Energy-dissipation anomaly in systems of localized waves

Area of Science:

• Wave propagation in disordered systems
• Condensed matter physics
• Statistical mechanics

Background:

• Wave propagation in disordered media often leads to Anderson localization.
• Dissipation is typically expected to decrease with vanishing damping.
• Understanding energy transport and loss in such systems is crucial.

Purpose of the Study:

• To investigate the statistics of dissipated power in a damped, one-dimensional disordered medium.
• To analyze the behavior of dissipated power as damping approaches zero.
• To identify the underlying physical mechanism for anomalous dissipation.

Main Methods:

• Analyzing the power statistics under imposed wave amplitude at one end.
• Investigating the singular limit of vanishing damping coefficient (ν→0).
• Relating the mean dissipated power to the integrated density of states.

Main Results:

• The typical dissipated power vanishes as damping approaches zero due to wave localization.
• A surprising, finite mean dissipated power (anomalous dissipation) is observed in the ν→0 limit.
• This anomalous dissipation is shown to be equal to the integrated density of states of the undamped system.

Conclusions:

• Anomalous dissipation in disordered systems is directly determined by the integrated density of states.
• This finding allows for exact calculations of anomalous dissipation using undamped system properties.
• The developed approach is applicable to various types of disorder and damping coefficients.