114 research outputs found
Quantum dot to disordered wire crossover: A complete solution in all length scales for systems with unitary symmetry
We present an exact solution of a supersymmetric nonlinear sigma model
describing the crossover between a quantum dot and a disordered quantum wire
with unitary symmetry. The system is coupled ideally to two electron reservoirs
via perfectly conducting leads sustaining an arbitrary number of propagating
channels. We obtain closed expressions for the first three moments of the
conductance, the average shot-noise power and the average density of
transmission eigenvalues. The results are complete in the sense that they are
nonperturbative and are valid in all regimes and length scales. We recover
several known results of the recent literature by taking particular limits.Comment: 4 page
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
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.
Universal Transport Properties of Disordered Quantum Wires
For disordered quantum wires which belong to all ten universality classes,
the universal quantities of transport properties are obtained through DMPK
approach. Calculated are the universal parts of one- and two-point correlation
functions for probability distribution functions of transmission eigenvalues.
In this analysis, the asymptotic solution of DMPK equation is used. Transport
properties for new universality classes(chiral and Bogoliubov-de Gennes
classes) are discussed comparing with those for standard class.Comment: 22 pages, 2 figure
Transmission through a many-channel random waveguide with absorption
We compute the statistical distribution of the transmittance of a random
waveguide with absorption in the limit of many propagating channels. We
consider the average and fluctuations of the conductance T = tr t^{\dagger} t,
where t is the transmission matrix, the density of transmission eigenvalues
\tau (the eigenvalues of t^{\dagger} t), and the distribution of the plane-wave
transmittances T_a and T_{ab}. For weak absorption (length L smaller than the
exponential absorption length \xi_a), we compute moments of the distributions,
while for strong absorption (L >> \xi_a), we can find the complete
distributions. Our findings explain recent experiments on the transmittance of
random waveguides by Stoytchev and Genack [Phys. Rev. Lett. 79, 309 (1997)].Comment: 13 pages, RevTeX; 9 figures include
Universal parametric correlations in the transmission eigenvalue spectra of disordered conductors
We study the response of the transmission eigenvalue spectrum of disordered
metallic conductors to an arbitrary external perturbation. For systems without
time-reversal symmetry we find an exact non-perturbative solution for the
two-point correlation function, which exhibits a new kind of universal behavior
characteristic of disordered conductors. Systems with orthogonal and symplectic
symmetries are studied in the hydrodynamic regime.Comment: 10 pages, written in plain TeX, Preprint OUTP-93-36S (University of
Oxford), to appear in Phys. Rev. B (Rapid Communication
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
A Brownian Motion Model of Parametric Correlations in Ballistic Cavities
A Brownian motion model is proposed to study parametric correlations in the
transmission eigenvalues of open ballistic cavities. We find interesting
universal properties when the eigenvalues are rescaled at the hard edge of the
spectrum. We derive a formula for the power spectrum of the fluctuations of
transport observables as a response to an external adiabatic perturbation. Our
formula correctly recovers the Lorentzian-squared behaviour obtained by
semiclassical approaches for the correlation function of conductance
fluctuations.Comment: 19 pages, written in RevTe
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