273 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
Conductance and Its Variance of Disordered Wires with Symplectic Symmetry in the Metallic Regime
The conductance of disordered wires with symplectic symmetry is studied by a
random-matrix approach. It has been shown that the behavior of the conductance
in the long-wire limit crucially depends on whether the number of conducting
channels is even or odd. We focus on the metallic regime where the wire length
is much smaller than the localization length, and calculate the
ensemble-averaged conductance and its variance for both the even- and
odd-channel cases. We find that the weak-antilocalization correction to the
conductance in the odd-channel case is equivalent to that in the even-channel
case. Furthermore, we find that the variance dose not depend on whether the
number of channels is even or odd. These results indicate that in contrast to
the long-wire limit, clear even-odd differences cannot be observed in the
metallic regime.Comment: 9pages, accepted for publication in JPS
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
Turbulence Hierarchy in a Random Fibre Laser
Turbulence is a challenging feature common to a wide range of complex
phenomena. Random fibre lasers are a special class of lasers in which the
feedback arises from multiple scattering in a one-dimensional disordered
cavity-less medium. Here, we report on statistical signatures of turbulence in
the distribution of intensity fluctuations in a continuous-wave-pumped
erbium-based random fibre laser, with random Bragg grating scatterers. The
distribution of intensity fluctuations in an extensive data set exhibits three
qualitatively distinct behaviours: a Gaussian regime below threshold, a mixture
of two distributions with exponentially decaying tails near the threshold, and
a mixture of distributions with stretched-exponential tails above threshold.
All distributions are well described by a hierarchical stochastic model that
incorporates Kolmogorov's theory of turbulence, which includes energy cascade
and the intermittence phenomenon. Our findings have implications for explaining
the remarkably challenging turbulent behaviour in photonics, using a random
fibre laser as the experimental platform.Comment: 9 pages, 5 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
Scaling and Crossover Functions for the Conductance in the Directed Network Model of Edge States
We consider the directed network (DN) of edge states on the surface of a
cylinder of length L and circumference C. By mapping it to a ferromagnetic
superspin chain, and using a scaling analysis, we show its equivalence to a
one-dimensional supersymmetric nonlinear sigma model in the scaling limit, for
any value of the ratio L/C, except for short systems where L is less than of
order C^{1/2}. For the sigma model, the universal crossover functions for the
conductance and its variance have been determined previously. We also show that
the DN model can be mapped directly onto the random matrix (Fokker-Planck)
approach to disordered quasi-one-dimensional wires, which implies that the
entire distribution of the conductance is the same as in the latter system, for
any value of L/C in the same scaling limit. The results of Chalker and Dohmen
are explained quantitatively.Comment: 10 pages, REVTeX, 2 eps figure
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