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ABSTRACT: We follow the temporal evolution of mesoscopic intensity fluctuations and correlation in strongly localized samples. We find an initial burst in relative transmission fluctuations in random one-dimensional (1D) samples due to fluctuations in the arrival time of ballistic transmission. Relative fluctuations subsequently rise, then drop to a minimum at a time tm, after which they increase rapidly in 1D simulations and quasi-1D (Q1D) measurements. For t>3tm, results in 1D and Q1D samples converge toward predictions of a dynamic single-parameter scaling model. These results reflect the changing number of modes participating appreciably in transmission as the impact of longer-lived modes grows with time delay.
Phys. Rev. B. 01/2010; 81.
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ABSTRACT: 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. Comment: 7 pages, 1 figure
07/2009;
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ABSTRACT: We argue from both technical and physical points of view that the main result shown in the Comment 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 1/L2. On the other hand, we believe that the result shows some evidence of T ln?L/L2 behavior found in S.~K.~Cheung and Z.~Q.~Zhang, Phys. Rev. B 72, 235102 (2005). More calculations with even larger L's are necessary to give a more definitive answer to this question.
Phys. Rev. B. 01/2009; 80(<[3]>).
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ABSTRACT: We have measured pulsed microwave transmission through quasi-one-dimensional (quasi-1D) samples with lengths up to three times the localization length as determined from measurements of the variance of intensity fluctuations. Measurements are analyzed using four complementary approaches, each appropriate in a specific time range: (i) diffusion theory; (ii) self-consistent localization theory (SCLT) with a renormalized diffusion coefficient in space and frequency, D(z,Omega); (iii) a dynamic single parameter scaling (DSPS) model, which reflects the decay of localized modes which do not overlap in space and frequency; and (iv) simulations of 1D random media. For times up to twice the diffusion time tauD, diffusion theory gives an excellent fit to the data. For times up to 4tauD, the slowing of the decay rate of transmission is in accord with SCLT. For longer times, transmission decays more slowly than the predictions of the SCLT, indicating the inability of this modified diffusion theory to capture the decay of long-lived localized states. Beyond the Heisenberg time, the decay rate approaches the predictions of the DSPS model, reflecting the increasing proportion of wave energy in long-lived localized states. The decay rates obtained from 1D simulations are then in good agreement with measurements in quasi-1D samples and coincide with decay rates given by the DSPS model.
Phys. Rev. B. 01/2009; 79(<[14]>).
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ABSTRACT: 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 theory of localization for the renormalized diffusion coefficient in space and frequency, D(z,\Omega). 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.
11/2007;
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ABSTRACT: 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.
10/2005;
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ABSTRACT: 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 <T(L)>~ln L/L^2. This is in contrast to the behavior of D(L)~1/L and <T(L)>~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., <T(L)>~ln L/L^2. Comment: 11 pages, 12 figures. Submitted to Phys. Rev. B on 3 May 2005
09/2005;
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ABSTRACT: 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, to the length, L, of the cylindrical sample with reflecting side walls and open ends. 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 only upon kl(0) for R/L>1, where k is the wave vector and l(0) is the bare mean free path.
Physical Review Letters 04/2004; 92(17):173902. · 7.37 Impact Factor
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ABSTRACT: We report the observation of nonexponential decay of pulsed microwave transmission through quasi-one-dimensional random dielectric media signaling the breakdown of the diffusion model. The decay rate of transmission falls nearly linearly in time corresponding to a nearly Gaussian distribution of the coupling strengths of quasinormal electromagnetic modes to free space at the sample surfaces. The peak and width of this distribution scale as L(-2.05) and L(-1.81), respectively.
Physical Review Letters 06/2003; 90(20):203903. · 7.37 Impact Factor
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ABSTRACT: We demonstrate that the shift of the stop-band position with increasing oblique angle in periodic structures results in a wide transverse exponential field distribution corresponding to strong angular confinement of the radiation. The beam expansion follows an effective diffusive equation depending only upon the spectral mode width. In the presence of gain, the beam cross section is limited only by the size of the gain area. As an example of an active periodic photonic medium, we calculate and measure laser emission from a dye-doped cholesteric liquid crystal film.
Physical Review Letters 03/2001; 86(9):1753-6. · 7.37 Impact Factor
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ABSTRACT: 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 $R/L\gg 1$. The value of $D(t)$ extrapolated to $t=0$, depends only upon the dimensionless conductance $g$ for $R/L \ll 1$ and upon $kl_0$ and $L$ for $R/L \gg 1$, where $k$ is the wave vector and $l_0$ is the bare mean free path.
