Scattering Phases and Density of States for Exterior Domain

For a bounded open domain $\Omega\in \real^2$ with connected complement and piecewise smooth boundary, we consider the Dirichlet Laplacian -\DO on $\Omega$ and the S-matrix on the complement $\Omega^c$. Using the restriction $A_E$ of $(-\Delta-E)^{-1}$ to the boundary of $\Omega$, we establish that $A_{E_0}^{-1/2}A_EA_{E_0}^{-1/2}-1$ is trace class when $E_0$ is negative and give bounds on the energy dependence of this difference. This allows for precise bounds on the total scattering phase, the definition of a $\zeta$-function, and a Krein spectral formula, which improve similar results found in the literature.Comment: 15 pages, Postscript, A

Description of nuclear systems with a self-consistent configuration-mixing approach. I: Theory, algorithm, and application to the 12^{12}C test nucleus

Although self-consistent multi-configuration methods have been used for decades to address the description of atomic and molecular many-body systems, only a few trials have been made in the context of nuclear structure. This work aims at the development of such an approach to describe in a unified way various types of correlations in nuclei, in a self-consistent manner where the mean-field is improved as correlations are introduced. The goal is to reconcile the usually set apart Shell-Model and Self-Consistent Mean-Field methods. This approach is referred as "variational multiparticle-multihole configuration mixing method". It is based on a double variational principle which yields a set of two coupled equations that determine at the same time the expansion coefficients of the many-body wave function and the single particle states. The formalism is derived and discussed in a general context, starting from a three-body Hamiltonian. Links to existing many-body techniques such as the formalism of Green's functions are established. First applications are done using the two-body D1S Gogny effective force. The numerical procedure is tested on the $^{12}$C nucleus in order to study the convergence features of the algorithm in different contexts. Ground state properties as well as single-particle quantities are analyzed, and the description of the first $2^+$ state is examined. This study allows to validate our numerical algorithm and leads to encouraging results. In order to test the method further, we will realize in the second article of this series, a systematic description of more nuclei and observables obtained by applying the newly-developed numerical procedure with the same Gogny force. As raised in the present work, applications of the variational multiparticle-multihole configuration mixing method will however ultimately require the use of an extended and more constrained Gogny force.Comment: 22 pages, 18 figures, accepted for publication in Phys. Rev. C. v2: minor corrections and references adde

Temporal relation between quiet-Sun transverse fields and the strong flows detected by IMaX/SUNRISE

Localized strongly Doppler-shifted Stokes V signals were detected by IMaX/SUNRISE. These signals are related to newly emerged magnetic loops that are observed as linear polarization features. We aim to set constraints on the physical nature and causes of these highly Doppler-shifted signals. In particular, the temporal relation between the appearance of transverse fields and the strong Doppler shifts is analyzed in some detail. We calculated the time difference between the appearance of the strong flows and the linear polarization. We also obtained the distances from the center of various features to the nearest neutral lines and whether they overlap or not. These distances were compared with those obtained from randomly distributed points on observed magnetograms. Various cases of strong flows are described in some detail. The linear polarization signals precede the appearance of the strong flows by on average 84+-11 seconds. The strongly Doppler-shifted signals are closer (0.19") to magnetic neutral lines than randomly distributed points (0.5"). Eighty percent of the strongly Doppler-shifted signals are close to a neutral line that is located between the emerging field and pre-existing fields. That the remaining 20% do not show a close-by pre-existing field could be explained by a lack of sensitivity or an unfavorable geometry of the pre-existing field, for instance, a canopy-like structure. Transverse fields occurred before the observation of the strong Doppler shifts. The process is most naturally explained as the emergence of a granular-scale loop that first gives rise to the linear polarization signals, interacts with pre-existing fields (generating new neutral line configurations), and produces the observed strong flows. This explanation is indicative of frequent small-scale reconnection events in the quiet Sun.Comment: 11 pages, 8 figure

A note on the Landauer principle in quantum statistical mechanics

The Landauer principle asserts that the energy cost of erasure of one bit of information by the action of a thermal reservoir in equilibrium at temperature T is never less than $kTlog 2$. We discuss Landauer's principle for quantum statistical models describing a finite level quantum system S coupled to an infinitely extended thermal reservoir R. Using Araki's perturbation theory of KMS states and the Avron-Elgart adiabatic theorem we prove, under a natural ergodicity assumption on the joint system S+R, that Landauer's bound saturates for adiabatically switched interactions. The recent work of Reeb and Wolf on the subject is discussed and compared

The formation and disintegration of magnetic bright points observed by Sunrise/IMaX

The evolution of the physical parameters of magnetic bright points (MBPs) located in the quiet Sun (mainly in the interwork) during their lifetime is studied. First we concentrate on the detailed description of the magnetic field evolution of three MBPs. This reveals that individual features follow different, generally complex, and rather dynamic scenarios of evolution. Next we apply statistical methods on roughly 200 observed MBP evolutionary tracks. MBPs are found to be formed by the strengthening of an equipartition field patch, which initially exhibits a moderate downflow. During the evolution, strong downdrafts with an average velocity of 2.4 km/s set in. These flows, taken together with the concurrent strengthening of the field, suggest that we are witnessing the occurrence of convective collapses in these features, although only 30% of them reach kG field strengths. This fraction might turn out to be larger when the new 4 m class solar telescopes are operational as observations of MBPs with current state of the art instrumentation could still be suffering from resolution limitations. Finally, when the bright point disappears (although the magnetic field often continues to exist) the magnetic field strength has dropped to the equipartition level and is generally somewhat weaker than at the beginning of the MBP's evolution. Noteworthy is that in about 10% of the cases we observe in the vicinity of the downflows small-scale strong (exceeding 2 km/s) intergranular upflows related spatially and temporally to these downflows.Comment: 19 pages, 13 figures; final version published in "The Astrophysical Journal

A Goldstone Theorem in Thermal Relativistic Quantum Field Theory

We prove a Goldstone Theorem in thermal relativistic quantum field theory, which relates spontaneous symmetry breaking to the rate of space-like decay of the two-point function. The critical rate of fall-off coincides with that of the massless free scalar field theory. Related results and open problems are briefly discussed