Best constants in Rosenthal-type inequalities and the Kruglov operator

Let $X$ be a symmetric Banach function space on $[0,1]$ with the Kruglov property, and let $\mathbf{f}=\{f_k\}_{{k=1}}^n$, $n\ge1$ be an arbitrary sequence of independent random variables in $X$. This paper presents sharp estimates in the deterministic characterization of the quantities $$\Biggl\|\sum_{{k=1}}^nf_k\Biggr\|_X,\Biggl\|\Biggl(\sum_{{k=1}}^n|f_k|^p\Biggr)^{1/p}\Biggr\|_X,\qquad 1\leq p<\infty,$$ in terms of the sum of disjoint copies of individual terms of $\mathbf{f}$. Our method is novel and based on the important recent advances in the study of the Kruglov property through an operator approach made earlier by the authors. In particular, we discover that the sharp constants in the characterization above are equivalent to the norm of the Kruglov operator in $X$.Comment: Published in at http://dx.doi.org/10.1214/10-AOP529 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

Design, Synthesis, and Structure of Copper Dithione Complexes: Redox‐Dependent Charge Transfer

Redox‐active ligands impart versatility in transition metal complexes, which are attractive for photosensitizers, dye sensitized solar cells, photothermal therapy, etc. Dithiolene (Dt) ligands can transition between fully reduced and fully oxidized states. Herein, we report the syntheses, characterization, crystal structures and electronic properties of four [Cu(R2Dt0)2]+/2+ (R = Me, iPr) complexes, [Cu(iPr2Dt0)2][PF6] (1a), [Cu(iPr2Dt0)2][PF6]2 (1b), and [Cu(Me2Dt0)2][PF6] (2a), [Cu(Me2Dt0)2][PF6]2 (2b), where iPr2Dt0 = N,N′‐diisopropyl‐1,2‐piperazine dithione and Me2Dt0 = N,N′‐dimethyl‐1,2‐piperazine dithione. In addition, the molecular structure of [Cu(iPr2Dt0)2][BF4]2(1c) is also reported. Complexes 1a and 2a crystallized in the triclinic, P1 space group, and 1c crystallized in the monoclinic crystal system, space group C2/c. The single‐crystal X‐ray diffraction measurements show that the Cu(I) complexes have a distorted tetrahedral geometry, whereas the Cu(II) complex exhibits a true square‐planar geometry. Cu(I) complexes exhibit a low energy charge‐transfer band (450–650 nm), which are not observed in Cu(II) complexes. Electrochemical studies of these complexes show both ligand‐ and metal‐based redox couples

Electron spin dynamics in quantum dots and related nanostructures due to hyperfine interaction with nuclei

We review and summarize recent theoretical and experimental work on electron spin dynamics in quantum dots and related nanostructures due to hyperfine interaction with surrounding nuclear spins. This topic is of particular interest with respect to several proposals for quantum information processing in solid state systems. Specifically, we investigate the hyperfine interaction of an electron spin confined in a quantum dot in an s-type conduction band with the nuclear spins in the dot. This interaction is proportional to the square modulus of the electron wave function at the location of each nucleus leading to an inhomogeneous coupling, i.e. nuclei in different locations are coupled with different strength. In the case of an initially fully polarized nuclear spin system an exact analytical solution for the spin dynamics can be found. For not completely polarized nuclei, approximation-free results can only be obtained numerically in sufficiently small systems. We compare these exact results with findings from several approximation strategies.Comment: 26 pages, 9 figures. Topical Review to appear in J. Phys.: Condens. Matte

Electron Spin-Relaxation Times of Phosphorus Donors in Silicon

Pulsed electron paramagnetic resonance measurements of donor electron spins in natural phosphorus-doped silicon (Si:P) and isotopically-purified 28Si:P show a strongly temperature-dependent longitudinal relaxation time, T1, due to an Orbach process with DeltaE = 126 K. The 2-pulse echo decay is exponential in 28Si:P, with the transverse relaxation (decoherence) time, T2, controlled by the Orbach process above ~12 K and by instantaneous diffusion at lower temperatures. Spin echo experiments with varying pulse turning angles show that the intrinsic T2 of an isolated spin in 28Si:P is ~60 ms at 7 K.Comment: Submitted to PRL on 02.28.200