226 research outputs found
Shot Noise of Single-Electron Tunneling in 1D Arrays
We have used numerical modeling and a semi-analytical calculation method to
find the low frequency value S_{I}(0) of the spectral density of fluctuations
of current through 1D arrays of small tunnel junctions, using the ``orthodox
theory'' of single-electron tunneling. In all three array types studied, at low
temperature (kT << eV), increasing current induces a crossover from the
Schottky value S_{I}(0)=2e to the ``reduced Schottky value''
S_{I}(0)=2e/N (where N is the array length) at some crossover current I_{c}.
In uniform arrays over a ground plane, I_{c} is proportional to exp(-\lambda
N), where 1/\lambda is the single-electron soliton length. In arrays without a
ground plane, I_{c} decreases slowly with both N and \lambda. Finally, we have
calculated the statistics of I_{c} for ensembles of arrays with random
background charges. The standard deviation of I_{c} from the ensemble average
is quite large, typically between 0.5 and 0.7 of , while the
dependence of on N or \lambda is so weak that it is hidden within the
random fluctuations of the crossover current.Comment: RevTex. 21 pages of text, 10 postscript figure
Collective Transport in Arrays of Quantum Dots
(WORDS: QUANTUM DOTS, COLLECTIVE TRANSPORT, PHYSICAL EXAMPLE OF KPZ)
Collective charge transport is studied in one- and two-dimensional arrays of
small normal-metal dots separated by tunnel barriers. At temperatures well
below the charging energy of a dot, disorder leads to a threshold for
conduction which grows linearly with the size of the array. For short-ranged
interactions, one of the correlation length exponents near threshold is found
from a novel argument based on interface growth. The dynamical exponent for the
current above threshold is also predicted analytically, and the requirements
for its experimental observation are described.Comment: 12 pages, 3 postscript files included, REVTEX v2, (also available by
anonymous FTP from external.nj.nec.com, in directory /pub/alan/dotarrays [as
separate files]) [replacement: FIX OF WRONG VERSION, BAD SHAR] March 17,
1993, NEC
Towards single-electron metrology
We review the status of the understanding of single-electron transport (SET)
devices with respect to their applicability in metrology. Their envisioned role
as the basis of a high-precision electrical standard is outlined and is
discussed in the context of other standards. The operation principles of single
electron transistors, turnstiles and pumps are explained and the fundamental
limits of these devices are discussed in detail. We describe the various
physical mechanisms that influence the device uncertainty and review the
analytical and numerical methods needed to calculate the intrinsic uncertainty
and to optimise the fabrication and operation parameters. Recent experimental
results are evaluated and compared with theoretical predictions. Although there
are discrepancies between theory and experiments, the intrinsic uncertainty is
already small enough to start preparing for the first SET-based metrological
applications.Comment: 39 pages, 14 figures. Review paper to be published in International
Journal of Modern Physics
Charge Solitons in 1-D Arrays of Serially Coupled Josephson Junctions
We study a 1-D array of Josephson coupled superconducting grains with kinetic
inductance which dominates over the Josephson inductance. In this limit the
dynamics of excess Cooper pairs in the array is described in terms of charge
solitons, created by polarization of the grains. We analyze the dynamics of
these topological excitations, which are dual to the fluxons in a long
Josephson junction, using the continuum sine-Gordon model. We find that their
classical relativistic motion leads to saturation branches in the I-V
characteristic of the array. We then discuss the semi-classical quantization of
the charge soliton, and show that it is consistent with the large kinetic
inductance of the array. We study the dynamics of a quantum charge soliton in a
ring-shaped array biased by an external flux through its center. If the
dephasing length of the quantum charge soliton is larger than the circumference
of the array, quantum phenomena like persistent current and coherent current
oscillations are expected. As the characteristic width of the charge soliton is
of the order of 100 microns, it is a macroscopic quantum object. We discuss the
dephasing mechanisms which can suppress the quantum behaviour of the charge
soliton.Comment: 26 pages, LaTex, 7 Postscript figure
Flux norm approach to finite dimensional homogenization approximations with non-separated scales and high contrast
We consider divergence-form scalar elliptic equations and vectorial equations
for elasticity with rough (, )
coefficients that, in particular, model media with non-separated scales
and high contrast in material properties. We define the flux norm as the
norm of the potential part of the fluxes of solutions, which is equivalent to
the usual -norm. We show that in the flux norm, the error associated with
approximating, in a properly defined finite-dimensional space, the set of
solutions of the aforementioned PDEs with rough coefficients is equal to the
error associated with approximating the set of solutions of the same type of
PDEs with smooth coefficients in a standard space (e.g., piecewise polynomial).
We refer to this property as the {\it transfer property}.
A simple application of this property is the construction of finite
dimensional approximation spaces with errors independent of the regularity and
contrast of the coefficients and with optimal and explicit convergence rates.
This transfer property also provides an alternative to the global harmonic
change of coordinates for the homogenization of elliptic operators that can be
extended to elasticity equations. The proofs of these homogenization results
are based on a new class of elliptic inequalities which play the same role in
our approach as the div-curl lemma in classical homogenization.Comment: Accepted for publication in Archives for Rational Mechanics and
Analysi
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