Spectral fluctuations of Schr\"odinger operators generated by critical points of the potential

Starting from the spectrum of Schr\"odinger operators on $\mathbb{R}^n$, we propose a method to detect critical points of the potential. We argue semi-classically on the basis of a mathematically rigorous version of Gutzwiller's trace formula which expresses spectral statistics in term of classical orbits. A critical point of the potential with zero momentum is an equilibrium of the flow and generates certain singularities in the spectrum. Via sharp spectral estimates, this fluctuation indicates the presence of a critical point and allows to reconstruct partially the local shape of the potential. Some generalizations of this approach are also proposed.\medskip keywords : Semi-classical analysis; Schr\"odinger operators; Equilibriums in classical mechanics.Comment: 18 pages, Final versio

The Atomic Slide Puzzle: Self-Diffusion of an Impure Atom

In a series of recent papers van Gastel et al have presented first experimental evidence that impure, Indium atoms, embedded into the first layer of a Cu(001) surface, are not localized within the close-packed surface layers but make concerted, long excursions visualized in a series of STM images. Such excursions occur due to continuous reshuffling of the surface following the position exchanges of both impure and host atoms with the naturally occuring surface vacancies. Van Gastel et al have also formulated an original lattice-gas type model with asymmetric exchange probabilities, whose numerical solution is in a good agreement with the experimental data. In this paper we propose an exact lattice solution of several versions of this model.Comment: Latex, 4 pages, 2 figures, to appear in Phys. Rev. E (RC

Semi- and Non-relativistic Limit of the Dirac Dynamics with External Fields

We show how to approximate Dirac dynamics for electronic initial states by semi- and non-relativistic dynamics. To leading order, these are generated by the semi- and non-relativistic Pauli hamiltonian where the kinetic energy is related to $\sqrt{m^2 + \xi^2}$ and $\xi^2 / 2m$, respectively. Higher-order corrections can in principle be computed to any order in the small parameter v/c which is the ratio of typical speeds to the speed of light. Our results imply the dynamics for electronic and positronic states decouple to any order in v/c << 1. To decide whether to get semi- or non-relativistic effective dynamics, one needs to choose a scaling for the kinetic momentum operator. Then the effective dynamics are derived using space-adiabatic perturbation theory by Panati et. al with the novel input of a magnetic pseudodifferential calculus adapted to either the semi- or non-relativistic scaling.Comment: 42 page

Force-velocity relation and density profiles for biased diffusion in an adsorbed monolayer

In this paper, which completes our earlier short publication [Phys. Rev. Lett. 84, 511 (2000)], we study dynamics of a hard-core tracer particle (TP) performing a biased random walk in an adsorbed monolayer, composed of mobile hard-core particles undergoing continuous exchanges with a vapor phase. In terms of an approximate approach, based on the decoupling of the third-order correlation functions, we obtain the density profiles of the monolayer particles around the TP and derive the force-velocity relation, determining the TP terminal velocity, V_{tr}, as the function of the magnitude of external bias and other system's parameters. Asymptotic forms of the monolayer particles density profiles at large separations from the TP, and behavior of V_{tr} in the limit of small external bias are found explicitly.Comment: Latex, 31 pages, 3 figure

Sequential decoupling of negative-energy states in Douglas-Kroll-Hess theory

Here, we review the historical development, current status, and prospects of Douglas--Kroll--Hess theory as a quantum chemical relativistic electrons-only theory.Comment: 15 page

Zitterbewegung and semiclassical observables for the Dirac equation

In a semiclassical context we investigate the Zitterbewegung of relativistic particles with spin 1/2 moving in external fields. It is shown that the analogue of Zitterbewegung for general observables can be removed to arbitrary order in \hbar by projecting to dynamically almost invariant subspaces of the quantum mechanical Hilbert space which are associated with particles and anti-particles. This not only allows to identify observables with a semiclassical meaning, but also to recover combined classical dynamics for the translational and spin degrees of freedom. Finally, we discuss properties of eigenspinors of a Dirac-Hamiltonian when these are projected to the almost invariant subspaces, including the phenomenon of quantum ergodicity

Low Caspofungin Exposure in Patients in Intensive Care Units

In critically ill patients, drug exposure may be influenced by altered drug distribution and clearance. Earlier studies showed that the variability in caspofungin exposure was high in Intensive Care Unit (ICU) patients. The primary objective of this study was to determine if the standard dose of caspofungin resulted in adequate exposure in critically ill patients. A multicenter prospective study in ICU patients with (suspected) invasive candidiasis was conducted in the Netherlands, from November 2013 to October 2015. Patients received standard caspofungin treatment and the exposure was determined on day 3 of treatment. An area under the concentration-time curve over 24 hours (AUC0-24h) of 98 mg*h/L was considered adequate exposure. In case of low exposure (i.e. <79 mg*h/L; ≥20% lower AUC0-24h), the caspofungin dose was increased and the exposure re-evaluated. Twenty patients were included in the study, of which 5 had a positive blood culture. The median caspofungin AUC0-24h at day 3 was 78 mg*h/L (interquartile range (IQR), 69 - 97 mg*h/L). A low AUC0-24h (<79 mg*h/L) was seen in 10 patients. The AUC0-24h was significantly and positively correlated with the caspofungin dose in mg/kg/day (P = 0.011). The median AUC0-24h with a caspofungin dose of 1 mg/kg was estimated using a pharmacokinetic model and was 114.9 mg*h/L (IQR, 103.2 - 143.5 mg*h/L). In conclusion, the caspofungin exposure in ICU patients in this study was low compared with healthy volunteers and other (non-)critically ill patients, most likely due to a larger volume of distribution. A weight-based dose regimen is probably more suitable for patients with substantially altered drug distribution

Antibody response to heat-inactivated hepatitis B vaccine (CLB-3mg) in hemodialysis patients and occupational risk personnel: a one year follow-up

Immune response against hepatitis B vaccine (CLB 3mg) was evaluated in 59 hemodialysis patients and 20 occupational risk personnel. Seroconversion was induced in 52.5% and 70.0% respectively. Twelve months after the first dose, 37.5% of patients and 60.0% of occupational risk personnel had detectable anti-HBs level. Antibody level was expressed in sample ratio units (SRU). Considering only the responders, in the patients group 38.7% had a low anti-HBs response (2.1-9.9 SRU) 32.3% a medium response (10-99.9 SRU) and 29.0% a high response (>100 SRU) while in occupational risk personnel these values were 14.3%, 64.3% and 21.4% respectively. The authors suggest the use of HBV vaccines with more elevated HBsAg concentration or a reinforced immunization schedule to improve the anti-HBs response not only for patients but also for healthy persons