Department of Chemistry, University of Rochester, Rochester, New York 14627, USA.
J Chem Phys. 2013 Feb 7;138(5):054104. doi: 10.1063/1.4788618.
In classical mechanics, discrete breathers (DBs) - a spatial time-periodic localization of energy - are predicted in a large variety of nonlinear systems. Motivated by a conceptual bridging of the DB phenomena in classical and quantum mechanical representations, we study their signatures in the dynamics of a quantum equivalent of a classical mechanical point in phase space - a coherent state. In contrast to the classical point that exhibits either delocalized or localized motion, the coherent state shows signatures of both localized and delocalized behavior. The transition from normal to local modes have different characteristics in quantum and classical perspectives. Here, we get an insight into the connection between classical and quantum perspectives by analyzing the decomposition of the coherent state into system's eigenstates, and analyzing the spacial distribution of the wave-function density within these eigenstates. We find that the delocalized and localized eigenvalue components of the coherent state are separated by a mixed region, where both kinds of behavior can be observed. Further analysis leads to the following observations. Considered as a function of coupling, energy eigenstates go through avoided crossings between tunneling and non-tunneling modes. The dominance of tunneling modes in the high nonlinearity region is compromised by the appearance of new types of modes - high order tunneling modes - that are similar to the tunneling modes but have attributes of non-tunneling modes. Certain types of excitations preferentially excite higher order tunneling modes, allowing one to study their properties. Since auto-correlation functions decrease quickly in highly nonlinear systems, short-time dynamics are sufficient for modeling quantum DBs. This work provides a foundation for implementing modern semi-classical methods to model quantum DBs, bridging classical and quantum mechanical signatures of DBs, and understanding spectroscopic experiments that involve a coherent state.
在经典力学中，离散呼吸子（DB）-能量的时空周期性局域化-在各种非线性系统中被预测。受将 DB 现象从经典和量子力学表示中桥接的概念的启发，我们研究了它们在经典力学点的量子等效相空间中的动力学中的特征 - 相干态。与表现出弥散或局域运动的经典点不同，相干态显示出局域和弥散行为的特征。从正常模式到局域模式的转变在量子和经典观点中具有不同的特征。在这里，我们通过分析相干态分解为系统本征态，并分析这些本征态内波函数密度的空间分布，深入了解经典和量子观点之间的联系。我们发现，相干态的弥散和局域本征值分量由混合区域分开，在该混合区域中可以观察到两种行为。进一步的分析导致以下观察结果。作为耦合的函数，能量本征态经历了隧穿和非隧穿模式之间的避免交叉。在高非线性区域中，隧穿模式的主导地位因新类型模式的出现而受到损害 - 高阶隧穿模式 - 这些模式类似于隧穿模式，但具有非隧穿模式的属性。某些类型的激发优先激发高阶隧穿模式，从而可以研究它们的性质。由于自相关函数在高度非线性系统中迅速减小，因此短时间动力学足以用于建模量子 DB。这项工作为实施现代半经典方法来模拟量子 DB 提供了基础，弥合了经典和量子力学中 DB 的特征，并理解了涉及相干态的光谱实验。
