Effects of quantum deformation on the spin-1/2 Aharonov-Bohm problem

In this letter we study the Aharonov-Bohm problem for a spin-1/2 particle in the quantum deformed framework generated by the $\kappa$-Poincar\'{e}-Hopf algebra. We consider the nonrelativistic limit of the $\kappa$-deformed Dirac equation and use the spin-dependent term to impose an upper bound on the magnitude of the deformation parameter $\varepsilon$. By using the self-adjoint extension approach, we examine the scattering and bound state scenarios. After obtaining the scattering phase shift and the $S$-matrix, the bound states energies are obtained by analyzing the pole structure of the latter. Using a recently developed general regularization prescription [Phys. Rev. D. \textbf{85}, 041701(R) (2012)], the self-adjoint extension parameter is determined in terms of the physics of the problem. For last, we analyze the problem of helicity conservation.Comment: 12 pages, no figures, submitted for publicatio

Remarks on the Aharonov-Casher dynamics in a CPT-odd Lorentz-violating background

The Aharonov-Casher problem in the presence of a Lorentz-violating background nonminimally coupled to a spinor and a gauge field is examined. Using an approach based on the self-adjoint extension method, an expression for the bound state energies is obtained in terms of the physics of the problem by determining the self-adjoint extension parameter.Comment: Matches published versio

Electronic Griffiths phase of the d=2 Mott transition

We investigate the effects of disorder within the T=0 Brinkman-Rice (BR) scenario for the Mott metal-insulator transition (MIT) in two dimensions (2d). For sufficiently weak disorder the transition retains the Mott character, as signaled by the vanishing of the local quasiparticles (QP) weights Z_{i} and strong disorder screening at criticality. In contrast to the behavior in high dimensions, here the local spatial fluctuations of QP parameters are strongly enhanced in the critical regime, with a distribution function P(Z) ~ Z^{\alpha-1} and \alpha tends to zero at the transition. This behavior indicates a robust emergence of an electronic Griffiths phase preceding the MIT, in a fashion surprisingly reminiscent of the "Infinite Randomness Fixed Point" scenario for disordered quantum magnets.Comment: 4+ pages, 5 figures, final version to appear in Physical Review Letter

Multifractal Properties of Aperiodic Ising Model: role of geometric fluctuations

The role of the geometric fluctuations on the multifractal properties of the local magnetization of aperiodic ferromagnetic Ising models on hierachical lattices is investigated. The geometric fluctuations are introduced by generalized Fibonacci sequences. The local magnetization is evaluated via an exact recurrent procedure encompassing a real space renormalization group decimation. The symmetries of the local magnetization patterns induced by the aperiodic couplings is found to be strongly (weakly) different, with respect to the ones of the corresponding homogeneous systems, when the geometric fluctuations are relevant (irrelevant) to change the critical properties of the system. At the criticality, the measure defined by the local magnetization is found to exhibit a non-trivial F(alpha) spectra being shifted to higher values of alpha when relevant geometric fluctuations are considered. The critical exponents are found to be related with some special points of the F(alpha) function and agree with previous results obtained by the quite distinct transfer matrix approach.Comment: 10 pages, 7 figures, 3 Tables, 17 reference

On the κ\kappa-Dirac Oscillator revisited

This Letter is based on the $\kappa$-Dirac equation, derived from the $\kappa$-Poincar\'{e}-Hopf algebra. It is shown that the $\kappa$-Dirac equation preserves parity while breaks charge conjugation and time reversal symmetries. Introducing the Dirac oscillator prescription, $\mathbf{p}\to\mathbf{p}-im\omega\beta\mathbf{r}$, in the $\kappa$-Dirac equation, one obtains the $\kappa$-Dirac oscillator. Using a decomposition in terms of spin angular functions, one achieves the deformed radial equations, with the associated deformed energy eigenvalues and eigenfunctions. The deformation parameter breaks the infinite degeneracy of the Dirac oscillator. In the case where $\varepsilon=0$, one recovers the energy eigenvalues and eigenfunctions of the Dirac oscillator.Comment: 5 pages, no figures, accepted for publication in Physics Letters