Group representations that resist random sampling

We show that there exists a family of groups G_n and nontrivial irreducible representations ρ_n such that, for any constant t, the average of ρ_n over t uniformly random elements has operator norm 1 with probability approaching 1 as . More quantitatively, we show that there exist families of finite groups for which random elements are required to bound the norm of a typical representation below 1. This settles a conjecture of A. Wigderson. © 2014 Wiley Periodicals, Inc. Random Struct. Alg., 47, 605–614, 2015     

Atomic spectral overlaps: A mathematical model and its use for studying line shape parameters

A mathematical model which describes an atomic spectral overlap is presented. The model is developed using hyperfine structure, overlap separation values, and line broadening calculations coupled with relative absorbance measurements of overlap and non-overlap situations. With good hyperfine structure data, the model can be used to determine the a-parameter values for both transitions of the overlap. Even in the absence of high quality data, the model can provide meaningful insights into line shapes, hyperfine structure, and wavelength assignments of overlapping spectral transitions.     

Equivalence of polynomial conjectures in additive combinatorics

We study two conjectures in additive combinatorics. The first is the polynomial Freiman-Ruzsa conjecture, which relates to the structure of sets with small doubling. The second is the inverse Gowers conjecture for U ³, which relates to functions which locally look like quadratics. In both cases a weak form, with exponential decay of parameters is known, and a strong form with only a polynomial loss of parameters is conjectured. Our main result is that the two conjectures are in fact equivalent.     

Rapid and robust spin state amplification

Electron and nuclear spins have been employed in many of the early demonstrations of quantum technology. However, applications in real world quantum technology are limited by the difficulty of measuring single spins. Here we show that it is possible to rapidly and robustly amplify a spin state using a lattice of ancillary spins. The model we employ corresponds to an extremely simple experimental system: a homogenous Ising-coupled spin lattice in one, two, or three dimensions, driven by a continuous microwave field. We establish that the process can operate at finite temperature (imperfect initial polarization) and under the effects of various forms of decoherence.     

The short-lived signaling state of the photoactive yellow protein photoreceptor revealed by combined structural probes

The signaling state of the photoactive yellow protein (PYP) photoreceptor is transiently developed via isomerization of its blue-light-absorbing chromophore. The associated structural rearrangements have large amplitude but, due to its transient nature and chemical exchange reactions that complicate NMR detection, its accurate three-dimensional structure in solution has been elusive. Here we report on direct structural observation of the transient signaling state by combining double electron electron resonance spectroscopy (DEER), NMR, and time-resolved pump-probe X-ray solution scattering (TR-SAXS/WAXS). Measurement of distance distributions for doubly spin-labeled photoreceptor constructs using DEER spectroscopy suggests that the signaling state is well ordered and shows that interspin-label distances change reversibly up to 19 ? upon illumination. The SAXS/WAXS difference signal for the signaling state relative to the ground state indicates the transient formation of an ordered and rearranged conformation, which has an increased radius of gyration, an increased maximum dimension, and a reduced excluded volume. Dynamical annealing calculations using the DEER derived long-range distance restraints in combination with short-range distance information from (1)H-(15)N HSQC perturbation spectroscopy give strong indication for a rearrangement that places part of the N-terminal domain in contact with the exposed chromophore binding cleft while the terminal residues extend away from the core. Time-resolved global structural information from pump-probe TR-SAXS/WAXS data supports this conformation and allows subsequent structural refinement that includes the combined energy terms from DEER, NMR, and SAXS/WAXS together. The resulting ensemble simultaneously satisfies all restraints, and the inclusion of TR-SAXS/WAXS effectively reduces the uncertainty arising from the possible spin-label orientations. The observations are essentially compatible with reduced folding of the I(2)' state (also referred to as the 'pB' state) that is widely reported, but indicates it to be relatively ordered and rearranged. Furthermore, there is direct evidence for the repositioning of the N-terminal region in the I(2)' state, which is structurally modeled by dynamical annealing and refinement calculations.     

A rate model of inductively coupled argon plasma analyte spectra

A model which explicitly considers the various rates of excitation, deexcitation, ionization and recombination for analyte species in an ICAP of defined electron density and temperature is presented. The model reveals that radiative decay, radiative recombination and radiative absorption affect the level populations of a fundamentally collisionally dominated plasma. In addition. Penning ionization is shown to have a negligible effect on spectrally derived temperatures except for elements of high second ionization potential.     

pH‐Responsive Non‐Ionic Diblock Copolymers: Ionization of Carboxylic Acid End‐Groups Induces an Order–Order Morphological Transition

A carboxylic acid based reversible additionfragmentation transfer (RAFT) agent is used to prepare gels composed of worm‐like diblock copolymers using two non‐ionic monomers, glycerol monomethacrylate (GMA) and 2‐hydroxypropyl methacrylate (HPMA). Ionization of the carboxylic acid end‐group on the PGMA stabilizer block induces a worm‐to‐sphere transition, which in turn causes immediate degelation. This morphological transition is fully reversible as determined by TEM and rheology studies and occurs because of a subtle change in the packing parameter for the copolymer chains. A control experiment where the methyl ester derivative of the RAFT agent is used to prepare the same diblock copolymer confirms that no pH‐responsive behavior occurs in this case. This end‐group ionization approach is important for the design of new pH‐responsive copolymer nano‐objects as, unlike polyacids or polybases, only a minimal amount of added base (or acid) is required to drive the morphological transition.     

Phonon-induced Rabi-frequency renormalization of optically driven single InGaAs/GaAs quantum dots

We study optically driven Rabi rotations of a quantum dot exciton transition between 5 and 50 K, and for pulse areas of up to 14π. In a high driving field regime, the decay of the Rabi rotations is nonmonotonic, and the period decreases with pulse area and increases with temperature. By comparing the experiments to a weak-coupling model of the exciton-phonon interaction, we demonstrate that the observed renormalization of the Rabi frequency is induced by fluctuations in the bath of longitudinal acoustic phonons, an effect that is a phonon analogy of the Lamb shift.