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 lo calized 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/r potential.Comment: 22 pages, 9 Figure

Presence of Legionellaceae in warm water supplies and typing of strains by polymerase chain reaction

Outbreaks of Legionnaire's disease present a public health challenge especially because fatal outcomes still remain frequent. The aim of this study was to describe the abundance and epidemiology of Legionellaceae in the human-made environment. Water was sampled from hot-water taps in private and public buildings across the area of Göttingen, Germany, including distant suburbs. Following isolation, we used polymerase chain reaction in order to generate strain specific banding profiles of legionella isolates. In total, 70 buildings were examined. Of these 18 (26%) had the bacterium in at least one water sample. Legionella pneumophila serogroups 1, 4, 5 and 6 could be identified in the water samples. Most of the buildings were colonized solely by one distinct strain, as proven by PCR. In three cases equal patterns were found in separate buildings. There were two buildings in this study where isolates with different serogroups were found at the same time

Asymptotic Freedom, Dimensional Transmutation, and an Infra-red Conformal Fixed Point for the δ\delta-Function Potential in 1-dimensional Relativistic Quantum Mechanics

We consider the Schr\"odinger equation for a relativistic point particle in an external 1-dimensional $\delta$-function potential. Using dimensional regularization, we investigate both bound and scattering states, and we obtain results that are consistent with the abstract mathematical theory of self-adjoint extensions of the pseudo-differential operator $H = \sqrt{p^2 + m^2}$. Interestingly, this relatively simple system is asymptotically free. In the massless limit, it undergoes dimensional transmutation and it possesses an infra-red conformal fixed point. Thus it can be used to illustrate non-trivial concepts of quantum field theory in the simpler framework of relativistic quantum mechanics

Fate of Accidental Symmetries of the Relativistic Hydrogen Atom in a Spherical Cavity

The non-relativistic hydrogen atom enjoys an accidental $SO(4)$ symmetry, that enlarges the rotational $SO(3)$ symmetry, by extending the angular momentum algebra with the Runge-Lenz vector. In the relativistic hydrogen atom the accidental symmetry is partially lifted. Due to the Johnson-Lippmann operator, which commutes with the Dirac Hamiltonian, some degeneracy remains. When the non-relativistic hydrogen atom is put in a spherical cavity of radius $R$ with perfectly reflecting Robin boundary conditions, characterized by a self-adjoint extension parameter $\gamma$, in general the accidental $SO(4)$ symmetry is lifted. However, for $R = (l+1)(l+2) a$ (where $a$ is the Bohr radius and $l$ is the orbital angular momentum) some degeneracy remains when $\gamma = \infty$ or $\gamma = \frac{2}{R}$. In the relativistic case, we consider the most general spherically and parity invariant boundary condition, which is characterized by a self-adjoint extension parameter. In this case, the remnant accidental symmetry is always lifted in a finite volume. We also investigate the accidental symmetry in the context of the Pauli equation, which sheds light on the proper non-relativistic treatment including spin. In that case, again some degeneracy remains for specific values of $R$ and $\gamma$.Comment: 27 pages, 7 figure

Majorana Fermions in a Box

Majorana fermion dynamics may arise at the edge of Kitaev wires or superconductors. Alternatively, it can be engineered by using trapped ions or ultracold atoms in an optical lattice as quantum simulators. This motivates the theoretical study of Majorana fermions confined to a finite volume, whose boundary conditions are characterized by self-adjoint extension parameters. While the boundary conditions for Dirac fermions in $(1+1)$-d are characterized by a 1-parameter family, $\lambda = - \lambda^*$, of self-adjoint extensions, for Majorana fermions $\lambda$ is restricted to $\pm i$. Based on this result, we compute the frequency spectrum of Majorana fermions confined to a 1-d interval. The boundary conditions for Dirac fermions confined to a 3-d region of space are characterized by a 4-parameter family of self-adjoint extensions, which is reduced to two distinct 1-parameter families for Majorana fermions. We also consider the problems related to the quantum mechanical interpretation of the Majorana equation as a single-particle equation. Furthermore, the equation is related to a relativistic Schr\"odinger equation that does not suffer from these problems.Comment: 23 pages, 2 figure

INVESTIGATION OF PATIENT PERCEPTION OF HOSPITAL NOISE AND SOUND LEVEL MEASUREMENTS: BEFORE, DURING, AND AFTER RENOVATIONS OF A HOSPITAL WING

Acoustic conditions in hospitals have been shown to influence a patient’s physical and psychological health. Noise levels in an Omaha, Nebraska, hospital were measured and compared between various times: before, during, and after renovations of a hospital wing. The renovations included cosmetic changes and the installation of new in-room patient audio-visual systems. Sound pressure levels were logged every 10-seconds over a four-day period in three different locations: at the nurses\u27 station, in the hallway, and in a nearby patient’s room. The resulting data were analyzed in terms of the hourly A-weighted equivalent sound pressure levels (eq) as well as various exceedence levels (). Additionally, a subjective noise perception patient survey was conducted to record the impressions of patients in the ward regarding noise. The relationships between a patient’s gender, age and responses to noise were examined. Results show that current noise level guidelines were exceeded regularly; despite this the surveys showed most patients were not very annoyed with the noise. Additionally, no relationships were found between a patient’s gender or age to various noise responses. The survey also asked participants to rank the most bothersome noise sources in the hospital environment and showed that the number of people annoyed by TV noise doubled from the during renovation to after renovation time periods. Overall this study did not find very large changes in sound levels or overall patient noise perception between the various time periods

Magnetic properties of antiferromagnetically coupled CoFeB/Ru/CoFeB

This work reports on the thermal stability of two amorphous CoFeB layers coupled antiferromagnetically via a thin Ru interlayer. The saturation field of the artificial ferrimagnet which is determined by the coupling, J, is almost independent on the annealing temperature up to more than 300 degree C. An annealing at more than 325 degree C significantly increases the coercivity, Hc, indicating the onset of crystallization.Comment: 4 pages, 3 figure

Nonstationary dynamics of the Alessandro-Beatrice-Bertotti-Montorsi model

We obtain an exact solution for the motion of a particle driven by a spring in a Brownian random-force landscape, the Alessandro-Beatrice-Bertotti-Montorsi (ABBM) model. Many experiments on quasi-static driving of elastic interfaces (Barkhausen noise in magnets, earthquake statistics, shear dynamics of granular matter) exhibit the same universal behavior as this model. It also appears as a limit in the field theory of elastic manifolds. Here we discuss predictions of the ABBM model for monotonous, but otherwise arbitrary, time-dependent driving. Our main result is an explicit formula for the generating functional of particle velocities and positions. We apply this to derive the particle-velocity distribution following a quench in the driving velocity. We also obtain the joint avalanche size and duration distribution and the mean avalanche shape following a jump in the position of the confining spring. Such non-stationary driving is easy to realize in experiments, and provides a way to test the ABBM model beyond the stationary, quasi-static regime. We study extensions to two elastically coupled layers, and to an elastic interface of internal dimension d, in the Brownian force landscape. The effective action of the field theory is equal to the action, up to 1-loop corrections obtained exactly from a functional determinant. This provides a connection to renormalization-group methods.Comment: 18 pages, 3 figure

Interacting Crumpled Manifolds: Exact Results to all Orders of Perturbation Theory

In this letter, we report progress on the field theory of polymerized tethered membranes. For the toy-model of a manifold repelled by a single point, we are able to sum the perturbation expansion in the strength g of the interaction exactly in the limit of internal dimension D -> 2. This exact solution is the starting point for an expansion in 2-D, which aims at connecting to the well studied case of polymers (D=1). We here give results to order (2-D)^4, where again all orders in g are resummed. This is a first step towards a more complete solution of the self-avoiding manifold problem, which might also prove valuable for polymers.Comment: 8 page