Paying off the mortgage, once a widespread rite of passage for homeowners approaching retirement, has become less common in recent years. Concerns are mounting that the increased prevalence of housing debt among older homeowners could compromise financial security in retirement by expanding housing affordability problems, crimping essential nonhousing spending, increasing vulnerability to home ...

This article provides a pedagogical review on Klein tunneling in graphene, i.e. the peculiar tunneling properties of two-dimensional massless Dirac electrons. We consider two simple situations in detail: a massless Dirac electron incident either on a potential step or on a potential barrier and use elementary quantum wave mechanics to obtain the transmission probability. We emphasize the connec...

The problem of the scalar pair production by a one-dimensional vector-potential A µ (x 3) is reduced to the S− matrix formalism of the theory with an unstable vacuum. Our choice of in-and out-states does not coincide with that of other authors and we argue extensively in favor of our choice. In terms of our classification the states that can be created by the field enter into the field operator...

We derive an exact analytic solution to a Klein-Gordon equation for a step potential barrier with cutoff plane wave initial conditions, in order to explore wave evolution in a classical forbidden region. We find that the relativistic solution rapidly evanesces within a depth 2xp inside the potential, where xp is the penetration length of the stationary solution. Beyond the characteristic distan...

We apply the dressing method to a string solution given by a static string wrapped around the equator of a three-sphere and find that the result is the single spike solution recently discussed in the literature. Further application of the method allows the construction of solutions with multiple spikes. In particular we construct the solution describing the scattering of two single spikes and c...

The established methods used for measuring labour productivity originally designed for the manufacturing sector do not fit the specific characteristics of knowledge work. We therefore propose a more appropriate understanding of the driving forces behind knowledge work productivity, focussing on process quality instead of result quantity. In a three step potential analysis, we assess (1) the kno...

Employing a particularly suitable higher order symplectic integration algorithm, we integrate the 1-d nonlinear Schrr odinger equation numerically for solitons moving in external potentials. In particular, we study the scattering oo an interface separating two regions of constant potential. We nd that the soliton can break up into two solitons, eventually accompanied by radiation of non-solitar...