Inelastic Coulomb scattering rate of a multisubband Q1D electron gas

In this work, the Coulomb scattering lifetimes of electrons in two coupled quantum wires have been studied by calculating the quasiparticle self-energy within a multisubband model of quasi-one-dimensional (Q1D) electron system. We consider two strongly coupled quantum wires with two occupied subbands. The intrasubband and intersubband inelastic scattering rates are caculated for electrons in different subbands. Contributions of the intrasubband, intersubband plasmon excitations, as well as the quasiparticle excitations are investigated. Our results shows that the plasmon exictations of the first subband are the most important scattering mechanism for electrons in both subbands.Comment: 9 pages, REVTEX, 2 figure

The Variable-Order Fractional Calculus of Variations

This book intends to deepen the study of the fractional calculus, giving special emphasis to variable-order operators. It is organized in two parts, as follows. In the first part, we review the basic concepts of fractional calculus (Chapter 1) and of the fractional calculus of variations (Chapter 2). In Chapter 1, we start with a brief overview about fractional calculus and an introduction to the theory of some special functions in fractional calculus. Then, we recall several fractional operators (integrals and derivatives) definitions and some properties of the considered fractional derivatives and integrals are introduced. In the end of this chapter, we review integration by parts formulas for different operators. Chapter 2 presents a short introduction to the classical calculus of variations and review different variational problems, like the isoperimetric problems or problems with variable endpoints. In the end of this chapter, we introduce the theory of the fractional calculus of variations and some fractional variational problems with variable-order. In the second part, we systematize some new recent results on variable-order fractional calculus of (Tavares, Almeida and Torres, 2015, 2016, 2017, 2018). In Chapter 3, considering three types of fractional Caputo derivatives of variable-order, we present new approximation formulas for those fractional derivatives and prove upper bound formulas for the errors. In Chapter 4, we introduce the combined Caputo fractional derivative of variable-order and corresponding higher-order operators. Some properties are also given. Then, we prove fractional Euler-Lagrange equations for several types of fractional problems of the calculus of variations, with or without constraints.Comment: The final authenticated version of this preprint is available online as a SpringerBrief in Applied Sciences and Technology at [https://doi.org/10.1007/978-3-319-94006-9]. In this version some typos, detected by the authors while reading the galley proofs, were corrected, SpringerBriefs in Applied Sciences and Technology, Springer, Cham, 201

Diffusion-limited deposition with dipolar interactions: fractal dimension and multifractal structure

Computer simulations are used to generate two-dimensional diffusion-limited deposits of dipoles. The structure of these deposits is analyzed by measuring some global quantities: the density of the deposit and the lateral correlation function at a given height, the mean height of the upper surface for a given number of deposited particles and the interfacial width at a given height. Evidences are given that the fractal dimension of the deposits remains constant as the deposition proceeds, independently of the dipolar strength. These same deposits are used to obtain the growth probability measure through Monte Carlo techniques. It is found that the distribution of growth probabilities obeys multifractal scaling, i.e. it can be analyzed in terms of its $f(\alpha)$ multifractal spectrum. For low dipolar strengths, the $f(\alpha)$ spectrum is similar to that of diffusion-limited aggregation. Our results suggest that for increasing dipolar strength both the minimal local growth exponent $\alpha_{min}$ and the information dimension $D_1$ decrease, while the fractal dimension remains the same.Comment: 10 pages, 7 figure

Dynamics of a network fluid within the liquid-gas coexistence region

Low-density networks of molecules or colloids are formed at low temperatures when the interparticle interactions are valence limited. Prototypical examples are networks of patchy particles, where the limited valence results from highly directional pairwise interactions. We combine extensive Langevin simulations and Wertheim's theory of association to study these networks. We find a scale-free (relaxation) dynamics within the liquid-gas coexistence region, which differs from that usually observed for isotropic particles. While for isotropic particles the relaxation dynamics is driven by surface tension (coarsening), when the valence is limited, the slow relaxation proceeds through the formation of an intermediate non-equilibrium gel via a geometrical percolation transition in the Random Percolation universality class

Diffusion-limited deposition of dipolar particles

Deposits of dipolar particles are investigated by means of extensive Monte Carlo simulations. We found that the effect of the interactions is described by an initial, non-universal, scaling regime characterized by orientationally ordered deposits. In the dipolar regime, the order and geometry of the clusters depend on the strength of the interactions and the magnetic properties are tunable by controlling the growth conditions. At later stages, the growth is dominated by thermal effects and the diffusion-limited universal regime obtains, at finite temperatures. At low temperatures the crossover size increases exponentially as T decreases and at T=0 only the dipolar regime is observed.Comment: 5 pages, 4 figure

Trilinear Neutral Gauge Boson Couplings in Effective Theories

We list all the lowest dimension effective operators inducing off-shell trilinear neutral gauge boson couplings Z-Z-Photon, Z-Photon-Photon, and ZZZ within the effective Lagrangian approach, both in the linear and nonlinear realizations of the SU(2)_{L} X U(1)_Y gauge symmetry. In the linear scenario we find that these couplings can be generated only by dimension eight operators necessarily including the Higgs boson field, whereas in the nonlinear case they are induced by dimension six operators. We consider the impact of these couplings on some precision measurements such as the magnetic and electric dipole moments of fermions, as well as the Z boson rare decay Z -> neutrino+antineutrino+ photon. If the underlying new physics is of a decoupling nature, it is not expected that trilinear neutral gauge boson couplings may affect considerably any of these observables. On the contrary, it is just in the nonlinear scenario where these couplings have the more promising prospects of being perceptible through high precision experiments.Comment: 21 pages, 2 figures, RevTex formatte

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