Irregular and multi--channel sampling of operators

The classical sampling theorem for bandlimited functions has recently been generalized to apply to so-called bandlimited operators, that is, to operators with band-limited Kohn-Nirenberg symbols. Here, we discuss operator sampling versions of two of the most central extensions to the classical sampling theorem. In irregular operator sampling, the sampling set is not periodic with uniform distance. In multi-channel operator sampling, we obtain complete information on an operator by multiple operator sampling outputs

Role of Phonon Scattering in Graphene Nanoribbon Transistors: Non-Equilibrium Green's Function Method with Real Space Approach

Mode space approach has been used so far in NEGF to treat phonon scattering for computational efficiency. Here we perform a more rigorous quantum transport simulation in real space to consider interband scatterings as well. We show a seamless transition from ballistic to dissipative transport in graphene nanoribbon transistors by varying channel length. We find acoustic phonon (AP) scattering to be the dominant scattering mechanism within the relevant range of voltage bias. Optical phonon scattering is significant only when a large gate voltage is applied. In a longer channel device, the contribution of AP scattering to the dc current becomes more significant

A new approach to the 2-variable subnormal completion problem

We study the Subnormal Completion Problem (SCP) for 2-variable weighted shifts. We use tools and techniques from the theory of truncated moment problems to give a general strategy to solve SCP. We then show that when all quadratic moments are known (equivalently, when the initial segment of weights consists of five independent data points), the natural necessary conditions for the existence of a subnormal completion are also sufficient. To calculate explicitly the associated Berger measure, we compute the algebraic variety of the associated truncated moment problem; it turns out that this algebraic variety is precisely the support of the Berger measure of the subnormal completion

Theoretical correction to the neutral B0B^0 meson asymmetry

Certain types of asymmetries in neutral meson physics have not been treated properly, ignoring the difference of normalization factors with an assumption of the equality of total decay width. Since the corrected asymmetries in $B^0$ meson are different from known asymmetries by a shift in the first order of CP- and CPT-violation parameters, experimental data should be analyzed with the consideration of this effect as in $K^0$ meson physics.Comment: 7 page

Hyponormality and subnormality for powers of commuting pairs of subnormal operators

Let H_0 (resp. H_\infty denote the class of commuting pairs of subnormal operators on Hilbert space (resp. subnormal pairs), and for an integer k>=1 let H_k denote the class of k-hyponormal pairs in H_0. We study the hyponormality and subnormality of powers of pairs in H_k. We first show that if (T_1,T_2) is in H_1, then the pair (T_1^2,T_2) may fail to be in H_1. Conversely, we find a pair (T_1,T_2) in H_0 such that (T_1^2,T_2) is in H_1 but (T_1,T_2) is not. Next, we show that there exists a pair (T_1,T_2) in H_1 such that T_1^mT_2^n is subnormal (all m,n >= 1), but (T_1,T_2) is not in H_\infty; this further stretches the gap between the classes H_1 and H_\infty. Finally, we prove that there exists a large class of 2-variable weighted shifts (T_1,T_2) (namely those pairs in H_0 whose cores are of tensor form) for which the subnormality of (T_1^2,T_2) and (T_1,T_2^2) does imply the subnormality of (T_1,T_2)