10,585 research outputs found
Revisiting the Polyak step size
This paper revisits the Polyak step size schedule for convex optimization
problems, proving that a simple variant of it simultaneously attains near
optimal convergence rates for the gradient descent algorithm, for all ranges of
strong convexity, smoothness, and Lipschitz parameters, without a-priory
knowledge of these parameters
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Intrinsic bidirectional dynamic nuclear polarization by optically pumped trions in quantum dots
This paper has been updated by the author to: arXiv:1012.0060v1
[cond-mat.mes-hall], titled "Collective Nuclear Stabilization by Optically
Excited Hole in Quantum Dot
General theory of feedback control of a nuclear spin ensemble in quantum dots
We present a microscopic theory of the nonequilibrium nuclear spin dynamics
driven by the electron and/or hole under continuous wave pumping in a quantum
dot. We show the correlated dynamics of the nuclear spin ensemble and the
electron and/or hole under optical excitation as a quantum feedback loop and
investigate the dynamics of the many nuclear spins as a nonlinear collective
motion. This gives rise to three observable effects: (i) hysteresis, (ii)
locking (avoidance) of the pump absorption strength to (from) the natural
resonance, and (iii) suppression (amplification) of the fluctuation of weakly
polarized nuclear spins, leading to prolonged (shortened) electron spin
coherence time. A single nonlinear feedback function as a "measurement" of the
nuclear field operator in the quantum feedback loop is constructed which
determines the different outcomes of the three effects listed above depending
on the feedback being negative or positive. The general theory also helps to
put in perspective the wide range of existing theories on the problem of a
single electron spin in a nuclear spin bath.Comment: 20 pages, 7 figure
Quark and Leptonic Mixing Patterns from the Breakdown of a Common Discrete Flavor Symmetry
Assuming the Majorana nature of neutrinos, we recently performed a scan of
leptonic mixing patterns derived from finite discrete groups of order less than
1536. Here we show that the 3 groups identified there as giving predictions
close to experiment, also contain another class of abelian subgroups that
predict an interesting leading order quark mixing pattern where only the
Cabibbo angle is generated at leading order. We further broaden our study by
assuming that neutrinos are Dirac particles and find 4 groups of order up to
200 that can predict acceptable quark and leptonic mixing angles. Since large
flavor groups allow for a multitude of leading order mixing patterns, we define
a measure that is suitable to compare the predictivity of a given flavor group
taking this fact into account. We give the result of this measure for a wide
range of discrete flavor groups and identify the group (Z_18 \times Z_6)
\rtimes S_3 as being most predictive in the sense of this measure. We further
discuss alternative measures and their implications.Comment: 11 pages, 4 figure
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