标题： 非线性伽莫夫矢量，激波和光学非局部介质中的不可逆性 显示英文标题

标题： Nonlinear Gamow vectors, shock waves and irreversibility in optically nonlocal media

摘要： 色散冲击波在哈密顿系统中主导波破裂现象。 在没有损耗的情况下，这些高度不规则和无序的波可能是可逆的。 然而，关于反转色散冲击波的动力学并将其转变为规则波前的可能性，还没有实验证据。 尽管如此，相反的情况，即平滑波生成湍流动力学，在实验中已被广泛研究和观察到。 在这里，我们引入了一种新的理论公式，用于描述由非线性薛定谔方程描述的高度非局部和焦散介质中的动力学。 我们的理论揭示了一个增强不可逆程度的机制。 这个机制解释了为什么即使有任意小量的损耗，色散冲击波也无法在演化中被反转。 我们的理论基于非线性伽莫夫矢量的概念，即哈密顿系统中反直觉且至今难以捉摸的指数衰减态的功率依赖推广。 我们理论上表明，非线性伽莫夫矢量在非线性薛定谔模型中起着根本作用：它们可以作为描述冲击波动力学的广义基，并影响波破裂现象的不可逆程度。 伽莫夫矢量允许解析计算时间反演破坏的程度，并与数值解有定量一致的结果。 我们还表明，非局部非线性光学介质可以作为量子不可逆模型（如反向谐波振子）实验研究的模拟器。 显示英文摘要

摘要： Dispersive shock waves dominate wave-breaking phenomena in Hamiltonian systems. In the absence of loss, these highly irregular and disordered waves are potentially reversible. However, no experimental evidence has been given about the possibility of inverting the dynamics of a dispersive shock wave and turn it into a regular wave-front. Nevertheless, the opposite scenario, i.e., a smooth wave generating turbulent dynamics is well studied and observed in experiments. Here we introduce a new theoretical formulation for the dynamics in a highly nonlocal and defocusing medium described by the nonlinear Schroedinger equation. Our theory unveils a mechanism that enhances the degree of irreversibility. This mechanism explains why a dispersive shock cannot be reversed in evolution even for an arbitrarirly small amount of loss. Our theory is based on the concept of nonlinear Gamow vectors, i.e., power dependent generalizations of the counter-intuitive and hereto elusive exponentially decaying states in Hamiltonian systems. We theoretically show that nonlinear Gamow vectors play a fundamental role in nonlinear Schroedinger models: they may be used as a generalized basis for describing the dynamics of the shock waves, and affect the degree of irreversibility of wave-breaking phenomena. Gamow vectors allow to analytically calculate the amount of breaking of time-reversal with a quantitative agreement with numerical solutions. We also show that a nonlocal nonlinear optical medium may act as a simulator for the experimental investigation of quantum irreversible models, as the reversed harmonic oscillator.