1,955 research outputs found
A topological realization of the congruence subgroup Kernel A
A number of years ago, Kumar Murty pointed out to me that the computation of
the fundamental group of a Hilbert modular surface ([7],IV,6), and the
computation of the congruence subgroup kernel of SL(2) ([6]) were surprisingly
similar. We puzzled over this, in particular over the role of elementary
matrices in both computations. We formulated a very general result on the
fundamental group of a Satake compactification of a locally symmetric space.
This lead to our joint paper [1] with Lizhen Ji and Les Saper on these
fundamental groups. Although the results in it were intriguingly similar to the
corresponding calculations of the congruence subgroup kernel of the underlying
algebraic group in [5], we were not able to demonstrate a direct connection
(cf. [1], 7). The purpose of this note is to explain such a connection. A
covering space is constructed from inverse limits of reductive Borel-Serre
compactifications. The congruence subgroup kernel then appears as the group of
deck transformations of this covering. The key to this is the computation of
the fundamental group in [1]
Property (T) and rigidity for actions on Banach spaces
We study property (T) and the fixed point property for actions on and
other Banach spaces. We show that property (T) holds when is replaced by
(and even a subspace/quotient of ), and that in fact it is
independent of . We show that the fixed point property for
follows from property (T) when 1
. For simple Lie groups and their lattices, we prove that the fixed point property for holds for any if and only if the rank is at least two. Finally, we obtain a superrigidity result for actions of irreducible lattices in products of general groups on superreflexive Banach spaces.Comment: Many minor improvement
Spin-orbit interaction and spin relaxation in a two-dimensional electron gas
Using time-resolved Faraday rotation, the drift-induced spin-orbit Field of a
two-dimensional electron gas in an InGaAs quantum well is measured. Including
measurements of the electron mobility, the Dresselhaus and Rashba coefficients
are determined as a function of temperature between 10 and 80 K. By comparing
the relative size of these terms with a measured in-plane anisotropy of the
spin dephasing rate, the D'yakonv-Perel' contribution to spin dephasing is
estimated. The measured dephasing rate is significantly larger than this, which
can only partially be explained by an inhomogeneous g-factor.Comment: 6 pages, 5 figure
Linear-time list recovery of high-rate expander codes
We show that expander codes, when properly instantiated, are high-rate list
recoverable codes with linear-time list recovery algorithms. List recoverable
codes have been useful recently in constructing efficiently list-decodable
codes, as well as explicit constructions of matrices for compressive sensing
and group testing. Previous list recoverable codes with linear-time decoding
algorithms have all had rate at most 1/2; in contrast, our codes can have rate
for any . We can plug our high-rate codes into a
construction of Meir (2014) to obtain linear-time list recoverable codes of
arbitrary rates, which approach the optimal trade-off between the number of
non-trivial lists provided and the rate of the code. While list-recovery is
interesting on its own, our primary motivation is applications to
list-decoding. A slight strengthening of our result would implies linear-time
and optimally list-decodable codes for all rates, and our work is a step in the
direction of solving this important problem
Semiclassical kinetic theory of electron spin relaxation in semiconductors
We develop a semiclassical kinetic theory for electron spin relaxation in
semiconductors. Our approach accounts for elastic as well as inelastic
scattering and treats Elliott-Yafet and motional-narrowing processes, such as
D'yakonov-Perel' and variable g-factor processes, on an equal footing. Focusing
on small spin polarizations and small momentum transfer scattering, we derive,
starting from the full quantum kinetic equations, a Fokker-Planck equation for
the electron spin polarization. We then construct, using a rigorous multiple
time scale approach, a Bloch equation for the macroscopic (-averaged)
spin polarization on the long time scale, where the spin polarization decays.
Spin-conserving energy relaxation and diffusion, which occur on a fast time
scale, after the initial spin polarization has been injected, are incorporated
and shown to give rise to a weight function which defines the energy averages
required for the calculation of the spin relaxation tensor in the Bloch
equation. Our approach provides an intuitive way to conceptualize the dynamics
of the spin polarization in terms of a ``test'' spin polarization which
scatters off ``field'' particles (electrons, impurities, phonons). To
illustrate our approach, we calculate for a quantum well the spin lifetime at
temperatures and densities where electron-electron and electron-impurity
scattering dominate. The spin lifetimes are non-monotonic functions of
temperature and density. Our results show that at electron densities and
temperatures, where the cross-over from the non-degenerate to the degenerate
regime occurs, spin lifetimes are particularly long.Comment: 29 pages, 10 figures, final versio
Stochastic make-to-stock inventory deployment problem: an endosymbiotic psychoclonal algorithm based approach
Integrated steel manufacturers (ISMs) have no specific product, they just produce finished product from the ore. This enhances the uncertainty prevailing in the ISM regarding the nature of the finished product and significant demand by customers. At present low cost mini-mills are giving firm competition to ISMs in terms of cost, and this has compelled the ISM industry to target customers who want exotic products and faster reliable deliveries. To meet this objective, ISMs are exploring the option of satisfying part of their demand by converting strategically placed products, this helps in increasing the variability of product produced by the ISM in a short lead time. In this paper the authors have proposed a new hybrid evolutionary algorithm named endosymbiotic-psychoclonal (ESPC) to decide what and how much to stock as a semi-product in inventory. In the proposed theory, the ability of previously proposed psychoclonal algorithms to exploit the search space has been increased by making antibodies and antigen more co-operative interacting species. The efficacy of the proposed algorithm has been tested on randomly generated datasets and the results compared with other evolutionary algorithms such as genetic algorithms (GA) and simulated annealing (SA). The comparison of ESPC with GA and SA proves the superiority of the proposed algorithm both in terms of quality of the solution obtained and convergence time required to reach the optimal/near optimal value of the solution
Fano resonances in a three-terminal nanodevice
The electron transport through a quantum sphere with three one-dimensional
wires attached to it is investigated. An explicit form for the transmission
coefficient as a function of the electron energy is found from the first
principles. The asymmetric Fano resonances are detected in transmission of the
system. The collapse of the resonances is shown to appear under certain
conditions. A two-terminal nanodevice with an additional gate lead is studied
using the developed approach. Additional resonances and minima of transmission
are indicated in the device.Comment: 11 pages, 5 figures, 2 equations are added, misprints in 5 equations
are removed, published in Journal of Physics: Condensed Matte
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