Analysis of the second order exchange self energy of a dense electron gas

We investigate the evaluation of the six-fold integral representation for the second order exchange contribution to the self energy of a three dimensional electron gas at the Fermi surface.Comment: 6 page

A momentum-space Argonne V18 interaction

This paper gives a momentum-space representation of the Argonne V18 potential as an expansion in products of spin-isospin operators with scalar coefficient functions of the momentum transfer. Two representations of the scalar coefficient functions for the strong part of the interaction are given. One is as an expansion in an orthonormal basis of rational functions and the other as an expansion in Chebyshev polynomials on different intervals. Both provide practical and efficient representations for computing the momentum-space potential that do not require integration or interpolation. Programs based on both expansions are available as supplementary material. Analytic expressions are given for the scalar coefficient functions of the Fourier transform of the electromagnetic part of the Argonne V18. A simple method for computing the partial-wave projections of these interactions from the operator expressions is also given.Comment: 61 pages. 26 figure

The scalar box integral and the Mellin - Barnes representation

We solve exactly the scalar box integral using the Mellin-Barnes representation. Firstly we recognize the hypergeometric functions resumming the series coming from the scalar integrals, then we perform an analytic continuation before applying the Laurent expansion in^2 = (d !' 4)=2 of the result.Comment: 13 pages, no figure

Driving quantum walk spreading with the coin operator

We generalize the discrete quantum walk on the line using a time dependent unitary coin operator. We find an analytical relation between the long-time behaviors of the standard deviation and the coin operator. Selecting the coin time sequence allows to obtain a variety of predetermined asymptotic wave-function spreadings: ballistic, sub-ballistic, diffusive, sub-diffusive and localized.Comment: 6 pages, 3 figures, appendix added. to appear in PR

Coulomb potential in one dimension with minimal length: A path integral approach

We solve the path integral in momentum space for a particle in the field of the Coulomb potential in one dimension in the framework of quantum mechanics with the minimal length given by $(\Delta X)_{0}=\hbar \sqrt{\beta}$, where $\beta$ is a small positive parameter. From the spectral decomposition of the fixed energy transition amplitude we obtain the exact energy eigenvalues and momentum space eigenfunctions

On the dissipative effects in the electron transport through conducting polymer nanofibers

Here, we study the effects of stochastic nuclear motions on the electron transport in doped polymer fibers assuming the conducting state of the material. We treat conducting polymers as granular metals and apply the quantum theory of conduction in mesoscopic systems to describe the electron transport between the metalliclike granules. To analyze the effects of nuclear motions we mimic them by the phonon bath, and we include the electron-phonon interactions in consideration. Our results show that the phonon bath plays a crucial part in the intergrain electron transport at moderately low and room temperatures suppressing the original intermediate state for the resonance electron tunneling, and producing new states which support the electron transport.Comment: 6 pages, 4 figures, minor changes are made in the Fig. 3, accepted for publication in J. of Chem. Phys

Stationary point approach to the phase transition of the classical XY chain with power-law interactions

The stationary points of the Hamiltonian H of the classical XY chain with power-law pair interactions (i.e., decaying like r^{-{\alpha}} with the distance) are analyzed. For a class of "spinwave-type" stationary points, the asymptotic behavior of the Hessian determinant of H is computed analytically in the limit of large system size. The computation is based on the Toeplitz property of the Hessian and makes use of a Szeg\"o-type theorem. The results serve to illustrate a recently discovered relation between phase transitions and the properties of stationary points of classical many-body Hamiltonian functions. In agreement with this relation, the exact phase transition energy of the model can be read off from the behavior of the Hessian determinant for exponents {\alpha} between zero and one. For {\alpha} between one and two, the phase transition is not manifest in the behavior of the determinant, and it might be necessary to consider larger classes of stationary points.Comment: 9 pages, 6 figure

Non-Gaussianity as a signature of thermal initial condition of inflation

We study non-Gaussianities in the primordial perturbations in single field inflation where there is radiation era prior to inflation. Inflation takes place when the energy density of radiation drops below the value of the potential of a coherent scalar field. We compute the thermal average of the two, three and four point correlation functions of inflaton fluctuations. The three point function is proportional to the slow roll parameters and there is an amplification in $f_{NL}$ by a factor of 65 to 90 due to the contribution of the thermal bath, and we conclude that the bispectrum is in the range of detectability with the 21-cm anisotropy measurements. The four point function on the other hand appears in this case due to the thermal averaging and the fact that thermal averaging of four-point correlation is not the same as the square of the thermal averaging of the two-point function. Due to this fact $\tau_{NL}$ is not proportional to the slow-roll parameters and can be as large as -42. The non-Gaussianities in the four point correlation of the order 10 can also be detected by 21-cm background observations. We conclude that a signature of thermal inflatons is a large trispectrum non-Gaussianity compared to the bispectrum non-Gaussianity.Comment: 17 RevTeX4 pages, 2 figures, One paragraph added in Introduction, No further changes made, Accepted for publication in PR

Spectrum in the broken phase of a λϕ4\lambda\phi^4 theory

We derive the spectrum in the broken phase of a $\lambda\phi^4$ theory, in the limit $\lambda\to\infty$, showing that this goes as even integers of a renormalized mass in agreement with recent lattice computations.Comment: 4 pages, 1 figure. Accepted for publication in International Journal of Modern Physics

Quantum transport of Dirac electrons in graphene in the presence of a spatially modulated magnetic field

We have investigated the electrical transport properties of Dirac electrons in a monolayer graphene sheet in the presence of a perpendicular magnetic field that is modulated weakly and periodically along one direction.We find that the Landau levels broaden into bands and their width oscillates as a function of the band index and the magnetic field.We determine the $\sigma_{yy}$ component of the magnetoconductivity tensor for this system which is shown to exhibit Weiss oscillations.We also determine analytically the asymptotic expressions for $\sigma_{yy}$.We compare these results with recently obtained results for electrically modulated graphene as well as those for magnetically modulated conventional two-dimensional electron gas (2DEG) system.We find that in the magnetically modulated graphene system cosidered in this work,Weiss oscillations in $\sigma_{yy}$ have a reduced amplitude compared to the 2DEG but are less damped by temperature while they have a higher amplitude than in the electrically modulated graphene system. We also find that these oscillations are out of phase by $\pi$ with those of the electrically modulated system while they are in phase with those in the 2DEG system.Comment: Accepted in PRB: 10 pages, 3 figure