论文标题
由绝热不变引起的呼吸器的冷冻动力学
Frozen dynamics of a breather induced by an adiabatic invariant
论文作者
论文摘要
离散的非线性schrödinger（DNLS）方程是一种哈密顿模型，当系统出现在系统中时，它显示出非常慢的放松过程。在[Iubini S，Chirondojan L，Oppo G L，Politi A和Politi P 2019物理评论信122 084102]中，有人推测，高呼吸的冰冻动态是由于存在绝热不变的（AI）。在这里，我们在单向DNLS方程的简化上下文中证明了猜想，其中呼吸是由不受呼吸器本身影响的背景“强迫”的。我们首先澄清，呼吸动力学的非线性和强迫术语的确定性都是存在冷冻动力学的必要成分。然后，我们通过基于能量通量的估计来实现规范的扰动理论，从而得出AI的扰动表达。对AI的准确识别可以揭示突然跳跃作为主要的呼吸稳定机制的存在和作用，并且与Lévy过程具有意外的相似性。
The Discrete Nonlinear Schrödinger (DNLS) equation is a Hamiltonian model displaying an extremely slow relaxation process when discrete breathers appear in the system. In [Iubini S, Chirondojan L, Oppo G L, Politi A and Politi P 2019 Physical Review Letters 122 084102], it was conjectured that the frozen dynamics of tall breathers is due to the existence of an adiabatic invariant (AI). Here, we prove the conjecture in the simplified context of a unidirectional DNLS equation, where the breather is "forced" by a background unaffected by the breather itself. We first clarify that the nonlinearity of the breather dynamics and the deterministic nature of the forcing term are both necessary ingredients for the existence of a frozen dynamics. We then derive perturbative expressions of the AI by implementing a canonical perturbation theory and via a more phenomenological approach based on the estimate of the energy flux. The resulting accurate identification of the AI allows revealing the presence and role of sudden jumps as the main breather destabilization mechanism, with an unexpected similarity with Lévy processes.
