Nonlocal SUSY deformations of periodic potentials
Irreducible 2-order Darboux transformations are applied to the periodic Schrödinger’s operators. It is shown that for the pairs of factorization energies inside of the same forbidden band they can create new non-singular potentials with periodicity defects and bound states embedded into the spectral gaps. The method is applied to the Lamé and periodic piece-wise transparent potentials. An interesting phenomenon of translational Darboux invariance reveals nonlocal aspects of the supersymmetric deformations. PACS: 03.65.Ge; 03.65.Fd; 03.65.Ca

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: 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: 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: 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: 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.

title: Using black hole physics to compute the energy loss of a quark in strongly coupled QCD
abstract: The AdS/CFT duality can be applied to study strongly coupled regimes of QCD, such as the quark-gluon plasma. Gravity is a key factor in the understanding of the duality and an intriguing correspondence between the gravitational properties of higher-dimensional black holes and quark/gluon physics can be established. In this context, I will show that the dual theory allows us to identify a new mechanism for the energy loss of a deconfined quark in this plasma, which can be described as Cherenkov radiation of vectorial mesons. The corresponding results might be observed in heavy-ion collision experiments.

title: Transport in Anisotropic Superfluids: A Holographic Description

title: Towards collisions of inhomogeneous shockwaves in AdS
abstract: A bstractWe perform a numerical simulation of the evolution of inhomogeneities with transverse profile in a collision of gravitational shockwaves in asymptotically anti-de Sitter spacetime. This constitutes a step closer towards an accurate holographic description of the thermalization of a strongly coupled plasma, which can model the dynamics of heavy ion collisions. The results indicate that the considered inhomogeneities typically become hydrodynamical earlier or at the same moment when hydrodynamics applies to the background, even though they decay slowly.