论文标题
可集成和不可集成的模型有多近：基于Salerno模型的参数案例研究
How close Are Integrable and Non-integrable Models: A Parametric Case Study Based on the Salerno Model
论文作者
论文摘要
在目前的工作中，我们将Salerno模型重新审视为典型的系统，该系统在众所周知的可集成系统（Ablowitz-Ladik晶格）和实验可探讨的不可汇总的系统（离散的非线性Schrödinger模型）之间进行了插值。我们提出的问题是：对于“通用”初始数据，与非整合模型的集成程度有多近？我们对这个问题的更精确的表述是：在不可综合的情况下，以前保守数量的恒定量如何？在研究了这一点后，我们发现，即使在Salerno模型的情况下，也可以通过测量这些以前保守的数量来敏感地感受到与集成性的偏差。但是，鉴于对这些数量的知识需要对系统进行深层的物理和数学分析，因此我们寻求更“通用”的诊断，以表现出可集成性破坏的表现。我们根据我们的Salerno模型计算来争辩说，Lyapunov指数的全范围可能是对此效果的敏感诊断。
In the present work we revisit the Salerno model as a prototypical system that interpolates between a well-known integrable system (the Ablowitz-Ladik lattice) and an experimentally tractable non-integrable one (the discrete nonlinear Schrödinger model). The question we ask is: for "generic" initial data, how close are the integrable to the non-integrable models? Our more precise formulation of this question is: how well is the constancy of formerly conserved quantities preserved in the non-integrable case? Upon examining this, we find that even slight deviations from integrability can be sensitively felt by measuring these formerly conserved quantities in the case of the Salerno model. However, given that the knowledge of these quantities requires a deep physical and mathematical analysis of the system, we seek a more "generic" diagnostic towards a manifestation of integrability breaking. We argue, based on our Salerno model computations, that the full spectrum of Lyapunov exponents could be a sensitive diagnostic to that effect.
