Abstract:
A number of comments are provided on Rogers's model experiment to measure the circular Unruh vacuum noise by means of a hyperbolic Penning trap inside a microwave cavity. It is suggested that cylindrical Penning traps, being geometrically simpler, and controlled almost at the same level of accuracy as the hyperbolic trap, might be a better choice for such an experiment. Besides, the microwave modes of the trap itself, of known analytical structure, can be directly used in trying to obtain measurable results for such a tiny noise effect.

Abstract:
Using a version of Witten's supersymmetric quantum mechanics proposed by Caticha, we relate Montroll's kink to a traveling, asymmetric Morse double-well potential suggesting in this way a connection between kink modes and vibrational degrees of freedom along microtubules

Abstract:
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 period

Abstract:
Many living organisms on Earth are strongly dependent on water, the natural liquid of the planet. A possible reason for that could be the conjecture of Ryoji Takahashi [Phys. Lett. A 141, 15 (1989)] that water microdrops release negentropy through a phase transition to a phase with zero surface tension. Biological cells could make use of such a phase transition in their duty cycle. We comment on the relative merit of this conjecture, and present it in wider theoretical context.

Abstract:
The bosonic strictly isospectral problem for Demkov-Ostrovsky (DO) effective potentials in the radially nodeless sector is first solved in the supersymmetric Darboux-Witten (DW) half line (or l-changing) procedure. As an application, for the \kappa =1 class, if one goes back to optics examples, it might be possible to think of a one-parameter family of Maxwell lenses having the same optical scattering properties in the nodeless radial sector. Although the relative changes in the index of refraction that one may introduce in this way are at the level of several percents, at most, for all DO orbital quantum numbers l\geq 0, the index profiles are different from the original Maxwell one, possessing an inflection point within the lens. I pass then to the DW full line (or N-changing) procedure, obtaining the corresponding Morse-type problem for which the supersymmetric results are well established, and finally come back to the half line with well-defined results

Abstract:
I employ heuristically the strictly isospectral double Darboux method based on the general superpotential of unbroken nonrelativistic supersymmetry suggesting a few small steps of principle for extending its range of applications toward relativistic (gauge) physics. The application of the method to minisuperspace quantum cosmology is also briefly presented

Abstract:
Within unbroken SUSYQM and for zero factorization energy, I present an iterative generalization of Mielnik's isospectral method by employing a Schroedinger true zero mode in the first-step general Riccati solution and imposing the physical condition of normalization at each iterative step. This procedure leads to a well-defined multiple-parameter structure within Mielnik's construction for both zero modes and potentials

Abstract:
A simple version of the q-deformed calculus is used to generate a pair of q-nonlocal, second-order difference operators by means of deformed counterparts of Darboux intertwining operators for zero factorization energy. These deformed non-local operators may be considered as supersymmetric partners and their structure contains contributions originating in both the Hermite operator and the quantum harmonic oscillator operator. There are also extra $\pm x$ contributions. The undeformed limit, in which all q-nonlocalities wash out, corresponds to the usual supersymmetric pair of quantum mechanical harmonic oscillator Hamiltonians. The more general case of negative factorization energy is briefly discussed as well

Abstract:
A short review of Schroedinger hamiltonians for which the spectral problem has been related in the literature to the distribution of the prime numbers is presented here. We notice a possible connection between prime numbers and centrifugal inversions in black holes and suggest that this remarkable link could be directly studied within trapped Bose-Einstein condensates. In addition, when referring to the factorizing operators of Pitkanen and Castro and collaborators, we perform a mathematical extension allowing a more standard supersymmetric approach