions and Wigner quasiprobability distributions. Our results exhibit an excellent agreement with numerical computations, and allow us to disentangle the different eigenfrequencies that govern the phase-space dynamics.
