Gradient corrections for semiclassical theories of atoms in strong magnetic fields

This paper is divided into two parts. In the first one the von Weizs\"acker term is introduced to the Magnetic TF theory and the resulting MTFW functional is mathematically analyzed. In particular, it is shown that the von Weizs\"acker term produces the Scott correction up to magnetic fields of order $B \ll Z^2$, in accordance with a result of V. Ivrii on the quantum mechanical ground state energy. The second part is dedicated to gradient corrections for semiclassical theories of atoms restricted to electrons in the lowest Landau band. We consider modifications of the Thomas-Fermi theory for strong magnetic fields (STF), i.e. for $B \ll Z^3$. The main modification consists in replacing the integration over the variables perpendicular to the field by an expansion in angular momentum eigenfunctions in the lowest Landau band. This leads to a functional (DSTF) depending on a sequence of one-dimensional densities. For a one-dimensional Fermi gas the analogue of a Weizs\"acker correction has a negative sign and we discuss the corresponding modification of the DSTF functional.Comment: Latex2e, 36 page

Scott correction for large atoms and molecules in a self-generated magnetic field

We consider a large neutral molecule with total nuclear charge $Z$ in non-relativistic quantum mechanics with a self-generated classical electromagnetic field. To ensure stability, we assume that Z\al^2\le \kappa_0 for a sufficiently small $\kappa_0$, where \al denotes the fine structure constant. We show that, in the simultaneous limit $Z\to\infty$, \al\to 0 such that \kappa =Z\al^2 is fixed, the ground state energy of the system is given by a two term expansion $c_1Z^{7/3} + c_2(\kappa) Z^2 + o(Z^2)$. The leading term is given by the non-magnetic Thomas-Fermi theory. Our result shows that the magnetic field affects only the second (so-called Scott) term in the expansion

Decoherence bounds on the capabilities of cold trapped ion quantum computers

Using simple physical arguments we investigate the capabilities of a quantum computer based on cold trapped ions of the type recently proposed by Cirac and Zoller. From the limitations imposed on such a device by decoherence due to spontaneous decay, laser phase coherence times, ion heating and other possible sources of error, we derive bounds on the number of laser interactions and on the number of ions that may be used. As a quantitative measure of the possible performance of these devices, the largest number which may be factored using Shor`s quantum factoring algorithm is determined for a variety of species of ion

Relativistic theory of elastic deformable astronomical bodies: perturbation equations in rotating spherical coordinates and junction conditions

In this paper, the dynamical equations and junction conditions at the interface between adjacent layers of different elastic properties for an elastic deformable astronomical body in the first post-Newtonian approximation of Einstein theory of gravity are discussed in both rotating Cartesian coordinates and rotating spherical coordinates. The unperturbed rotating body (the ground state) is described as uniformly rotating, stationary and axisymmetric configuration in an asymptotically flat space-time manifold. Deviations from the equilibrium configuration are described by means of a displacement field. In terms of the formalism of relativistic celestial mechanics developed by Damour, Soffel and Xu, and the framework established by Carter and Quintana the post Newtonian equations of the displacement field and the symmetric trace-free shear tensor are obtained. Corresponding post-Newtonian junction conditions at interfaces also the outer surface boundary conditions are presented. The PN junction condition is an extension of Wahr's one which is a Newtonian junction conditions without rotating.Comment: Revtex4, 14 page

Dynamics of viscoelastic membranes

We determine both the in-plane and out-of-plane dynamics of viscoelastic membranes separating two viscous fluids in order to understand microrheological studies of such membranes. We demonstrate the general viscoelastic signatures in the dynamics of shear, bending, and compression modes. We also find a screening of the otherwise two-dimensional character of the response to point forces due to the presence of solvent. Finally, we show that there is a linear, hydrodynamic coupling between the in-plane compression modes of the membrane and the out-of-plane bending modes in the case where the membrane separates two different fluids or environments

Itinerant Ferromagnetism in the Periodic Anderson Model

We introduce a novel mechanism for itinerant ferromagnetism, based on a simple two-band model. The model includes an uncorrelated and dispersive band hybridized with a second band which is narrow and correlated. The simplest Hamiltonian containing these ingredients is the Periodic Anderson Model (PAM). Using quantum Monte Carlo and analytical methods, we show that the PAM and an extension of it contain the new mechanism and exhibit a non-saturated ferromagnetic ground state in the intermediate valence regime. We propose that the mechanism, which does not assume an intra atomic Hund's coupling, is present in both the iron group and in some f electron compounds like Ce(Rh_{1-x} Ru_x)_3 B_2, La_x Ce_{1-x} Rh_3 B_2 and the uranium monochalcogenides US, USe, and UTe

QED and the High Polarization of the Thermal Radiation from Neutron Stars

The thermal emission of strongly magnetized neutron-star atmospheres is thought to be highly polarized. However, because of the different orientations of the magnetic field over the surface of the neutron star (NS), it is commonly assumed that the net observed polarization will be significantly reduced as the polarization from different regions will cancel each other. We show that the birefringence of the magnetized QED vacuum decouples the polarization modes in the magnetosphere; therefore, the direction of the polarization follows the direction of the magnetic field up to a large distance from the stellar surface. At this distance, the rays that leave the surface and are destined for our detectors pass through only a small solid angle; consequently, the polarization direction of the emission originating in different regions will tend to align together. The net observed polarization of the thermal radiation of NSs should therefore be very large. Measurement of this polarization will be the first direct evidence of the birefringence of the magnetized vacuum due to QED and a direct probe of behavior of the vacuum at magnetic fields of order of and above the critical QED field of 4.4 x 10 13 G. The large observable polarization will also help us learn more about the atmospheric properties of NSs.Comment: 6 pages, 2 figures, minor changes to reflect accepted versio

Evaluation of treatment, prognostic factors, and survival in 198 vulvar melanoma patients: implications for clinical practice

Objective. To identify clinicopathological characteristics, treatment patterns, clinical outcomes and prognostic factors in patients with vulvar melanoma (VM). Materials & methods. This retrospective multicentre cohort study included 198 women with VM treated in eight cancer centres in the Netherlands and UK between 1990 and 2017. Clinicopathological features, treatment, recurrence, and survival data were collected. Overall and recurrence-free survival was estimated with the Kaplan-Meier method. Prognostic parameters were identified with multivariable Cox regression analysis. Results. The majority of patients (75.8%) had localized disease at diagnosis. VM was significantly associated with high-riskclinicopathological features, including age, tumour thickness, ulceration, positive resection margins and involved lymph nodes. Overall survival was 48% (95% CI 40?56%) and 31% (95% CI 23?39%) after 2 and 5 years respectively and did not improve in patients diagnosed after 2010 compared to patients diagnosed between 1990 and 2009. Recurrence occurred in 66.7% of patients, of which two-third was non-local. In multivariable analysis, age and tumour size were independent prognostic factors for worse survival. Prognostic factors for recurrence were tumour size and tumour type. Only the minority of patients were treated with immuno- or targeted therapy. Conclusion. Our results show that even clinically early-stage VM is an aggressive disease associated with poor clinical outcome due to distant metastases. Further investigation into the genomic landscape and the immune microenvironment in VM may pave the way to novel therapies to improve clinical outcomes in these aggressive tumours. Clinical trials with immunotherapy or targeted therapy in patients with high-risk, advanced or metastatic disease are highly needed.Objective. To identify clinicopathological characteristics, treatment patterns, clinical outcomes and prognostic factors in patients with vulvar melanoma (VM).Materials & methods. This retrospective multicentre cohort study included 198 women with VM treated in eight cancer centres in the Netherlands and UK between 1990 and 2017. Clinicopathological features, treatment, recurrence, and survival data were collected. Overall and recurrence-free survival was estimated with the Kaplan-Meier method. Prognostic parameters were identified with multivariable Cox regression analysis.Results. The majority of patients (75.8%) had localized disease at diagnosis. VM was significantly associated with high-riskclinicopathological features, including age, tumour thickness, ulceration, positive resection margins and involved lymph nodes. Overall survival was 48% (95% CI 40-56%) and 31% (95% CI 23-39%) after 2 and 5 years respectively and did not improve in patients diagnosed after 2010 compared to patients diagnosed between 1990 and 2009. Recurrence occurred in 66.7% of patients, of which two-third was non-local. In multivariable analysis, age and tumour size were independent prognostic factors for worse survival. Prognostic factors for recurrence were tumour size and tumour type. Only the minority of patients were treated with immuno-or targeted therapy.Conclusion. Our results show that even clinically early-stage VM is an aggressive disease associated with poor clinical outcome due to distant metastases. Further investigation into the genomic landscape and the immune microenvironment in VM may pave the way to novel therapies to improve clinical outcomes in these aggressive tumours. Clinical trials with immunotherapy or targeted therapy in patients with high-risk, advanced or metastatic disease are highly needed. (c) 2021 The Authors. Published by Elsevier Inc. This is an open access article under the CC BY license (http:// creativecommons.org/licenses/by/4.0/).Cervix cance