Shechao Feng

Correlations in coherent multiple scattering

Abstract We present details of calculations and a comprehensive review on the various correlation functions for coherent electronic or classical wave transmission through a disordered scattering medium, in the diffusive limit λ 《 l∗ 《 Lφ, where λ is the wavelength, l∗ is the transport mean free path, and Lφ is the phase coherence length. The connection between mesoscopic conductance fluctuations in disordered metals and speckle pattern fluctuations for classical waves is reviewed. The short-range correlation function C(1) is shown to be responsible for the conventional speckle pattern fluctuations and the so called “memory effect”. The long-range correlation function C(2) is shown to dominate in the correlations and fluctuations of the total transmission coefficient. The “infinite range” background correlation function C(3) is shown to be related to the universal conductance fluctuations in disordered mesoscopic conductors. We also discuss many generalized correlation functions such as those for frequency correlations, spatial correlations, correlations in Fabry-Perot interferometer devices, and in reflection geometries. A special kind of correlation function, corresponding to the sensitivity of speckle pattern intensities to the motion of impurities, will also be reviewed. Finally, the equivalence between the angular correlation functions and the auto-correlation functions in “diffusing wave spectroscopy” will be discussed.

Acoustical nondestructive evaluation of heterogeneous materials in the multiple scattering regime

Multiple scattering blurs the distinction between different material systems beyond a certain distance from the observation point, thereby rendering most random systems cloudy in appearance and opaque in the sense of structure delineation. However, based on a theoretical analysis, it will be shown that, due to the phase coherent nature of wave propagation through random media, some remnant information is still present which can be used to detect and locate new growing cracks. This offers the possibility to extend acoustic nondestructive evaluation techniques in the realm of highly heterogeneous media, such as composites or concrete analyzed by high‐frequency sound waves.

Quantum transport in the presence of phase-breaking scattering : generalized landauer formula

Abstract The problem of quantum transport in the presence of phase-breaking scattering is formulated, using a model Hamiltonian for the electron-phonon coupling which can be solved exactly. This allows one to write down a generalized Landauer formula, which is valid in the presence of phase-breaking scattering, thus opening up an entire new regime of possible analytical and numerical calculations of electron transport properties at finite temperatures. We illustrate the applications of this new transport formalism with a phase-breaking scattering by an Einstein phonon model, and the suppression of hc/e oscillations of a ballistic Aharonov-Bohm ring.

Non-Destructive Evaluations in Multiple-Scattering Media

It has recently been shown theoretically that imaging of a new defect in a multiple-scattering medium is in principle possible using speckle pattern correlations. We perform extensive numerical simulations and analytical calculations to illustrate the feasibility of detecting a new crack in a single given sample already containing many cracks using speckle pattern averaging technique at many different frequencies. Potential applications of our approach can be found in medical and industrial imaging needs in highly scattering systems.

Can sound be localized in granular media

Abstract Liu and Nagel have reported recently [Phys. Rev. Lett. 68 (1992) 2301] a set of measurements involving sound propagation in an unconsolidated granular glass beads system (an artificial “sand”). In order to rationalize qualitatively and quantitatively the reported results, we propose the physical picture that sound waves are multiply scattered at grain-grain contacts and are thus in the diffusive regime, close to Anderson localization. This suggests a deep link between the quest for experimental observation of strong localization for classical waves and the physics of unconsolidated granular media.

Magnetoplasmons in a quasi-one-dimensional quantum wire

Plasmon spectra in a quasi-1D quantum wire under a transverse magnetic field are calculated within the random phase approximation (RPA) in the long-wavelength limit. We find interesting collective behaviours corresponding to the edge state electrons in both intrasubband and intersubband (between occupied subbands) excitations. The various plasmon modes show anomalous magnetic field dependences. The intrasubband and some segments of the intersubband excitation frequencies decrease with increasing field. These results are in good agreement with experiment.

Nondestructive evaluations in multiple scattering media

Due to its tendency to scramble the structural information, multiple scattering blurs the distinction between different materials containing different kinds and numbers of defects, or their configurations, beyond the scattering mean‐free‐path distance from the observation point, thereby rendering most random systems cloudy in appearance and opaque in the sense of structure delineation. However, it has recently been shown theoretically [Feng and Sornette, J. Acoust. Soc. Am. 90, 1742–1747 (1991)] that imaging of a new defect in a multiple scattering medium is in principle possible using speckle pattern correlations. Extensive numerical simulations and analytical calculations were performed to demonstrate the feasibility of detecting a new crack in a single given sample already containing many cracks using speckle pattern averaging technique at many different frequencies. Potential applications of this approach can be found in medical and industrial imaging needs in highly scattering systems.

Wide variable integer quantum Hall plateaus in macroscopic high mobility 2DEG with a smooth confining potential

Abstract We consider theoretically the integer quantum Hall effect (IQHE) in macroscopic high mobility 2DEG systems subject to a smooth confining potential V ( y ), within the framework of the semiclassical approximation. We find that edge state transport, which has so far been associated with the IQHE in narrow channel devices, dominates also in this case, as V ( y ) serves to break the degeneracy among different Landau states. This leads to variable wide quantum Hall plateaus, such that the dissipative “riser” region can be significantly reduced experimentally by adjusting the confining potential V ( y ) via appropriate multiple or resistive gate voltages.

Collective excitations of edge state electrons in quasi-one-dimensional quantum well wires

Abstract Collective excitations of edge state electrons in a quasi-one-dimensional quantum well wire under a large transverse magnetic field at zero temperature are investigated theoretically. The plasmon modes for both intrasubband and intersubband excitations are found at different magnetic field strengths and quasi-1D electron density, in the long wavelength limit. The plasmon dispersion relations, which are all acoustic-like, also show an anisotropy which can be attributed to the applied field and the finite width of the wire. These predictions are amenable to experimental verifications.

Conductance of a quantum channel containing a small number of impurities

Abstract The crossover properties of the quantum conductance in a 1D constriction from the ballistic to the diffusive regime are investigated analytically. In the ballistic regime, the well-known plateau structures are found. As more impurities are added to the system, we are able to show that interesting “dip” structures should be found when new quantum channels become open. The higher the new quantum channel index, the deeper the dip will be. When the degree of disorder increases, the ensemble-averaged conductance is shown to be reduced, but the dip structure can still be seen as long as the diffusive regime is not reached. Our analytical results are in agreement with recent experiments as well as numerical simulations.