70 research outputs found
Some extremal problems for Gaussian and Empirical random fields.
Some important problems of probability and statistics can be reduced to the evaluation of supremum of some homogeneous functional defined on the Strasses ball in the space of smooth functions on the square. We give the solution of this extremal problem in two particular cases: when the functional is linear and continuous and when it is a superposition of two seminorms. As a result we obtain the rough large deviation asymptotic for Lp-norms of Brownian fields on the square, some Strassen type laws of iterated logarithm for functional of Brownian fields, and describe the conditions of local Bahadur optimality for some nonparametric independence tests such as generalized rank correlation coefficients.Brownian field; Strassen ball; large deviations; tail asymptotics; rank correlations
Casimir elements from the Brauer-Schur-Weyl duality
We consider Casimir elements for the orthogonal and symplectic Lie algebras
constructed with the use of the Brauer algebra. We calculate the images of
these elements under the Harish-Chandra isomorphism and thus show that they
(together with the Pfaffian-type element in the even orthogonal case) are
algebraically independent generators of the centers of the corresponding
universal enveloping algebras.Comment: 19 page
Characteristic maps for the Brauer algebra
The classical characteristic map associates symmetric functions to characters
of the symmetric groups. There are two natural analogues of this map involving
the Brauer algebra. The first of them relies on the action of the orthogonal or
symplectic group on a space of tensors, while the second is provided by the
action of this group on the symmetric algebra of the corresponding Lie algebra.
We consider the second characteristic map both in the orthogonal and symplectic
case, and calculate the images of central idempotents of the Brauer algebra in
terms of the Schur polynomials. The calculation is based on the
Okounkov--Olshanski binomial formula for the classical Lie groups. We also
reproduce the hook dimension formulas for representations of the classical
groups by deriving them from the properties of the primitive idempotents of the
symmetric group and the Brauer algebra.Comment: 23 pages, minor changes made, a reference adde
Full Counting Statistics of Charge Transfer in Coulomb Blockade Systems
Full counting statistics (FCS) of charge transfer in mesoscopic systems has
recently become a subject of significant interest, since it proves to reveal an
important information about the system which can be hardly assessed by other
means. While the previous research mostly addressed the FCS of non- interacting
systems, the present paper deals with the FCS in the limit of strong
interaction. In this Coulomb blockade limit the electron dynamics is known to
be governed by a master equation. We develop a general scheme to evaluate the
FCS in such case, this being the main result of the work presented. We
illustrate the scheme, by applying it to concrete systems. For generic case of
a single resonant level we establish the equivalence of scattering and master
equation approach to FCS. Further we study a single Coulomb blockade island
with two and three leads attached and compare the FCS in this case with our
recent results concerning an open dot either with two and three terminals. We
demonstrate that Coulomb interaction suppresses the relative probabilities of
large current fluctuations.Comment: 17 pages, 16 figure
Nonequilibrium Josephson effect in short-arm diffusive SNS interferometers
We study non-equilibrium Josephson effect and phase-dependent conductance in
three-terminal diffusive interferometers with short arms. We consider strong
proximity effect and investigate an interplay of dissipative and Josephson
currents co-existing within the same proximity region. In junctions with
transparent interfaces, the suppression of the Josephson current appears at
rather large voltage, , and the current vanishes at
. Josephson current inversion becomes possible in junctions with
resistive interfaces, where the inversion occurs within a finite interval of
the applied voltage. Due to the presence of considerably large and
phase-dependent injection current, the critical current measured in a current
biased junction does not coincide with the maximum Josephson current, and
remains finite when the true Josephson current is suppressed. The voltage
dependence of the conductance shows two pronounced peaks, at the bulk gap
energy, and at the proximity gap energy; the phase oscillation of the
conductance exhibits qualitatively different form at small voltage ,
and at large voltage .Comment: 11 pages, 9 figures, revised version, to be published in Phys. Rev.
Coherent Charge Transport in Metallic Proximity Structures
We develop a detailed microscopic analysis of electron transport in normal
diffusive conductors in the presence of proximity induced superconducting
correlation. We calculated the linear conductance of the system, the profile of
the electric field and the densities of states. In the case of transparent
metallic boundaries the temperature dependent conductance has a non-monotoneous
``reentrant'' structure. We argue that this behavior is due to nonequilibrium
effects occuring in the normal metal in the presence of both superconducting
correlations and the electric field there. Low transparent tunnel barriers
suppress the nonequilibrium effects and destroy the reentrant behavior of the
conductance. If the wire contains a loop, the conductance shows Aharonov-Bohm
oscillations with the period as a function of the magnetic flux
inside the loop. The amplitude of these oscillations also demonstrates
the reentrant behavior vanishing at and decaying as at relatively
large temperatures. The latter behavior is due to low energy correlated
electrons which penetrate deep into the normal metal and ``feel'' the effect of
the magnetic flux . We point out that the density of states and thus the
``strengh'' of the proximity effect can be tuned by the value of the flux
inside the loop. Our results are fully consistent with recent experimental
findings.Comment: 16 pages RevTeX, 23 Postscript figures, submitted to Phys. Rev.
Weak Charge Quantization on Superconducting Islands
We consider the Coulomb blockade on a superconductive quantum dot strongly
coupled to a lead through a tunnelling barrier and/or normal diffusive metal.
Andreev transport of the correlated pairs leads to quantum fluctuations of the
charge on the dot. These fluctuations result in exponential renormalization of
the effective charging energy. We employ two complimentary ways to approach the
problem, leading to the coinciding results: the instanton and the functional RG
treatment of the non-linear sigma model. We also derive the charging energy
renormalization in terms of arbitrary transmission matrix of the multi-channel
interface.Comment: 21 pages, 4 eps figures, RevTe
Theory of Interaction Effects in N-S Junctions out of Equilibrium
We consider a normal metal - superconductor (N-S) junction in the regime,
when electrons in the normal metal are driven out of equilibrium. We show that
the non-equilibrium fluctuations of the electron density in the N-layer cause
the fluctuations of the phase of the order parameter in the S-layer. As a
result, the density of states in the superconductor deviates from the BCS form,
most notably the density of states in the gap becomes finite. This effect can
be viewed as a result of the time reversal symmetry breaking due to the
non-equilibrium, and can be described in terms of a low energy collective mode
of the junction, which couples normal currents in N-layer and supercurrents.
This mode is analogous to the Schmid-Sch\"{o}n mode. To interpret their
measurements of the tunneling current, Pothier {\em et. al} [Phys. Rev. Lett.
{\bf 79}, 3490 (1997)] had to assume that the energy relaxation rate in the
normal metal is surprisingly high. The broadening of the BCS singularity of the
density of states in the S-layer manifest itself similarly to the broadening of
the distribution function. Mechanism suggested here can be a possible
explanation of this experimental puzzle. We also propose an independent
experiment to test our explanation.Comment: 16 pages, 2 .eps figure
Superconducting proximity effect in clean ferromagnetic layers
We investigate superconducting proximity effect in clean ferromagnetic layers
with rough boundaries. The subgap density of states is formed by Andreev bound
states at energies which depend on trajectory length and the ferromagnetic
exchange field. At energies above the gap, the spectrum is governed by resonant
scattering states. The resulting density of states, measurable by tunneling
spectroscopy, exhibits a rich structure, which allows to connect the
theoretical parameters from experiments.Comment: 11 pages, 5 figures (included
Long-Range Coulomb Interaction and the Crossover between Quantum and Shot Noise in Diffusive Conductors
Frequency-dependent nonequilibrium noise in quantum-coherent diffusive
conductors is calculated with account taken of long-range Coulomb interaction.
For long and narrow contacts with strong external screening the crossover
between quantum and shot noise takes place at frequencies much smaller than the
voltage drop across the contact. We also show that under certain frequency
limitations, the semiclassical and quantum-coherent approaches to shot noise
are mathematically equivalent.Comment: 13 pages, RevTex, 7 ps figures, more details of derivation give
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