Parametric Competition in non-autonomous Hamiltonian Systems

In this work we use the formalism of chord functions (\emph{i.e.} characteristic functions) to analytically solve quadratic non-autonomous Hamiltonians coupled to a reservoir composed by an infinity set of oscillators, with Gaussian initial state. We analytically obtain a solution for the characteristic function under dissipation, and therefore for the determinant of the covariance matrix and the von Neumann entropy, where the latter is the physical quantity of interest. We study in details two examples that are known to show dynamical squeezing and instability effects: the inverted harmonic oscillator and an oscillator with time dependent frequency. We show that it will appear in both cases a clear competition between instability and dissipation. If the dissipation is small when compared to the instability, the squeezing generation is dominant and one can see an increasing in the von Neumann entropy. When the dissipation is large enough, the dynamical squeezing generation in one of the quadratures is retained, thence the growth in the von Neumann entropy is contained

Tuning the electronic structure of graphene by ion irradiation

Mechanically exfoliated graphene layers deposited on SiO2 substrate were irradiated with Ar+ ions in order to experimentally study the effect of atomic scale defects and disorder on the low-energy electronic structure of graphene. The irradiated samples were investigated by scanning tunneling microscopy and spectroscopy measurements, which reveal that defect sites, besides acting as scattering centers for electrons through local modification of the on-site potential, also induce disorder in the hopping amplitudes. The most important consequence of the induced disorder is the substantial reduction in the Fermi velocity, revealed by bias-dependent imaging of electron-density oscillations observed near defect sites

Ambiguities in the gravitational correction of quantum electrodynamics

We verify that quadratic divergences stemming from gravitational corrections to QED which have been conjectured to lead to asymptotic freedom near Planck scale are arbitrary (regularization dependent) and compatible with zero. Moreover we explicitly show that such arbitrary term contributes to the beta function of QED in a gauge dependent way in the gravitational sector

Small oscillations of a chiral Gross-Neveu system

We study the small oscillations regime (RPA approximation) of the time-dependent mean-field equations, obtained in a previous work, which describe the time evolution of one-body dynamical variables of a uniform Chiral Gross-Neveu system. In this approximation we obtain an analytical solution for the time evolution of the one-body dynamical variables. The two-fermion physics can be explored through this solution. The condition for the existence of bound states is examined.Comment: 21pages, Latex, 1postscript figur

Conductivity of Coulomb interacting massless Dirac particles in graphene: Regularization-dependent parameters and symmetry constraints

We compute the Coulomb correction $\mathcal{C}$ to the a. c. conductivity of interacting massless Dirac particles in graphene in the collisionless limit using the polarization tensor approach in a regularization independent framework. Arbitrary parameters stemming from differences between logarithmically divergent integrals are fixed on physical grounds exploiting only spatial $O(2)$ rotational invariance of the model which amounts to transversality of the polarization tensor. Consequently $\mathcal{C}$ is unequivocally determined to be $(19- 6\pi)/12$ within this effective model. We compare our result with explicit regularizations and discuss the origin of others results for $\mathcal{C}$ found in the literature

Charge transfer and Fermi level shift in p-doped single-walled carbon nanotubes

The electronic properties of p-doped single-walled carbon nanotube (SWNT) bulk samples were studied by temperature-dependent resistivity and thermopower, optical reflectivity, and Raman spectroscopy. These all give consistent results for the Fermi level downshift (Delta E(F)) induced by doping. We find Delta E(F) approximate to 0.35 eV and 0.50 eV for concentrated nitric and sulfuric acid doping respectively. With these values, the evolution of Raman spectra can be explained by variations in the resonance condition as E(F) moves down into the valence band. Furthermore, we find no evidence for diameter-selective doping, nor any distinction between doping responses of metallic and semiconducting tubes

Some aspects of mathematical and chemical modeling of complex chemical processes

Some theoretical questions involved in the mathematical modeling of the kinetics of complex chemical process are discussed. The analysis is carried out for the homogeneous oxidation of ethylbenzene in the liquid phase. Particular attention is given to the determination of the general characteristics of chemical systems from an analysis of mathematical models developed on the basis of linear algebra

Symmetries and Ambiguities in the linear sigma model with light quarks

We investigate the role of undetermined finite contributions generated by radiative corrections in a $SU(2)\times SU(2)$ linear sigma model with quarks. Although some of such terms can be absorbed in the renormalization procedure, one such contribution is left in the expression for the pion decay constant. This arbitrariness is eliminated by chiral symmetry.Comment: 9 pages. Added references through the text; an author was added due to an important contribution; corrected typos; the title also was changed. Submitted to Modern Physics Letter