1,477 research outputs found
Logarithm laws for flows on homogeneous spaces
We prove that almost all geodesics on a noncompact locally symmetric space of
finite volume grow with a logarithmic speed -- the higher rank generalization
of a theorem of D. Sullivan (1982). More generally, under certain conditions on
a sequence of subsets of a homogeneous space ( a semisimple
Lie group, a non-uniform lattice) and a sequence of elements of
we prove that for almost all points of the space, one has for infinitely many .
The main tool is exponential decay of correlation coefficients of smooth
functions on . Besides the aforementioned application to geodesic
flows, as a corollary we obtain a new proof of the classical Khinchin-Groshev
theorem in simultaneous Diophantine approximation, and settle a related
conjecture recently made by M. Skriganov
Magnetic moment of an electron gas on the surface of constant negative curvature
The magnetic moment of an electron gas on the surface of constant negative
curvature is investigated. It is shown that the surface curvature leads to the
appearance of the region of the monotonic dependence at low magnetic
fields. At high magnetic fields, the dependence of the magnetic moment on a
magnetic field is the oscillating one. The effect of the surface curvature is
to increase the region of the monotonic dependence of the magnetic moment and
to break the periodicity of oscillations of the magnetic moment as a function
of an inverse magnetic field.Comment: 4 pages, 1 figur
Khintchine-type theorems on manifolds: the convergence case for standard and multiplicative versions
An analogue of the convergence part of the Khintchine-Groshev theorem, as
well as its multiplicative version, is proved for nondegenerate smooth
submanifolds in . The proof combines methods from metric number
theory with a new approach involving the geometry of lattices in Euclidean
spaces.Comment: 27 page
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
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
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
Dichlorido(4,7-diaza-1-azoniacyclononane-κ2 N 4,N 7)palladium(II) p-toluenesulfonate
The title compound, [PdCl2(C6H16N3)](C7H7SO3), consists of a PdII atom bonded to two N atoms of the 1,4,7-triazacyclononane (TACN) ligand and two chloride ions, which define a distorted square-planar geometry. The third N atom of the TACN ligand is protonated and hydrogen bonds to the p-toluenesulfonate anion. The Cl—Pd—Cl angle is larger than the N—Pd—N angle. The packing is dominated by layers, which are formed by the criss-crossing of two different hydrogen-bonded chains. One chain is composed of hydrogen-bonded Pd(TACNH)Cl2
+ cations, while the second is formed through hydrogen bonding between the p-toluenesulfonate anion and the Pd(TACNH)Cl2
+ cation
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