Self-adjoint extensions for confined electrons: From a particle in a spherical cavity to the hydrogen atom in a sphere and on a cone

In a recent study of the self-adjoint extensions of the Hamiltonian of a particle confined to a finite region of space, in which we generalized the Heisenberg uncertainty relation to a finite volume, we encountered bound states localized at the wall of the cavity. In this paper, we study this situation in detail both for a free particle and for a hydrogen atom centered in a spherical cavity. For appropriate values of the self-adjoint extension parameter, the bound states localized at the wall resonate with the standard hydrogen bound states. We also examine the accidental symmetry generated by the Runge–Lenz vector, which is explicitly broken in a spherical cavity with general Robin boundary conditions. However, for specific radii of the confining sphere, a remnant of the accidental symmetry persists. The same is true for an electron moving on the surface of a finite circular cone, bound to its tip by a 1/r1/r potential.

Illusions of fusions: assessing cervical vertebral fusion on lateral cephalograms, multidetector computed tomographs, and cone-beam computed tomographs

INTRODUCTION The aims of this study were to compare lateral cephalograms with other radiologic methods for diagnosing suspected fusions of the cervical spine and to validate the assessment of congenital fusions and osteoarthritic changes against the anatomic truth. METHODS Four cadaver heads were selected with fusion of vertebrae C2 and C3 seen on a lateral cephalogram. Multidetector computed tomography (MDCT) and cone-beam computed tomography (CBCT) were performed and assessed by 5 general radiologists and 5 oral radiologists, respectively. Vertebrae C2 and C3 were examined for osseous fusions, and the left and right facet joints were diagnosed for osteoarthritis. Subsequently, the C2 and C3 were macerated and appraised by a pathologist. Descriptive analysis was performed, and interrater agreements between and within the groups were computed. RESULTS All macerated specimens showed osteoarthritic findings of varying degrees, but no congenital bony fusion. All observers agreed that no fusion was found on MDCT or CBCT. They disagreed on the prevalence of osteoarthritic deformities (general radiologists/MDCT, 100%; oral radiologists/CBCT, 93.3%) and joint space assessment in the facet joints (kappa = 0.452). The agreement within the rater groups differed considerably (general radiologists/MDCT, kappa = 0.612; oral radiologists/CBCT, kappa = 0.240). CONCLUSIONS Lateral cephalograms do not provide dependable data to assess the cervical spine for fusions and cause false-positive detections. Both MDCT interpreted by general radiologists and CBCT interpreted by oral radiologists are reliable methods to exclude potential fusions. Degenerative osteoarthritic changes are diagnosed more accurately and consistently by general radiologists evaluating MDCT.

Light-cone Wilson loop in classical lattice gauge theory

The transverse broadening of an energetic jet passing through a non-Abelian plasma is believed to be described by the thermal expectation value of a light-cone Wilson loop. In this exploratory study, we measure the light-cone Wilson loop with classical lattice gauge theory simulations. We observe, as suggested by previous studies, that there are strong interactions already at short transverse distances, which may lead to more efficient jet quenching than in leading-order perturbation theory. We also verify that the asymptotics of the Wilson loop do not change qualitatively when crossing the light cone, which supports arguments in the literature that infrared contributions to jet quenching can be studied with dimensionally reduced simulations in the space-like domain. Finally we speculate on possibilities for full four-dimensional lattice studies of the same observable, perhaps by employing shifted boundary conditions in order to simulate ensembles boosted by an imaginary velocity.

A versatile toolkit to produce sensitive FRET biosensors to visualize signaling in time and space

Genetically encoded, ratiometric biosensors based on fluorescence resonance energy transfer (FRET) are powerful tools to study the spatiotemporal dynamics of cell signaling. However, many biosensors lack sensitivity. We present a biosensor library that contains circularly permutated mutants for both the donor and acceptor fluorophores, which alter the orientation of the dipoles and thus better accommodate structural constraints imposed by different signaling molecules while maintaining FRET efficiency. Our strategy improved the brightness and dynamic range of preexisting RhoA and extracellular signal-regulated protein kinase (ERK) biosensors. Using the improved RhoA biosensor, we found micrometer-sized zones of RhoA activity at the tip of F-actin bundles in growth cone filopodia during neurite extension, whereas RhoA was globally activated throughout collapsing growth cones. RhoA was also activated in filopodia and protruding membranes at the leading edge of motile fibroblasts. Using the improved ERK biosensor, we simultaneously measured ERK activation dynamics in multiple cells using low-magnification microscopy and performed in vivo FRET imaging in zebrafish. Thus, we provide a construction toolkit consisting of a vector set, which enables facile generation of sensitive biosensors.