Supersymmetry of FRW barotropic cosmologies

Barotropic FRW cosmologies are presented from the standpoint of nonrelativistic supersymmetry. First, we reduce the barotropic FRW system of differential equations to simple harmonic oscillator differential equations. Employing the factorization procedure, the solutions of the latter equations are divided into the two classes of bosonic (nonsingular) and fermionic (singular) cosmological solutions. We next introduce a coupling parameter denoted by K between the two classes of solutions and obtain barotropic cosmologies with dissipative features acting on the scale factors and spatial curvature of the universe. The K-extended FRW equations in comoving time are presented in explicit form in the low coupling regime. The standard barotropic FRW cosmologies correspond to the dissipationless limit K =0Comment: 6 page

Supersymmetric Fokker-Planck strict isospectrality

I report a study of the nonstationary one-dimensional Fokker-Planck solutions by means of the strictly isospectral method of supesymmetric quantum mechanics. The main conclusion is that this technique can lead to a space-dependent (modulational) damping of the spatial part of the nonstationary Fokker-Planck solutions, which I call strictly isospectral damping. At the same time, using an additive decomposition of the nonstationary solutions suggested by the strictly isospectral procedure and by an argument of Englefield [J. Stat. Phys. 52, 369 (1988)], they can be normalized and thus turned into physical solutions, i.e., Fokker-Planck probability densities. There might be applications to many physical processes during their transient periodComment: revised version, scheduled for PRE 56 (1 August 1997) as a B

Generalized Hamiltonian structures for Ermakov systems

We construct Poisson structures for Ermakov systems, using the Ermakov invariant as the Hamiltonian. Two classes of Poisson structures are obtained, one of them degenerate, in which case we derive the Casimir functions. In some situations, the existence of Casimir functions can give rise to superintegrable Ermakov systems. Finally, we characterize the cases where linearization of the equations of motion is possible

Supersymmetric pairing of kinks for polynomial nonlinearities

We show how one can obtain kink solutions of ordinary differential equations with polynomial nonlinearities by an efficient factorization procedure directly related to the factorization of their nonlinear polynomial part. We focus on reaction-diffusion equations in the travelling frame and damped-anharmonic-oscillator equations. We also report an interesting pairing of the kink solutions, a result obtained by reversing the factorization brackets in the supersymmetric quantum mechanical style. In this way, one gets ordinary differential equations with a different polynomial nonlinearity possessing kink solutions of different width but propagating at the same velocity as the kinks of the original equation. This pairing of kinks could have many applications. We illustrate the mathematical procedure with several important cases, among which the generalized Fisher equation, the FitzHugh-Nagumo equation, and the polymerization fronts of microtubulesComment: 13 pages, 2 figures, revised during the 2nd week of Dec. 200

Benchmarking acid and base dopants with respect to enabling the ice V to XIII and ice VI to XV hydrogen-ordering phase transitions

Doping the hydrogen-disordered phases of ice V, VI and XII with hydrochloric acid (HCl) has led to the discovery of their hydrogen-ordered counterparts ices XIII, XV and XIV. Yet, the mechanistic details of the hydrogen-ordering phase transitions are still not fully understood. This includes in particular the role of the acid dopant and the defect dynamics that it creates within the ices. Here we investigate the effects of several acid and base dopants on the hydrogen ordering of ices V and VI with calorimetry and X-ray diffraction. HCl is found to be most effective for both phases which is attributed to a favourable combination of high solubility and strong acid properties which create mobile H3O+ defects that enable the hydrogen-ordering processes. Hydrofluoric acid (HF) is the second most effective dopant highlighting that the acid strengths of HCl and HF are much more similar in ice than they are in liquid water. Surprisingly, hydrobromic acid doping facilitates hydrogen ordering in ice VI whereas only a very small effect is observed for ice V. Conversely, lithium hydroxide (LiOH) doping achieves a performance comparable to HF-doping in ice V but it is ineffective in the case of ice VI. Sodium hydroxide, potassium hydroxide (as previously shown) and perchloric acid doping are ineffective for both phases. These findings highlight the need for future computational studies but also raise the question why LiOH-doping achieves hydrogen-ordering of ice V whereas potassium hydroxide doping is most effective for the 'ordinary' ice Ih.Comment: 18 pages, 7 figures, 1 tabl

Shape invariance through Crum transformation

We show in a rigorous way that Crum's result on equal eigenvalue spectrum of Sturm-Liouville problems can be obtained iteratively by successive Darboux transformations. It can be shown that all neighbouring Darboux-transformed potentials of higher order, u_{k} and u_{k+1}, satisfy the condition of shape invariance provided the original potential u does. We use this result to proof that under the condition of shape invariance the n-th iteration of the original Sturm-Liouville problem defined through shape invariance is equal to the n-th Crum transformationComment: 26 pp, one more reference, J.-M. Sparenberg and D. Baye, J. Phys. A 28, 5079 (1995), has been added as Ref. 18 in the published version, which has 47 ref

Hydrogen atom as an eigenvalue problem in 3D spaces of constant curvature and minimal length

An old result of A.F. Stevenson [Phys. Rev.} 59, 842 (1941)] concerning the Kepler-Coulomb quantum problem on the three-dimensional (3D) hypersphere is considered from the perspective of the radial Schr\"odinger equations on 3D spaces of any (either positive, zero or negative) constant curvature. Further to Stevenson, we show in detail how to get the hypergeometric wavefunction for the hydrogen atom case. Finally, we make a comparison between the ``space curvature" effects and minimal length effects for the hydrogen spectrumComment: 6 pages, v

Iso-spectral potential and inflationary quantum cosmology

Using the factorization approach of quantum mechanics, we obtain a family of isospectral scalar potentials for power law inflationary cosmology. The construction is based on a scattering Wheeler-DeWitt solution. These iso-spectrals have new features, they give a mechanism to end inflation, as well as the possibility to have new inflationary epochs. The procedure can be extended to other cosmological models.Comment: 14 pages, 5 figure