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We show the following. \begin{theorem} Let $M$ be an finite-state ergodic time-reversible Markov chain with transition matrix $P$ and conductance $\phi$. Let $\lambda \in (0,1)$ be an eigenvalue of $P$. Then, $$\phi^2 + \lambda^2 \leq 1$$…
The time-dependent diffusion spreadability $\mathcal{S}(t)$ is a powerful dynamical probe of the microstructure of two-phase heterogeneous media across length scales [Torquato, S., \emph{Phys. Rev. E.}, 104 054102 (2021)]. It has been shown…
We study the phase mixing and dissipation of a packet of standing shear Alfv\'en waves localized in a region with non-uniform Alfv\'en background velocity. We investigate the validity of the exponential damping law in time, $\exp(-At^3)$,…
We study the effect of localisation on the propagation of a pulse through a multi-mode disordered waveguide. The correlator <u(omega1)u*(omega2)> of the transmitted wave amplitude u at two frequencies differing by delta_omega has for large…
We investigate the asymptotic behavior of a perturbation around a spatially non homogeneous stable stationary state of a one-dimensional Vlasov equation. Under general hypotheses, after transient exponential Landau damping, a perturbation…
The low-temperature transport coefficients of the degenerate periodic SU(N) Anderson model are calculated in the limit of infinite correlation between {\it f} electrons, within the framework of dynamical mean-field theory. We establish the…
We study the propagation of radiation through a disordered waveguide with a complex dielectric constant $\epsilon$, and show that dual systems, which differ only in the sign of the imaginary part of $\epsilon$, have the same localization…
We study the dominant effect of a long wavelength density perturbation $\delta(\lambda_L)$ on short distance physics. In the non-relativistic limit, the result is a uniform acceleration, fixed by the equivalence principle, and typically has…
Low-loss waveguides are required for quantum communication at distances beyond the chip-scale for any low-temperature solid-state implementation of quantum information processors. We measure and analyze the attenuation constant of…
A one-way wave equation is an evolution equation in one of the space directions that describes (approximately) a wave field. The exact wave field is approximated in a high frequency, microlocal sense. Here we derive the pseudodifferential…
The scaling properties of the conductance of a Kondo impurity connected to two leads that are in or out of equilibrium has been extensively studied, both experimentally and theoretically. From these studies, a consensus has emerged…
This is a review of the dynamics of wave propagation through a disordered N-mode waveguide in the localized regime. The basic quantities considered are the Wigner-Smith and single-mode delay times, plus the time-dependent power spectrum of…
We investigate a time-harmonic wave problem in a waveguide. By means of asymptotic analysis techniques, we justify the so-called Fano resonance phenomenon. More precisely, we show that the scattering matrix considered as a function of a…
We perform a statistical study on the frequency-dependent damping of slow waves propagating along polar plumes and interplumes in the solar corona. Analysis of a large sample of extreme ultraviolet (EUV) imaging data with high spatial and…
New results for attenuation and damping of electromagnetic fields in rigid conducting media are derived under the conjugate influence of inertia due to charge carriers and displacement current. Inertial effects are described by a relaxation…
Aims. To determine the effect of the Hall term in the generalised Ohm's law on the damping and phase mixing of Alfven waves in the ion cyclotron range of frequencies in uniform and non-uniform equilibrium plasmas. Methods. Wave damping in a…
We consider a beam and a wave equations coupled on an elastic beam through transmission conditions. The damping which is locally distributed acts through one of the two equations only; its effect is transmitted to the other equation through…
We have measured pulsed microwave transmission through quasi-1D samples with lengths up to three localization lengths. For times approaching four times the diffusion time \tau_D, transmission is diffusive in accord with the self-consistent…
A new rigorous approach for precise and efficient calculation of light propagation along non-uniform waveguides is presented. Resonant states of a uniform waveguide, which satisfy outgoing-wave boundary conditions, form a natural basis for…
The equations for Four-Wave-Mixing in a Photonic Crystal waveguide are derived accurately. The dispersive nature of slow-light enhancement, the impact of Bloch mode reshaping in the nonlinear overlap integrals and the tensor nature of the…