Conductance of Disordered Wires with Symplectic Symmetry: Comparison between Odd- and Even-Channel Cases

The conductance of disordered wires with symplectic symmetry is studied by numerical simulations on the basis of a tight-binding model on a square lattice consisting of M lattice sites in the transverse direction. If the potential range of scatterers is much larger than the lattice constant, the number N of conducting channels becomes odd (even) when M is odd (even). The average dimensionless conductance g is calculated as a function of system length L. It is shown that when N is odd, the conductance behaves as g --> 1 with increasing L. This indicates the absence of Anderson localization. In the even-channel case, the ordinary localization behavior arises and g decays exponentially with increasing L. It is also shown that the decay of g is much faster in the odd-channel case than in the even-channel case. These numerical results are in qualitative agreement with existing analytic theories.Comment: 4 page

Intensity correlations in electronic wave propagation in a disordered medium: the influence of spin-orbit scattering

We obtain explicit expressions for the correlation functions of transmission and reflection coefficients of coherent electronic waves propagating through a disordered quasi-one-dimensional medium with purely elastic diffusive scattering in the presence of spin-orbit interactions. We find in the metallic regime both large local intensity fluctuations and long-range correlations which ultimately lead to universal conductance fluctuations. We show that the main effect of spin-orbit scattering is to suppress both local and long-range intensity fluctuations by a universal symmetry factor 4. We use a scattering approach based on random transfer matrices.Comment: 15 pages, written in plain TeX, Preprint OUTP-93-42S (University of Oxford), to appear in Phys. Rev.

Path Integral Approach to the Scattering Theory of Quantum Transport

The scattering theory of quantum transport relates transport properties of disordered mesoscopic conductors to their transfer matrix \bbox{T}. We introduce a novel approach to the statistics of transport quantities which expresses the probability distribution of \bbox{T} as a path integral. The path integal is derived for a model of conductors with broken time reversal invariance in arbitrary dimensions. It is applied to the Dorokhov-Mello-Pereyra-Kumar (DMPK) equation which describes quasi-one-dimensional wires. We use the equivalent channel model whose probability distribution for the eigenvalues of \bbox{TT}^{\dagger} is equivalent to the DMPK equation independent of the values of the forward scattering mean free paths. We find that infinitely strong forward scattering corresponds to diffusion on the coset space of the transfer matrix group. It is shown that the saddle point of the path integral corresponds to ballistic conductors with large conductances. We solve the saddle point equation and recover random matrix theory from the saddle point approximation to the path integral.Comment: REVTEX, 9 pages, no figure

Vacuum polarization by topological defects in de Sitter spacetime

In this paper we investigate the vacuum polarization effects associated with a massive quantum scalar field in de Sitter spacetime in the presence of gravitational topological defects. Specifically we calculate the vacuum expectation value of the field square, $$. Because this investigation has been developed in a pure de Sitter space, here we are mainly interested on the effects induced by the presence of the defects.Comment: Talk presented at the 1st. Mediterranean Conference on Classical and Quantum Gravity (MCCQG

On the distribution of transmission eigenvalues in disordered wires

We solve the Dorokhov-Mello-Pereyra-Kumar equation which describes the evolution of an ensamble of disordered wires of increasing length in the three cases $\beta=1,2,4$. The solution is obtained by mapping the problem in that of a suitable Calogero-Sutherland model. In the $\beta=2$ case our solution is in complete agreement with that recently found by Beenakker and Rejaei.Comment: 4 pages, Revtex, few comments added at the end of the pape

Quantum and Boltzmann transport in the quasi-one-dimensional wire with rough edges

We study quantum transport in Q1D wires made of a 2D conductor of width W and length L>>W. Our aim is to compare an impurity-free wire with rough edges with a smooth wire with impurity disorder. We calculate the electron transmission through the wires by the scattering-matrix method, and we find the Landauer conductance for a large ensemble of disordered wires. We study the impurity-free wire whose edges have a roughness correlation length comparable with the Fermi wave length. The mean resistance and inverse mean conductance 1/ are evaluated in dependence on L. For L -> 0 we observe the quasi-ballistic dependence 1/ = = 1/N_c + \rho_{qb} L/W, where 1/N_c is the fundamental contact resistance and \rho_{qb} is the quasi-ballistic resistivity. As L increases, we observe crossover to the diffusive dependence 1/ = = 1/N^{eff}_c + \rho_{dif} L/W, where \rho_{dif} is the resistivity and 1/N^{eff}_c is the effective contact resistance corresponding to the N^{eff}_c open channels. We find the universal results \rho_{qb}/\rho_{dif} = 0.6N_c and N^{eff}_c = 6 for N_c >> 1. As L exceeds the localization length \xi, the resistance shows onset of localization while the conductance shows the diffusive dependence 1/ = 1/N^{eff}_c + \rho_{dif} L/W up to L = 2\xi and the localization for L > 2\xi only. On the contrary, for the impurity disorder we find a standard diffusive behavior, namely 1/ = = 1/N_c + \rho_{dif} L/W for L < \xi. We also derive the wire conductivity from the semiclassical Boltzmann equation, and we compare the semiclassical electron mean-free path with the mean free path obtained from the quantum resistivity \rho_{dif}. They coincide for the impurity disorder, however, for the edge roughness they strongly differ, i.e., the diffusive transport is not semiclassical. It becomes semiclassical for the edge roughness with large correlation length

Exact Solution for the Distribution of Transmission Eigenvalues in a Disordered Wire and Comparison with Random-Matrix Theory

An exact solution is presented of the Fokker-Planck equation which governs the evolution of an ensemble of disordered metal wires of increasing length, in a magnetic field. By a mapping onto a free-fermion problem, the complete probability distribution function of the transmission eigenvalues is obtained. The logarithmic eigenvalue repulsion of random-matrix theory is shown to break down for transmission eigenvalues which are not close to unity. ***Submitted to Physical Review B.****Comment: 20 pages, REVTeX-3.0, INLO-PUB-931028

Reflectance Fluctuations in an Absorbing Random Waveguide

We study the statistics of the reflectance (the ratio of reflected and incident intensities) of an $N$-mode disordered waveguide with weak absorption $\gamma$ per mean free path. Two distinct regimes are identified. The regime $\gamma N^2\gg1$ shows universal fluctuations. With increasing length $L$ of the waveguide, the variance of the reflectance changes from the value $2/15 N^2$, characteristic for universal conductance fluctuations in disordered wires, to another value $1/8 N^2$, characteristic for chaotic cavities. The weak-localization correction to the average reflectance performs a similar crossover from the value $1/3 N$ to $1/4 N$. In the regime $\gamma N^2\ll1$, the large-$L$ distribution of the reflectance $R$ becomes very wide and asymmetric, $P(R)\propto (1-R)^{-2}$ for $R\ll 1-\gamma N$.Comment: 7 pages, RevTeX, 2 postscript figure

Random-Matrix Theory of Electron Transport in Disordered Wires with Symplectic Symmetry

The conductance of disordered wires with symplectic symmetry is studied by a random-matrix approach. It has been believed that Anderson localization inevitably arises in ordinary disordered wires. A counterexample is recently found in the systems with symplectic symmetry, where one perfectly conducting channel is present even in the long-wire limit when the number of conducting channels is odd. This indicates that the odd-channel case is essentially different from the ordinary even-channel case. To study such differences, we derive the DMPK equation for transmission eigenvalues for both the even- and odd- channel cases. The behavior of dimensionless conductance is investigated on the basis of the resulting equation. In the short-wire regime, we find that the weak-antilocalization correction to the conductance in the odd-channel case is equivalent to that in the even-channel case. We also find that the variance does not depend on whether the number of channels is even or odd. In the long-wire regime, it is shown that the dimensionless conductance in the even-channel case decays exponentially as --> 0 with increasing system length, while --> 1 in the odd-channel case. We evaluate the decay length for the even- and odd-channel cases and find a clear even-odd difference. These results indicate that the perfectly conducting channel induces clear even-odd differences in the long-wire regime.Comment: 28pages, 5figures, Accepted for publication in J. Phys. Soc. Jp