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

Equivalence of Fokker-Planck approach and non-linear σ\sigma-model for disordered wires in the unitary symmetry class

The exact solution of the Dorokhov-Mello-Pereyra-Kumar-equation for quasi one-dimensional disordered conductors in the unitary symmetry class is employed to calculate all $m$-point correlation functions by a generalization of the method of orthogonal polynomials. We obtain closed expressions for the first two conductance moments which are valid for the whole range of length scales from the metallic regime ($L\ll Nl$) to the insulating regime ($L\gg Nl$) and for arbitrary channel number. In the limit $N\to\infty$ (with $L/(Nl)=const.$) our expressions agree exactly with those of the non-linear $\sigma$-model derived from microscopic Hamiltonians.Comment: 9 pages, Revtex, one postscript figur

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

Generalized Fokker-Planck Equation For Multichannel Disordered Quantum Conductors

The Dorokhov-Mello-Pereyra-Kumar (DMPK) equation, which describes the distribution of transmission eigenvalues of multichannel disordered conductors, has been enormously successful in describing a variety of detailed transport properties of mesoscopic wires. However, it is limited to the regime of quasi one dimension only. We derive a one parameter generalization of the DMPK equation, which should broaden the scope of the equation beyond the limit of quasi one dimension.Comment: 8 pages, abstract, introduction and summary rewritten for broader readership. To be published in Phys. Rev. Let

Influência da compactação em características químicas e propriedades físicas de amostras de solo cultivadas com feijoeiro (Phaseolus Vulgaris. L.)

No experimento foram utilizadas amostras de terra Oxisol e um Alfisol, sujeitas a compactação

Fokker-Planck description of the transfer matrix limiting distribution in the scattering approach to quantum transport

The scattering approach to quantum transport through a disordered quasi-one-dimensional conductor in the insulating regime is discussed in terms of its transfer matrix \bbox{T}. A model of $N$ one-dimensional wires which are coupled by random hopping matrix elements is compared with the transfer matrix model of Mello and Tomsovic. We derive and discuss the complete Fokker-Planck equation which describes the evolution of the probability distribution of \bbox{TT}^{\dagger} with system length in the insulating regime. It is demonstrated that the eigenvalues of \ln\bbox{TT}^{\dagger} have a multivariate Gaussian limiting probability distribution. The parameters of the distribution are expressed in terms of averages over the stationary distribution of the eigenvectors of \bbox{TT}^{\dagger}. We compare the general form of the limiting distribution with results of random matrix theory and the Dorokhov-Mello-Pereyra-Kumar equation.Comment: 25 pages, revtex, no figure

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

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

Total Cost of Ownership of Digital vs. Analog Radio-Over-Fiber Architectures for 5G Fronthauling

The article analyzes the total cost of ownership (TCO) of 5G fronthauling solutions based on analog and digital radio-over-fiber (RoF) architectures in cloud radio access networks (C-RANs). The capital and operational expenditures (CAPEX, OPEX) are assessed, for a 10-year period, considering three different RoF techniques: intermediate frequency analog RoF (IF-A-RoF), digital signal processing (DSP) assisted analog RoF (DSP-A-RoF), and digital RoF (D-RoF) based on the common public radio interface (CPRI) specifications. The greenfield deployment scenario under exam includes both fiber trenching (FT) and fiber leasing (FL) options. The TCO is assessed while varying (i) the number of aggregated subcarriers, (ii) the number of three-sector antennas located at the base station, and (iii) the mean fiber-hop length. The comparison highlights the significance that subcarrier aggregation has on the cost efficiency of the analog RoF solutions. In addition, the analysis details the contribution of each cost category to the overall CAPEX and OPEX values. The obtained results indicate that subcarrier aggregation via DSP results in high cost efficiency for a mobile fronthaul network, while a CPRI-based architecture together with FL brings the highest OPEX value

Statistical Scattering of Waves in Disordered Waveguides: from Microscopic Potentials to Limiting Macroscopic Statistics

We study the statistical properties of wave scattering in a disordered waveguide. The statistical properties of a "building block" of length (delta)L are derived from a potential model and used to find the evolution with length of the expectation value of physical quantities. In the potential model the scattering units consist of thin potential slices, idealized as delta slices, perpendicular to the longitudinal direction of the waveguide; the variation of the potential in the transverse direction may be arbitrary. The sets of parameters defining a given slice are taken to be statistically independent from those of any other slice and identically distributed. In the dense-weak-scattering limit, in which the potential slices are very weak and their linear density is very large, so that the resulting mean free paths are fixed, the corresponding statistical properties of the full waveguide depend only on the mean free paths and on no other property of the slice distribution. The universality that arises demonstrates the existence of a generalized central-limit theorem. Our final result is a diffusion equation in the space of transfer matrices of our system, which describes the evolution with the length L of the disordered waveguide of the transport properties of interest. In contrast to earlier publications, in the present analysis the energy of the incident particle is fully taken into account.Comment: 75 pages, 10 figures, submitted to Phys. Rev