Energy-dissipation anomaly in systems of localized waves

摘要

We study the statistics of the power P dissipated by waves propagating in a one-dimensional disordered medium with damping coefficient ν. An operator imposes the wave amplitude at one end, therefore injecting a power P that balances dissipation. The typical realization of P vanishes for ν → 0: Disorder leads to localization and total reflection of the wave energy back to the emitter, with negligible losses. More surprisingly, the mean dissipated power

averaged over the disorder reaches a finite limit for ν → 0. We show that this “anomalous dissipation” lim_(ν→0)

is directly given by the integrated density of states of the undamped system. In some cases, this allows us to compute the anomalous dissipation exactly, using properties of the undamped system only. As an example, we compute the anomalous dissipation for weak correlated disorder and for Gaussian white noise of arbitrary strength. Although the focus is on the singular limit ν → 0, we finally show that this approach is easily extended to arbitrary ν.