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Concentration-of-measure theory for structures and fluctuations of waves. (arXiv:1807.00961v1 [cond-mat.stat-mech])
来源于:arXiv
The emergence of nonequilibrium phenomena in individual complex wave systems
has long been of fundamental interests. Its analytic studies remain notoriously
difficult. Using the mathematical tool of the concentration of measure (CM), we
develop a theory for structures and fluctuations of waves in individual
disordered media. We find that, for both diffusive and localized waves,
fluctuations associated with the change in incoming waves ("wave-to-wave"
fluctuations) exhibit a new kind of universalities, which does not exist in
conventional mesoscopic fluctuations associated with the change in disorder
realizations ("sample-to-sample" fluctuations), and originate from the
coherence between the natural channels of waves -- the transmission
eigenchannels. Using the results obtained for wave-to-wave fluctuations, we
find the criterion for almost all stationary scattering states to exhibit the
same spatial structure such as the diffusive steady state. We further show that
the expectations of 查看全文>>