Long-time asymptotics and conservation laws in integrable systems

Understand

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.