New hydrogen-like potentials
Using the modified factorization method employed in , we construct a new class of radial potentials whose spectrum for l=0 coincides exactly with that of the hydrogen atom. A limiting case of our family coincides with the potentials previously derived by Abraham and Moses .

title: Hamiltonians with two-ladder spectra and solutions to the Painlevé IV equation
abstract: Some supersymmetric partners of the harmonic oscillator Hamiltonian possess third-order differential ladder operators and, thus, they realize the second-order polynomial Heisenberg algebras. The corresponding spectra consist of an infinite ladder of energy levels plus a finite one that can be placed at any position with respect to the infinite ladder. Both of them have equally spaced energy levels. Departing from these Hamiltonians several families of real and complex solutions to the Painleve IV equation with real parameters will be generated.

title: New exactly-solvable potentials from inverted oscillator
abstract: In this article we will apply the firstand second-order supersymmetric quantum mechanics to obtain new exactly-solvable real potentials departing from the inverted oscillator potential. This system has some properties which make it special, in particular, only very specific second-order transformations produce non-singular real potentials. It will be shown that these transformations turn out to be the so-called ‘complex’ ones.

title: The confluent algorithm in second-order supersymmetric quantum mechanics
abstract: The confluent algorithm, a degenerate case of the second-order supersymmetric quantum mechanics, is studied. It is shown that the transformation function must asymptotically vanish to induce non-singular final potentials. The technique can be used to create a single level above the initial ground state energy. The method is applied to the free particle, one-soliton well and harmonic oscillator.

title: Evolution loops and spin 1/2 systems
abstract: The derivation of a new family of magnetic fields inducing exactly solvable spin evolutions is presented. The conditions for which these fields generate the evolution loops (dynamical processes for which any spin state evolves cyclically) are studied. Their natural connection with geometric phases and the corresponding calculation is also elaborated.

title: Non-hermitian Hamiltonians and the Painlevé IV equation with real parameters
abstract: In this Letter we will use higher-order supersymmetric quantum mechanics to obtain several families of complex solutions g ( x ; a , b ) of the Painleve IV equation with real parameters a , b . We shall also study the algebraic structure, the eigenfunctions and the energy spectra of the corresponding non-hermitian Hamiltonians.

title: Cherenkov mesons as in-medium quark energy loss
abstract: We recently showed that a heavy quark moving sufficiently fast through a quark-gluon plasma may lose energy by Cherenkov-radiating mesons . Here we review our previous holographic calculation of the energy loss in $ \mathcal{N} = 4 $ Super Yang-Mills and extend it to longitudinal vector mesons and scalar mesons. We also discuss phenomenological implications for heavy-ion collision experiments. Although the Cherenkov energy loss is an $ \mathcal{O}\left(  \left/ {{{N_c}}} \right.}} \right) $ effect, a ballpark estimate yields a value of dE/dx for Nc = 3 which is comparable to that of other mechanisms.

title: Jet quenching in a strongly coupled anisotropic plasma
abstract: A bstractThe jet quenching parameter of an anisotropic plasma depends on the relative orientation between the anisotropic direction, the direction of motion of the parton, and the direction along which the momentum broadening is measured. We calculate the jet quenching parameter of an anisotropic, strongly coupled $ \mathcal{N} = 4 $ plasma by means of its gravity dual. We present the results for arbitrary orientations and arbitrary values of the anisotropy. The anisotropic value can be larger or smaller than the isotropic one, and this depends on whether the comparison is made at equal temperatures or at equal entropy densities. We compare our results to analogous calculations for the real-world quark-gluon plasma and find agreement in some cases and disagreement in others.

title: Varying electric charge in multiscale spacetimes
abstract: We derive the covariant equations of motion for Maxwell field theory and electrodynamics in multi-scale spacetimes with weighted Laplacian. An effective spacetime- dependent electric charge of geometric origin naturally emerges from the theory, thus giving rise to a varying fine-structure constant. The theory is compared with other varying- coupling models, such as those with a varying electric charge or varying speed of light. The theory is also confronted with cosmological observations, which can place constraints on the characteristic scales in the multi-fractional measure. We note that the model considered here is fundamentally different from those previously proposed in the literature, either of the varying-e or varying-c persuasion.