On an extension of the Iwatsuka model

We prove absolute continuity for an extended class of two-dimensional magnetic Hamiltonians that were initially studied by A. Iwatsuka. In particular, we add an electric field that is translation invariant in the same direction as the magnetic field is. As an example, we study the effective Hamiltonian for a thin quantum layer in a homogeneous magnetic field

The magnetic Laplacian in shrinking tubular neighbourhoods of hypersurfaces

16 pagesInternational audienceThe Dirichlet Laplacian between two parallel hypersurfaces in Euclidean spaces of any dimension in the presence of a magnetic field is considered in the limit when the distance between the hypersurfaces tends to zero. We show that the Laplacian converges in a norm-resolvent sense to a Schrödinger operator on the limiting hypersurface whose electromagnetic potential is expressed in terms of principal curvatures and the projection of the ambient vector potential to the hypersurface. As an application, we obtain an effective approximation of bound-state energies and eigenfunctions in thin quantum layers

Effects of psychological interventions and patients' affect on short-term quality of life in patients undergoing colorectal surgery

Psychological interventions can improve Quality of Life (QoL). Object of interest was if different psychological interventions influence short-term QoL after colonic resection for carcinoma. Furthermore, we wanted to see if there is a correlation between patients` preoperative affect and postoperative QoL. Sixty patients that underwent colorectal surgery were divided into three groups. Group one (n = 20) received Guided Imagery and group 2 (n = 22) Progressive Muscle Relaxation. The third group (Control, n = 18) had no intervention. Quality of Life (QoL) was measured using the EORTC QLQ-C30 and the Gastrointestinal Quality of life Index (GIQLI). Patients' affect was measured by the PANAS questionnaire. The higher the preoperative Negative Affect was, the lower were the scores for QoL on the 30th postoperative day. Patients' QoL was highest preoperatively and lowest on the third postoperative day. On the 30th postoperative day scores for QoL were almost as high as preoperative without difference between the three groups. Neither Guided Imagery nor Progressive Relaxation was influencing short-term QoL measured by the EORTC QLQ-C30 and the GIQLI questionnaire after colorectal surgery for cancer. Screening patients' with the PANAS questionnaire might help to identify individuals that are more likely to have a worse QoL postoperatively

Atoms confined by very thin layers

The Hamiltonian of an atom with $N$ electrons and a fixed nucleus of infinite mass between two parallel planes is considered in the limit when the distance $a$ between the planes tends to zero. We show that this Hamiltonian converges in the norm resolvent sense to a Schr\"{o}dinger operator acting effectively in $L^{2}(\mathbb{R}^{2N})$ whose potential part depends on $a$. Moreover, we prove that after an appropriate regularization this Schr\"{o}dinger operator tends, again in the norm resolvent sense, to the Hamiltonian of a two-dimensional atom (with the three-dimensional Coulomb potential-one over distance), as $a\to 0$. This makes possible to locate the discrete spectrum of the full Hamiltonian once we know the spectrum of the latter one. Our results also provide a mathematical justification for the interest in the two-dimensional atoms with the three-dimensional Coulomb potential