We study metastable behavior in a discrete nonlinear Schrodinger equation from the viewpoint of Hamiltonian systems theory. When there are $n < \infty$ sites in this equation, we consider initial conditions in which almost all the energy is concentrated in one end of the system. We are interested in understanding how energy flows through the system, so we add a dissipation of size $\gamma$ at the opposite end of the chain, and we show that the energy decreases extremely slowly. Furthermore, the motion is localized in the phase space near a family of breather solutions for the undamped system. We give rigorous, asymptotic estimates for the rate of evolution along the family of breathers and the width of the neighborhood within which the trajectory is confined.

中文翻译：

---

耗散下哈密顿呼吸器的衰减

我们从哈密顿系统理论的角度研究离散非线性薛定谔方程中的亚稳态行为。当这个方程中有 $n < \infty$ 位点时，我们考虑几乎所有能量都集中在系统一端的初始条件。我们有兴趣了解能量如何流经系统，因此我们在链的另一端添加了大小为 $\gamma$ 的耗散，并且我们表明能量下降非常缓慢。此外，运动位于无阻尼系统的呼吸器解决方案系列附近的相空间中。我们对沿呼吸器家族的进化速率和轨迹所限制的邻域的宽度给出了严格的渐近估计。