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

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