Discrete analogues of maximally modulated singular integrals of Stein-Wainger type: ℓp\ell^p bounds for p>1p>1

It is proved that certain discrete analogues of maximally modulated singular integrals of Stein-Wainger type are bounded on $\ell^p(\mathbb{Z}^n)$ for all $p\in (1,\infty)$. This extends earlier work of the authors concerning the case $p=2$. Some open problems for further investigation are briefly discussed.Comment: 15 pages; changed title, final version to appear in JF

Discrete analogues of maximally modulated singular integrals of Stein-Wainger type

Consider the maximal operator $$\mathscr{C} f(x) = \sup_{\lambda\in\mathbb{R}}\Big|\sum_{\substack{y\in\mathbb{Z}^n\setminus\{0\}}} f(x-y) e(\lambda |y|^{2d}) K(y)\Big|,\quad (x\in\mathbb{Z}^n),$$ where $d$ is a positive integer, $K$ a Calder\'on-Zygmund kernel and $n\ge 1$. This is a discrete analogue of a real-variable operator studied by Stein and Wainger. The nonlinearity of the phase introduces a variety of new difficulties that are not present in the real-variable setting. We prove $\ell^2(\mathbb{Z}^n)$-bounds for $\mathscr{C}$, answering a question posed by Lillian Pierce.Comment: 24 pages. Additional details inserted; final version to appear in JEM

THE COMPLETE STORY: A POPULATION‐ BASED PERSPECTIVE ON SCHOOL PERFORMANCE AND EDUCATIONAL TESTING

All children born in Manitoba in 1984 were tracked for 18 years to assess their grade‐ 12 performance on a provincial examination according to a student’s socio‐economic status. The proportion of youths in families receiving social assistance judged to have passed their language arts exam dropped from 80 per cent to 12 per cent, depending on whether one counts only those in the cohort who took the test on time in 2002 or all youths born in 1984 who should have taken the test in 2002. Getting better data on performance and doing something about the discrepancies should become a Canadian priority. Key words: educational opportunity, exam performance, socio‐economic status, testing, longitudinal studies Tous les enfants nés au Manitoba en 1984 ont été suivis sur une période de 18 ans en vue d’évaluer leur rendement en 12e année lors d’un examen provincial, tenant compte de leur statut socioéconomique. La proportion de jeunes issus des familles recevant de l’aide sociale et considérés comme ayant réussi leur examen au plan des compétences linguistiques passe de 80 % à 12 %, selon que l’on compte seulement ceux qui, dans la cohorte, ont subi l’examen à temps en 2002 ou tous les jeunes nés en 1984 qui auraient dû subir l’examen. En matière d’égalité des chances, la performance du système scolaire actuel au Canada laisse à désirer. Mots clés: possibilités éducatives, résultats d’examen, statut socioéconomique, analyse longitudinale.

Environment-assisted quantum transport in a 10-qubit network

The way in which energy is transported through an interacting system governs fundamental properties in many areas of physics, chemistry, and biology. Remarkably, environmental noise can enhance the transport, an effect known as environment-assisted quantum transport (ENAQT). In this paper, we study ENAQT in a network of coupled spins subject to engineered static disorder and temporally varying dephasing noise. The interacting spin network is realized in a chain of trapped atomic ions and energy transport is represented by the transfer of electronic excitation between ions. With increasing noise strength, we observe a crossover from coherent dynamics and Anderson localization to ENAQT and finally a suppression of transport due to the quantum Zeno effect. We found that in the regime where ENAQT is most effective the transport is mainly diffusive, displaying coherences only at very short times. Further, we show that dephasing characterized by non-Markovian noise can maintain coherences longer than white noise dephasing, with a strong influence of the spectral structure on the transport effciency. Our approach represents a controlled and scalable way to investigate quantum transport in many-body networks under static disorder and dynamic noise.Comment: Mai