Divisibility questions in commutative algebraic groups

Let $k$ be a number field, let ${\mathcal{A}}$ be a commutative algebraic group defined over $k$ and let $p$ be a prime number. Let ${\mathcal{A}}[p]$ denote the $p$-torsion subgroup of ${\mathcal{A}}$. We give some sufficient conditions for the local-global divisibility by $p$ in ${\mathcal{A}}$ and the triviality of $Sha (k,{\mathcal{A}}[p])$. When ${\mathcal{A}}$ is an abelian variety principally polarized, those conditions imply that the elements of the Tate-Shafarevich group $Sha(k,{\mathcal{A}})$ are divisible by $p$ in the Weil-Ch\^atelet group $H^1(k,{\mathcal{A}})$ and the local-global principle for divisibility by $p$ holds in $H^r(k,{\mathcal{A}})$, for all $r\geq 0$

Mentoring Meetings Increase Student Performance on “High Stakes” Projects in STEM

The current project addresses whether one-on-one, mentoring meetings to discuss poster rough drafts will impact learning more consistently.https://digitalscholarship.unlv.edu/btp_expo/1070/thumbnail.jp

Dynamical suppression of telegraph and 1/f noise due to quantum bistable fluctuator

We study dynamical decoupling of a qubit from non gaussian quantum noise due to discrete sources, as bistable fluctuators and 1/f noise. We obtain analytic and numerical results for generic operating point. For very large pulse frequency, where dynamic decoupling compensates decoherence, we found universal behavior. At intermediate frequencies noise can be compensated or enhanced, depending on the nature of the fluctuators and on the operating point. Our technique can be applied to a larger class of non-gaussian environments.Comment: Revtex 4, 5 pages, 3 figures. Title revised and some other minor changed. Final version as published in PR

Optimal operating conditions of an entangling two-transmon gate

We identify optimal operating conditions of an entangling two-qubit gate realized by a capacitive coupling of two superconducting charge qubits in a transmission line resonator (the so called "transmons"). We demonstrate that the sensitivity of the optimized gate to 1/f flux and critical current noise is suppressed to leading order. The procedure only requires a preliminary estimate of the 1/f noise amplitudes. No additional control or bias line beyond those used for the manipulation of individual qubits are needed. The proposed optimization is effective also in the presence of relaxation processes and of spontaneous emission through the resonator (Purcell effect).Comment: 12 pages, 5 figure

Preperiodic points for rational functions defined over a global field in terms of good reductions

Let $\phi$ be an endomorphism of the projective line defined over a global field $K$. We prove a bound for the cardinality of the set of $K$-rational preperiodic points for $\phi$ in terms of the number of places of bad reduction. The result is completely new in the function fields case and it is an improvement of the number fields case. An important tool is an $S$-unit equation theorem in 2 variables

On preperiodic points of rational functions defined over Fp(t)\mathbb{F}_p(t)

Let $P\in\mathbb{P}_1(\mathbb{Q})$ be a periodic point for a monic polynomial with coefficients in $\mathbb{Z}$. With elementary techniques one sees that the minimal periodicity of $P$ is at most $2$. Recently we proved a generalization of this fact to the set of all rational functions defined over ${\mathbb{Q}}$ with good reduction everywhere (i.e. at any finite place of $\mathbb{Q}$). The set of monic polynomials with coefficients in $\mathbb{Z}$ can be characterized, up to conjugation by elements in PGL$_2({\mathbb{Z}})$, as the set of all rational functions defined over $\mathbb{Q}$ with a totally ramified fixed point in $\mathbb{Q}$ and with good reduction everywhere. Let $p$ be a prime number and let ${\mathbb{F}}_p$ be the field with $p$ elements. In the present paper we consider rational functions defined over the rational global function field ${\mathbb{F}}_p(t)$ with good reduction at every finite place. We prove some bounds for the cardinality of orbits in ${\mathbb{F}}_p(t)\cup \{\infty\}$ for periodic and preperiodic points.Comment: arXiv admin note: substantial text overlap with arXiv:1403.229

Structured environments in solid state systems: crossover from Gaussian to non-Gaussian behavior

The variety of noise sources typical of the solid state represents the main limitation toward the realization of controllable and reliable quantum nanocircuits, as those allowing quantum computation. Such ``structured environments'' are characterized by a non-monotonous noise spectrum sometimes showing resonances at selected frequencies. Here we focus on a prototype structured environment model: a two-state impurity linearly coupled to a dissipative harmonic bath. We identify the time scale separating Gaussian and non-Gaussian dynamical regimes of the Spin-Boson impurity. By using a path-integral approach we show that a qubit interacting with such a structured bath may probe the variety of environmental dynamical regimes.Comment: 8 pages, 9 figures. Proceedings of the DECONS '06 Conferenc