弱耦合非线性链中的游荡呼吸子和自陷：宏观隧穿量子动力学的经典对应
Wandering breathers and self-trapping in weakly coupled nonlinear chains: classical counterpart of macroscopic tunneling quantum dynamics
摘要：
我们提出了分析和数值研究的相位相干动力学的内在本地化激发（呼吸）在两个弱耦合非线性振子链的系统。我们发现，有两个定性不同的动力学制度的耦合呼吸者，无论是固定的或缓慢移动：周期性的横向平移（徘徊）的低振幅呼吸链之间，和一个链本地化的高振幅呼吸。这两种耦合非线性激励模式涉及到大量的非简谐振子，可以映射到单摆方程的两个解上，由分界线模式分开。我们还研究了双链呼吸子，它可以看作是耦合链中具有不同对称性和中心位置的离散呼吸子的束缚态，以及反相双链呼吸子到单链呼吸子的分岔。描述了由多个并联耦合非线性链组成的二维系统中一维呼吸子的离域跃迁，即当呼吸子的频率或幅值低于阈值时，在给定链中初始受激的呼吸子突然将其振动能量扩散到整个二维系统.在二维系统中，阈值呼吸频率高于截止声子频率，阈值呼吸振幅与链间耦合常数的平方根成比例。二维和三维耦合非线性链系统中离散振动呼吸子的离域跃迁与二维和三维光晶格中玻色-爱因斯坦凝聚体的离域跃迁具有相似性。
英文摘要：
We present analytical and numerical studies of phase-coherent dynamics of intrinsically localized excitations (breathers) in a system of two weakly coupled nonlinear oscillator chains. We show that there are two qualitatively different dynamical regimes of the coupled breathers, either immovable or slowly-moving: the periodic transverse translation (wandering) of low-amplitude breather between the chains, and the one-chain-localization of high-amplitude breather. These two modes of coupled nonlinear excitations, which involve large number of anharmonic oscillators, can be mapped onto two solutions of a single pendulum equation, detached by a separatrix mode. We also study two-chain breathers, which can be considered as bound states of discrete breathers with different symmetry and center locations in the coupled chains, and bifurcation of the anti-phase two-chain breather into the one-chain one. Delocalizing transition of 1D breather in 2D system of a large number of parallel coupled nonlinear chains is described, in which the breather, initially excited in a given chain, abruptly spreads its vibration energy in the whole 2D system upon decreasing breather frequency or amplitude below the threshold one. The threshold breather frequency is above the cut off phonon frequency in 2D system, and the threshold breather amplitude scales as square root of the inter-chain coupling constant. Delocalizing transition of discrete vibrational breather in 2D and 3D systems of coupled nonlinear chains has an analogy with delocalizing transition for Bose-Einstein condensates in 2D and 3D optical lattices.
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