Raising and lowering operators and their factorization for generalized orthogonal polynomials of hypergeometric type on homogeneous and non-homogeneous lattice

We complete the construction of raising and lowering operators, given in a previous work, for the orthogonal polynomials of hypergeometric type on non-homogeneous lattice, and extend these operators to the generalized orthogonal polynomials, namely, those difference of orthogonal polynomials that satisfy a similar difference equation of hypergeometric type.Comment: LaTeX, 19 pages, (late submission to arXiv.org

Evaporation of (quantum) black holes and energy conservation

We consider Hawking radiation as due to a tunneling process in a black hole were quantum corrections, derived from Quantum Einstein Gravity, are taken into account. The consequent derivation, satisfying conservation laws, leads to a deviation from an exact thermal spectrum. The non-thermal radiation is shown to carry information out of the black hole. Under the appropriate approximation, a quantum corrected temperature is assigned to the black hole. The evolution of the quantum black hole as it evaporates is then described by taking into account the full implications of energy conservation as well as the back-scattered radiation. It is shown that, as a critical mass of the order of Planck's mass is reached, the evaporation process decelerates abruptly while the black hole mass decays towards this critical mass.Comment: 16 pages, 2 figure

The mechanism why colliders could create quasi-stable black holes

It has been postulated that black holes could be created in particle collisions within the range of the available energies for nowadays colliders (LHC). In this paper we analyze the evaporation of a type of black holes that are candidates for this specific behaviour, namely, small black holes on a brane in a world with large extra-dimensions. We examine their evolution under the assumption that energy conservation is satisfied during the process and compare it with the standard evaporation approach. We claim that, rather than undergoing a quick total evaporation, black holes become quasi-stable. We comment on the (absence of) implications for safety of this result. We also discuss how the presence of black holes together with the correctness of the energy conservation approach might be experimentally verified.Comment: 16 pages, 3 figure

Representations of the discrete inhomogeneous Lorentz group and Dirac wave equation on the lattice

We propose the fundamental and two dimensional representation of the Lorentz groups on a (3+1)-dimensional hypercubic lattice, from which representations of higher dimensions can be constructed. For the unitary representation of the discrete translation group we use the kernel of the Fourier transform. From the Dirac representation of the Lorentz group (including reflections) we derive in a natural way the wave equation on the lattice for spin 1/2 particles. Finally the induced representation of the discrete inhomogeneous Lorentz group is constructed by standard methods and its connection with the continuous case is discussed.Comment: LaTeX, 20 pages, 1 eps figure, uses iopconf.sty (late submission

Quenching of magnetic excitations in single adsorbates at surfaces: Mn on CuN/Cu(100)

The lifetimes of spin excitations of Mn adsorbates on CuN/Cu(100) are computed from first-principles. The theory is based on a strong-coupling T-matrix approach that evaluates the decay of a spin excitation due to electron-hole pair creation. Using a previously developed theory [Phys. Rev. Lett. {\bf 103}, 176601 (2009) and Phys. Rev. B {\bf 81}, 165423 (2010)], we compute the excitation rates by a tunneling current for all the Mn spin states. A rate equation approach permits us to simulate the experimental results by Loth and co-workers [Nat. Phys. {\bf 6}, 340 (2010)] for large tunnelling currents, taking into account the finite population of excited states. Our simulations give us insight into the spin dynamics, in particular in the way polarized electrons can reveal the existence of an excited state population. In addition, it reveals that the excitation process occurs in a way very different from the deexcitation one. Indeed, while excitation by tunnelling electrons proceeds via the s and p electrons of the adsorbate, deexcitation mainly involves the d electrons

Raising and lowering operators, factorization and differential/difference operators of hypergeometric type

Starting from Rodrigues formula we present a general construction of raising and lowering operators for orthogonal polynomials of continuous and discrete variable on uniform lattice. In order to have these operators mutually adjoint we introduce orthonormal functions with respect to the scalar product of unit weight. Using the Infeld-Hull factorization method, we generate from the raising and lowering operators the second order self-adjoint differential/difference operator of hypergeometric type.Comment: LaTeX, 24 pages, iopart style (late submission

A cotunneling mechanism for all-electrical Electron Spin Resonance of single adsorbed atoms

The recent development of all-electrical electron spin resonance (ESR) in a scanning tunneling microscope (STM) setup has opened the door to vast applications. Despite the fast growing number of experimental works on STM-ESR, the fundamental principles remains unclear. By using a cotunneling picture, we show that the spin resonance signal can be explained as a time-dependent variation of the tunnel barrier induced by the alternating electric driving field. We demonstrate how this variation translates into the resonant frequency response of the direct current. Our cotunneling theory explains the main experimental findings. Namely, the linear dependence of the Rabi flop rate with the alternating bias amplitude, the absence of resonant response for spin-unpolarized currents, and the weak dependence on the actual atomic species.Comment: 11 pages, 3 figure