arXiv subjects

S. K. Cheung

Publications and source records attributed to S. K. Cheung.

6 recordsLinked to original sources

arXiv2009

Reply to arXiv:0709.2619 "Comment on 'Scaling behavior of classical wave transport in mesoscopic media at the localization transition' [arXiv:cond-mat/0509381]"

We argue from both technical and physical points of view that the main result shown in the Comment [arXiv:0709.2619] by Cherrolet et al. [Phys. Rev. B 80, 037101 (2009)] as well as the authors' interpretations of the result are not sufficient to draw the conclusion that the scaling law at the mobility edge takes the form T \propto 1/L^2. On the other hand, we believe that the result shows some evidence of T \propto ln L/L^2 behavior found in S. K. Cheung and Z. Q. Zhang, Phys. Rev. B 72, 235102 (2005) [arXiv:cond-mat/0509381]. More calculations with even larger L's are necessary to give a more definitive answer to this question.

cond-mat.dis-nn↗

arXiv2008

Dynamics of Localized Waves

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 τ_D, transmission is diffusive in accord with the self-consistent theory of localization for the renormalized diffusion coefficient in space and frequency, D(z,Ω). For longer times, the transmission decay rate first agrees with and later falls increasingly below the self-consistent theory. Beyond the Heisenberg time, the decay rate approaches the predictions of a dynamic single parameter scaling model which reflects the decay of long-lived localized modes and converges to the results of 1D simulations.

cond-mat.dis-nn↗

arXiv2005

Large Photonic Band Gaps in Certain Periodic and Quasi-Periodic Networks in two and three dimensions

The photonic band structures in certain two- and three-dimensional periodic networks made of one-dimensional waveguides are studied by using the Floquet-Bloch theorem. We find that photonic band gaps exist only in those structures where the fundamental loop exhibits anti-resonant transmission. This is also true for quasi-periodic networks in two and three dimensions, where the photonic band structures are calculated from the spectra of total transmission arising from a source inside the samples. In all the cases we have studied, it is also found that the gap positions in a network are dictated by the frequencies at which the anti-resonance occurs.

cond-mat.dis-nn↗

arXiv2005

The Scaling Behavior of Classical Wave Transport in Mesoscopic Media at the Localization Transition

The propagation of classical wave in disordered media at the Anderson localization transition is studied. Our results show that the classical waves may follow a different scaling behavior from that for electrons. For electrons, the effect of weak localization due to interference of recurrent scattering paths is limited within a spherical volume because of electron-electron or electron-phonon scattering, while for classical waves, it is the sample geometry that determine the amount of recurrent scattering paths that contribute. It is found that the weak localization effect is weaker in both cubic and slab geometry than in spherical geometry. As a result, the averaged static diffusion constant D(L) scales like ln(L)/L in cubic or slab geometry and the corresponding transmission follows ~ln L/L^2. This is in contrast to the behavior of D(L)~1/L and ~1/L^2 obtained previously for electrons or spherical samples. For wave dynamics, we solve the Bethe-Salpeter equation in a disordered slab with the recurrent scattering incorporated in a self-consistent manner. All of the static and dynamic transport quantities studied are found to follow the scaling behavior of D(L). We have also considered position-dependent weak localization effects by using a plausible form of position-dependent diffusion constant D(z). The same scaling behavior is found, i.e., ~ln L/L^2.

cond-mat.dis-nn↗

arXiv2005

Impact of Weak Localization on Wave Dynamics: Crossover from Quasi-1D to Slab Geometry

We study the dynamics of wave propagation in nominally diffusive samples by solving the Bethe-Salpeter equation with recurrent scattering included in a frequency-dependent vertex function, which renormalizes the mean free path of the system. We calculate the renormalized time-dependent diffusion coefficient, D(t), following pulsed excitation of the system. For cylindrical samples with reflecting side walls and open ends, we observe a crossover in dynamics in the transformation from a quasi-1D to a slab geometry implemented by varying the ratio of the radius, R, to the length, L. Immediately after the peak of the transmitted pulse, D(t) falls linearly with a nonuniversal slope that approaches an asymptotic value for R/L>>1. The value of D(t) extrapolated to t=0, depends only upon the dimensionless conductance g for R/L<<1 and upon kl and L for R/L>>1, where k is the wave vector and l is the bare mean free path.

cond-mat.dis-nn↗

arXiv2003

Impact of weak localization in the time domain

We find a renormalized "time-dependent diffusion coefficient", D(t), for pulsed excitation of a nominally diffusive sample by solving the Bethe-Salpeter equation with recurrent scattering. We observe a crossover in dynamics in the transformation from a quasi-1D to a slab geometry implemented by varying the ratio of the radius, R, of the cylindrical sample with reflecting walls and the sample length, L. Immediately after the peak of the transmitted pulse, D(t) falls linearly with a nonuniversal slope that approaches an asymptotic value for R/L >> 1. The value of D(t) extrapolated to t = 0 depends only upon the dimensionless conductance, g, for R/L << l 1 and only upon kl for R/L >> 1, where k is the wave vector and l is the bare mean free path.

cond-mat.dis-nn↗