José Weberszpil

On a connection between a class of q-deformed algebras and the Hausdorff derivative in a medium with fractal metric

Over the recent decades, diverse formalisms have emerged that are adopted to approach complex systems. Amongst those, we may quote the q-calculus in Tsallis’ version of Non-Extensive Statistics with its undeniable success whenever applied to a wide class of different systems; Kaniadakis’ approach, based on the compatibility between relativity and thermodynamics; Fractional Calculus (FC), that deals with the dynamics of anomalous transport and other natural phenomena, and also some local versions of FC that claim to be able to study fractal and multifractal spaces and to describe dynamics in these spaces by means of fractional differential equations.

Extending the D’alembert solution to space–time Modified Riemann–Liouville fractional wave equations

Abstract In the realm of complexity, it is argued that adequate modeling of TeV-physics demands an approach based on fractal operators and fractional calculus (FC). Non-local theories and memory effects are connected to complexity and the FC. The non-differentiable nature of the microscopic dynamics may be connected with time scales. Based on the Modified Riemann–Liouville definition of fractional derivatives, we have worked out explicit solutions to a fractional wave equation with suitable initial conditions to carefully understand the time evolution of classical fields with a fractional dynamics. First, by considering space–time partial fractional derivatives of the same order in time and space, a generalized fractional D’alembertian is introduced and by means of a transformation of variables to light-cone coordinates, an explicit analytical solution is obtained. To address the situation of different orders in the time and space derivatives, we adopt different approaches, as it will become clear throughout this paper. Aspects connected to Lorentz symmetry are analyzed in both approaches.

A resonant tunneling diode based on a Ga1 xMnxAs=GaAs double barrier structure

Abstract We introduce here a device capable of producing a strongly spin-polarized current. It can be useful in spintronics as a polarizer, an analyzer and other applications. Consequently, it could be useful in quantum computing. The device consists of a resonant tunneling diode with a ferromagnetic well made of Ga1−xMnxAs. The levels at the well are spin polarized and so is the current through the system. To study the transport properties of the system we use a new formalism capable of treating, in an exact and very efficient way, an open system. The result is that the current could be polarized parallel or antiparallel to the magnetization of the well, depending on the applied bias.

Variational approach and deformed derivatives

Recently, we have demonstrated that there exists a possible relationship between q-deformed algebras in two different contexts of Statistical Mechanics, namely, the Tsallis’ framework and the Kaniadakis’ scenario, with a local form of fractional-derivative operators for fractal media, the so-called Hausdorff derivatives, mapped into a continuous medium with a fractal measure. Here, in this paper, we present an extension of the traditional calculus of variations for systems containing deformed-derivatives embedded into the Lagrangian and the Lagrangian densities for classical and field systems. The results extend the classical Euler–Lagrange equations and the Hamiltonian formalism. The resulting dynamical equations seem to be compatible with those found in the literature, specially with mass-dependent and with nonlinear equations for systems in classical and quantum mechanics. Examples are presented to illustrate applications of the formulation. Also, the conserved ​Noether current is worked out.

A double-barrier heterostructure generator of terahertz phonons: many-body effects

In this paper we study the generation of coherent terahertz phonons in a double-barrier heterostructure (DBH) under the influence of an external applied bias. The system is characterized by an energy difference between the two lowest levels in the well, which resonates with the optical phonon energy, producing a high rate of emission of longitudinal optical (LO) phonons. The strong electron-phonon interaction in a polar semiconductor leads to the formation of a polaron that is relevant close to this resonance. Therefore the levels corresponding to the first excited state and the satellite of the ground state anticross in two polaronic branches. The LO phonon has a very short lifetime. It decays by stimulated emission of a pair of phonons (LO + TA) (where TA stands for transverse acoustic). As a consequence an intense beam of TA coherent phonons is produced, which could have several important applications. A rough model of this system has already been presented (Makler S S, Vasilevskiy M I, Weberszpil J, Anda E V, Tuyarot D E and Pastawski H M 1998 J. Phys.: Condens. Matter 10 5905). Several improvements to that model are presented here. Besides the more accurate treatment of the electron-phonon interaction, the phonon-phonon interaction is considered here taking into account the fact that the whole system is out of equilibrium. The results confirm that the proposed phonon laser is reliable.

Generalized Maxwell Relations in Thermodynamics with Metric Derivatives

In this contribution, we develop the Maxwell generalized thermodynamical relations via the metric derivative model upon the mapping to a continuous fractal space. This study also introduces the total q-derivative expressions depending on two variables, to describe nonextensive statistical mechanics and also the α -total differentiation with conformable derivatives. Some results in the literature are re-obtained, such as the physical temperature defined by Sumiyoshi Abe.

Angular correlation measurements in (Ag, In)/CdCr2Se4

We report time differential perturbed angular correlation (TDPAC) measurements above and below the Curie temperature of the ferromagnetic semiconductor (Ag, In)/CdCr2Se4. The TDPAC spectra for the Ag and In dopants have profound differences which we attribute to distinct site occupations of these impurities in the spinel structure.

Structural scale q-derivative and the LLG equation in a scenario with fractionality

In the present contribution, we study the Landau-Lifshitz-Gilbert equation with two versions of structural derivatives recently proposed: the scale

Fractional Canonical Quantization: a Parallel with Noncommutativity

q-

A many body study of the SASER dynamics

derivative in the non-extensive statistical mechanics and the axiomatic metric derivative, which presents Mittag-Leffler functions as eigenfunctions. The use of structural derivatives aims to take into account long-range forces, possible non-manifest or hidden interactions and the dimensionality of space. Having this purpose in mind, we build up an evolution operator and a deformed version of the LLG equation. Damping in the oscillations naturally show up without an explicit Gilbert damping term.