Bound states of bosons and fermions in a mixed vector-scalar coupling with unequal shapes for the potentials

The Klein-Gordon and the Dirac equations with vector and scalar potentials are investigated under a more general condition, $V_{v}+V_{s}= \mathrm{constant}$. These intrinsically relativistic and isospectral problems are solved in a case of squared hyperbolic potential functions and bound states for either particles or antiparticles are found. The eigenvalues and eigenfuntions are discussed in some detail and the effective Compton wavelength is revealed to be an important physical quantity. It is revealed that a boson is better localized than a fermion when they have the same mass and are subjected to the same potentials.Comment: 3 figure

On Duffin-Kemmer-Petiau particles with a mixed minimal-nonminimal vector coupling and the nondegenerate bound states for the one-dimensional inversely linear background

The problem of spin-0 and spin-1 bosons in the background of a general mixing of minimal and nonminimal vector inversely linear potentials is explored in a unified way in the context of the Duffin-Kemmer-Petiau theory. It is shown that spin-0 and spin-1 bosons behave effectively in the same way. An orthogonality criterion is set up and it is used to determine uniquely the set of solutions as well as to show that even-parity solutions do not exist.Comment: 10 page

The peremptory influence of a uniform background for trapping neutral fermions with an inversely linear potential

The problem of neutral fermions subject to an inversely linear potential is revisited. It is shown that an infinite set of bound-state solutions can be found on the condition that the fermion is embedded in an additional uniform background potential. An apparent paradox concerning the uncertainty principle is solved by introducing the concept of effective Compton wavelength

Dynamical Renormalization Group Study for a Class of Non-local Interface Equations

We provide a detailed Dynamic Renormalization Group study for a class of stochastic equations that describe non-conserved interface growth mediated by non-local interactions. We consider explicitly both the morphologically stable case, and the less studied case in which pattern formation occurs, for which flat surfaces are linearly unstable to periodic perturbations. We show that the latter leads to non-trivial scaling behavior in an appropriate parameter range when combined with the Kardar-Parisi-Zhang (KPZ) non-linearity, that nevertheless does not correspond to the KPZ universality class. This novel asymptotic behavior is characterized by two scaling laws that fix the critical exponents to dimension-independent values, that agree with previous reports from numerical simulations and experimental systems. We show that the precise form of the linear stabilizing terms does not modify the hydrodynamic behavior of these equations. One of the scaling laws, usually associated with Galilean invariance, is shown to derive from a vertex cancellation that occurs (at least to one loop order) for any choice of linear terms in the equation of motion and is independent on the morphological stability of the surface, hence generalizing this well-known property of the KPZ equation. Moreover, the argument carries over to other systems like the Lai-Das Sarma-Villain equation, in which vertex cancellation is known {\em not to} imply an associated symmetry of the equation.Comment: 34 pages, 9 figures. Journal of Statistical Mechanics: Theory and Experiments (in press

Turning waves and breakdown for incompressible flows

We consider the evolution of an interface generated between two immiscible incompressible and irrotational fluids. Specifically we study the Muskat and water wave problems. We show that starting with a family of initial data given by (\al,f_0(\al)), the interface reaches a regime in finite time in which is no longer a graph. Therefore there exists a time $t^*$ where the solution of the free boundary problem parameterized as (\al,f(\al,t)) blows-up: \|\da f\|_{L^\infty}(t^*)=\infty. In particular, for the Muskat problem, this result allows us to reach an unstable regime, for which the Rayleigh-Taylor condition changes sign and the solution breaks down.Comment: 15 page

Gains from the upgrade of the cold neutron triple-axis spectrometer FLEXX at the BER-II reactor

The upgrade of the cold neutron triple-axis spectrometer FLEXX is described. We discuss the characterisation of the gains from the new primary spectrometer, including a larger guide and double focussing monochromator, and present measurements of the energy and momentum resolution and of the neutron flux of the instrument. We found an order of magnitude gain in intensity (at the cost of coarser momentum resolution), and that the incoherent elastic energy widths are measurably narrower than before the upgrade. The much improved count rate should allow the use of smaller single crystals samples and thus enable the upgraded FLEXX spectrometer to continue making leading edge measurements.Comment: 8 pages, 7 figures, 5 table

The Coulomb impurity problem in graphene

We address the problem of an unscreened Coulomb charge in graphene, and calculate the local density of states and displaced charge as a function of energy and distance from the impurity. This is done non-perturbatively in two different ways: (1) solving the problem exactly by studying numerically the tight-binding model on the lattice; (2) using the continuum description in terms of the 2D Dirac equation. We show that the Dirac equation, when properly regularized, provides a qualitative and quantitative low energy description of the problem. The lattice solution shows extra features that cannot be described by the Dirac equation, namely bound state formation and strong renormalization of the van Hove singularities.Comment: 3 Figures; minor typo corrections and minor update in Fig. 3