可积系统的长时间渐近性和守恒律
Long-time asymptotics and conservation laws in integrable systems
摘要：
一维系统有时会表现出病态的电流缓慢衰减。这种鲁棒性可以追溯到这样一个事实，即可积模型是附近的参数空间。在可积模型中，电流的某些部分可以守恒，解释了这种缓慢的衰减。不幸的是，虽然这个守恒定律在形式上是可以预期的，但在实践中却很难在具体的例子中找到，比如海森堡模型。我们研究这个问题的分析和数值计算，发现适当的守恒定律可以是一个非解析的组合已知的本地守恒律，因此是不可见的基本假设。
英文摘要：
One dimensional systems sometimes show pathologically slow decay of currents. This robustness can be traced to the fact that an integrable model is nearby in parameter space. In integrable models some part of the current can be conserved, explaining this slow decay. Unfortunately, although this conservation law is formally anticipated, in practice it has been difficult to find in concrete cases, such as the Heisenberg model. We investigate this issue both analytically and numerically and find that the appropriate conservation law can be a non-analytic combination of the known local conservation laws and hence is invisible to elementary assumptions.
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