Absorption problems for quantum walks in one dimension

This paper treats absorption problems for the one-dimensional quantum walk determined by a 2 times 2 unitary matrix U on a state space {0,1,...,N} where N is finite or infinite by using a new path integral approach based on an orthonormal basis P, Q, R and S of the vector space of complex 2 times 2 matrices. Our method studied here is a natural extension of the approach in the classical random walk.Comment: 15 pages, small corrections, journal reference adde

On the Heisenberg invariance and the Elliptic Poisson tensors

We study different algebraic and geometric properties of Heisenberg invariant Poisson polynomial quadratic algebras. We show that these algebras are unimodular. The elliptic Sklyanin-Odesskii-Feigin Poisson algebras $q_{n,k}(\mathcal E)$ are the main important example. We classify all quadratic $H-$invariant Poisson tensors on ${\mathbb C}^n$ with $n\leq 6$ and show that for $n\leq 5$ they coincide with the elliptic Sklyanin-Odesskii-Feigin Poisson algebras or with their certain degenerations.Comment: 14 pages, no figures, minor revision, typos correcte

Reciprocal Prospective Relationships Between Loneliness and Weight Status in Late Childhood and Early Adolescence

Adolescents who do not conform to weight ideals are vulnerable to disapproval and victimization from peers in school. But, missing from the literature is a prospective examination of weight status and feelings of loneliness that might come from those experiences. Using data from the Québec Longitudinal Study of Child Development, we filled that gap by examining the prospective associations between loneliness and weight status when the sample was aged 10 to 13 years. At ages 10, 12, and 13 years, 1042 youth (572 females; 92% from French speaking homes) reported on their loneliness and were weighed and measured. Family income sufficiency was included in our analyses given its relationship with weight status, but also its possible link with loneliness during early adolescence. The findings showed that (1) weight status and loneliness were not associated concurrently; (2) weight status predicted increases in loneliness from ages 12 to 13 years; and (3) loneliness predicted increases in weight from ages 12 to 13 years among female adolescents, but weight loss among male adolescents. The fact that loneliness was involved in weight gain for females suggests that interventions focused on reducing loneliness and increasing connection with peers during early adolescence could help in reducing obesity