We investigate long-range intensity correlations on both sides of the Anderson transition of classical waves in a three-dimensional disordered material. Our ultrasonic experiments are designed to unambiguously detect a recently predicted infinite-range C0 contribution, due to local density of states fluctuations near the source. We find that these C0 correlations, in addition to C2 and C3 contributions, are significantly enhanced near mobility edges. Separate measurements of the inverse participation ratio reveal a link between C0 and the anomalous dimension Δ2, implying that C0 may also be used to explore the critical regime of the Anderson transition.
We report an in-depth investigation of the Anderson localization transition for classical waves in three dimensions (3D). Experimentally, we observe clear signatures of Anderson localization by measuring the transverse confinement of transmitted ultrasound through slab-shaped mesoglass samples. We compare our experimental data with predictions of the self-consistent theory of Anderson localization for an open medium with the same geometry as our samples. This model describes the transverse confinement of classical waves as a function of the localization (correlation) length, ξ (ζ), and is fitted to our experimental data to quantify the transverse spreading/confinement of ultrasound all of the way through the transition between diffusion and localization. Hence we are able to precisely identify the location of the mobility edges at which the Anderson transitions occur.
PACS 43.35.Yb, 63.50.+x Using ultrasonic techniques, the phonon diffusion coefficient and density of states have been measured at intermediate frequencies in a porous solid network of sintered glass beads. A transition to a very strong scattering regime is observed, whereupon the diffusion coefficient becomes independent of frequency. Near crossover, the density of states is enhanced and exhibits a broad maximum. These data are in good overall agreement with a lattice-based percolation model, and give additional insight into the effects of strong scattering on phonon transport in disorderd media. 1 Introduction Porous media form an interesting class of mesoscopic materials, whose structure at length scales between atomic dimensions and bulk dramatically influence their phonon properties. Examples include packed powders, porous sintered particle networks, aerogels and foams [1][2][3][4][5]. In the low frequency, long wavelength limit, the medium appears uniform and the phonons propagate ballistically, but with a reduced velocity that reflects the weakening of the structure due to its porosity. By contrast, at intermediate frequencies where the wavelength is comparable with the pore size, the scattering can become very strong and the nature of wave propagation is substantially modified. Thus, wave propagation is expected to become diffusive, and the phonons may even become localized. In materials such as sinters, where the basic building block of the structure is much larger than atomic dimensions, a third high frequency regime exists at wavelengths less than the particle size, where phonons propagate freely inside the particles and their character is similar to uniform bulk materials.In this paper, we study the intermediate frequency regime, using ultrasonic techniques to investigate the vibrational modes of a model porous material formed from sintered networks of spherical glass particles. We show that very strong scattering is indeed observed, and directly measure the phonon diffusion coefficient over more than a decade in frequency. The transition to the strong scattering regime is marked by the onset of a plateau in the diffusion coefficient, which is found to be remarkably small. To obtain complementary information on the nature of the vibrational modes of these sintered networks, we also investigate the density of states in and above the crossover region using a novel mode counting technique [5]. Insight into these experimental results is provided by numerical simulations of phonon transport in a model 3D lattice percolation system [6,7], originally performed to elucidate the thermal conductivity plateau in glasses, and by the extensive theoretical work on vibrational localization and transport in random media stimulated by the pioneering ideas of Alexander and Orbach [8].
Temporal fluctuations in the phase of waves transmitted through a dynamic, strongly scattering, mesoscopic sample are investigated using ultrasonic waves, and compared with theoretical predictions based on circular Gaussian statistics. The fundamental role of phase in Diffusing Acoustic Wave Spectroscopy is revealed, and phase statistics are also shown to provide a sensitive and accurate way to probe scatterer motions at both short and long time scales.PACS numbers: 43.35.+d, 42.25.Dd, 43.60.Cg, 81.70.Cv For all waves, phase is irrefutably the most fundamental property. On macroscopic scales, however, phase is randomized by multiple scattering or obscured by decoherence. It is now generally accepted that a mesoscopic regime exists where wave phenomena persist on even hydrodynamic scales. Mesoscopic fluctuations can sometimes be long-range and non-Gaussian [1,2]. The universal conductance fluctuations are best known, originally discovered for electrons [3], and later also observed with visible light [4] and microwaves [5]. In the optics of soft condensed matter, the existence of dynamic mesoscopic fluctuations has led to a new technique called diffusing wave spectroscopy (DWS) [6]. In the acoustic counterpart, diffusing acoustic wave spectroscopy (DAWS) [7], the fluctuations of the scattered wave field are measured directly to probe the dynamics of disordered media. In seismology, the closely related technique of Coda Wave Interferometry [8] is extending the range of applications being studied.For acoustic, seismic or radio waves, the phase can be easily extracted. While many applications, including interferometric techniques such as InSAR [9], make use of phase for precise measurements, the phase of multiply scattered waves has often been neglected, since it is generally more challenging to extract useful information from phase in multiple-scattering systems. Mesoscopic studies have revealed the fundamental relation of phase to the screening of zeros of random fields [10], but most of the literature has focussed on quantities such as the probability distribution functions of intensity, transmission or conductance [1], and does not address the phase directly. Recent studies with microwaves [11], infrared light [12] and Terahertz radiation [13] have explored frequency correlations of the phase. In this Letter, we study time-dependent phase fluctuations of ultrasound in a dynamic, strongly scattering medium, and examine the statistics of both the wrapped and cumulative phase evolution. This combination of theory and experiment reveals a deeper insight into the mesoscopic physics of multiply scattered waves, and explicitly shows the relationship between the average phase evolution of a typical multiple scattering path -a crucial concept in D(A)WS modelling [6,7] -and the measured phase evolution of the transmitted waves. We also find that phase statistics can sometimes provide a more accurate method of measuring the dynamics than the field autocorrelation method that is used in D(A)WS. In our materials, the tempo...
A statistical method for measuring the modal density of elastic waves through direct mode counting in strongly scattering disordered systems is presented. To illustrate this approach, the results of ultrasonic experiments in a highly porous sintered glass bead network are reported. This method is shown to yield a reliable and robust measurement of the density of states, enabling mode-counting techniques to be applied to increasingly complex systems, where modal overlap and sensitivity to experimental conditions have previously hampered definitive results.
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