Effective-Mass Klein-Gordon-Yukawa Problem for Bound and Scattering States

Bound and scattering state solutions of the effective-mass Klein-Gordon equation are obtained for the Yukawa potential with any angular momentum $\ell$. Energy eigenvalues, normalized wave functions and scattering phase shifts are calculated as well as for the constant mass case. Bound state solutions of the Coulomb potential are also studied as a limiting case. Analytical and numerical results are compared with the ones obtained before.Comment: 13 pages, 1 figur

Perturbation Theory of Coulomb Gauge Yang-Mills Theory Within the First Order Formalism

Perturbative Coulomb gauge Yang-Mills theory within the first order formalism is considered. Using a differential equation technique and dimensional regularization, analytic results for both the ultraviolet divergent and finite parts of the two-point functions at one-loop order are derived. It is shown how the non-ultraviolet divergent parts of the results are finite at spacelike momenta with kinematical singularities on the light-cone and subsequent branch cuts extending into the timelike region.Comment: 23 pages, 6 figure

Volume Dependence of Bound States with Angular Momentum

We derive general results for the mass shift of bound states with angular momentum l >= 1 in a finite periodic volume. Our results have direct applications to lattice simulations of hadronic molecules as well as atomic nuclei. While the binding of S-wave bound states increases at finite volume, we show that the binding of P-wave bound states decreases. The mass shift for D-wave bound states as well as higher partial waves depends on the representation of the cubic rotation group. Nevertheless, the multiplet-averaged mass shift for any angular momentum l can be expressed in a simple form, and the sign of the shift alternates for even and odd l. We verify our analytical results with explicit numerical calculations. We also show numerically that similar volume corrections appear in three-body bound states.Comment: 4 pages, 3 figures, final versio

Coherent Destruction of Photon Emission from a Single Molecule Source

The behavior of a single molecule driven simultaneously by a laser and by an electric radio frequency field is investigated using a non-Hermitian Hamiltonian approach. Employing the renormalization group method for differential equations we calculate the average waiting time for the first photon emission event to occur, and determine the conditions for the suppression and enhancement of photon emission. An abrupt transition from localization-like behavior to delocalization behavior is found.Comment: 5 pages, 4 figure

Closed-orbit theory for spatial density oscillations

We briefly review a recently developed semiclassical theory for quantum oscillations in the spatial (particle and kinetic energy) densities of finite fermion systems and present some examples of its results. We then discuss the inclusion of correlations (finite temperatures, pairing correlations) in the semiclassical theory.Comment: LaTeX, 10pp., 2 figure

Controlling Polymer Capture and Translocation by Electrostatic Polymer-Pore Interactions

Polymer translocation experiments typically involve anionic polyelectrolytes such as DNA molecules driven through negatively charged nanopores. Quantitative modelling of polymer capture to the nanopore followed by translocation therefore necessitates the consideration of the electrostatic barrier resulting from like-charge polymer-pore interactions. To this end, in this work we couple mean-field level electrohydrodynamic equations with the Smoluchowski formalism to characterize the interplay between the electrostatic barrier, the electrophoretic drift, and the electro-osmotic liquid flow. In particular, we find that due to distinct ion density regimes where the salt screening of the drift and barrier effects occur, there exists a characteristic salt concentration maximizing the probability of barrier-limited polymer capture into the pore. We also show that in the barrier-dominated regime, the polymer translocation time increases exponentially with the membrane charge and decays exponentially fast with the pore radius and the salt concentration. These results suggest that the alteration of these parameters in the barrier-driven regime can be an efficient way to control the duration of the translocation process and facilitate more accurate measurements of the ionic current signal in the pore

Stability analysis of the Witten black hole (cigar soliton) under world-sheet RG flow

We analyze the stability of the Euclidean Witten black hole (the cigar soliton in mathematics literature) under first-order RG (Ricci) flow of the world-sheet sigma model. This analysis is from the target space point of view. We find that the Witten black hole has no unstable normalizable perturbative modes in a linearized mode analysis in which we consider circularly symmetric perturbations. Finally, we discuss a result from mathematics that implies the existence of a non-normalizable mode of the Witten black hole under which the geometry flows to the sausage solution studied by Fateev, Onofri and Zamolodchikov.Comment: 17 pages, version to appear in Physical Review D, and now has complete proof of stability for circularly symmetric perturbations, in response to referee comment

Impedance of a sphere oscillating in an elastic medium with and without slip

The dynamic impedance of a sphere oscillating in an elastic medium is considered. Oestreicher's formula for the impedance of a sphere bonded to the surrounding medium can be expressed simply in terms of three lumped impedances associated with the displaced mass and the longitudinal and transverse waves. If the surface of the sphere slips while the normal velocity remains continuous, the impedance formula is modified by adjusting the definition of the transverse impedance to include the interfacial impedance.Comment: 10 pages, 2 figure

Reflection and Transmission at the Apparent Horizon during Gravitational Collapse

We examine the wave-functionals describing the collapse of a self-gravitating dust ball in an exact quantization of the gravity-dust system. We show that ingoing (collapsing) dust shell modes outside the apparent horizon must necessarily be accompanied by outgoing modes inside the apparent horizon, whose amplitude is suppressed by the square root of the Boltzmann factor at the Hawking temperature. Likewise, ingoing modes in the interior must be accompanied by outgoing modes in the exterior, again with an amplitude suppressed by the same factor. A suitable superposition of the two solutions is necessary to conserve the dust probability flux across the apparent horizon, thus each region contains both ingoing and outgoing dust modes. If one restricts oneself to considering only the modes outside the apparent horizon then one should think of the apparent horizon as a partial reflector, the probability for a shell to reflect being given by the Boltzmann factor at the Hawking temperature determined by the mass contained within it. However, if one considers the entire wave function, the outgoing wave in the exterior is seen to be the transmission through the horizon of the interior outgoing wave that accompanies the collapsing shells. This transmission could allow information from the interior to be transferred to the exterior.Comment: 19 pages, no figures. To appear in Phys. Rev.

Energy conditions for a generally coupled scalar field outside a reflecting sphere

We calculate the stress-energy tensor for a scalar field with general curvature coupling, outside a perfectly reflecting sphere with Dirichlet boundary conditions. For conformal coupling we find that the null energy condition is always obeyed, and therefore the averaged null energy condition (ANEC) is also obeyed. Since the ANEC is independent of curvature coupling, we conclude that the ANEC is obeyed for scalar fields with any curvature coupling in this situation. We also show how the spherical case goes over to that of a flat plate as one approaches the sphere.Comment: Accepted for publication in Phys. Rev.