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

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

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

Inference of entropies of discrete random variables with unknown cardinalities

We examine the recently introduced NSB estimator of entropies of severely undersampled discrete variables and devise a procedure for calculating the involved integrals. We discover that the output of the estimator has a well defined limit for large cardinalities of the variables being studied. Thus one can estimate entropies with no a priori assumptions about these cardinalities, and a closed form solution for such estimates is given.Comment: 8 page

Long-lived and unstable modes of Brownian suspensions in microchannels

We investigate the stability of the pressure-driven, low-Reynolds flow of Brownian suspensions with spherical particles in microchannels. We find two general families of stable/unstable modes: (i) degenerate modes with symmetric and anti-symmetric patterns; (ii) single modes that are either symmetric or anti-symmetric. The concentration profiles of degenerate modes have strong peaks near the channel walls, while single modes diminish there. Once excited, both families would be detectable through high-speed imaging. We find that unstable modes occur in concentrated suspensions whose velocity profiles are sufficiently flattened near the channel centreline. The patterns of growing unstable modes suggest that they are triggered due to Brownian migration of particles between the central bulk that moves with an almost constant velocity, and highly-sheared low-velocity region near the wall. Modes are amplified because shear-induced diffusion cannot efficiently disperse particles from the cavities of the perturbed velocity field.Comment: 11 pages, accepted for publication in Journal of Fluid Mechanic

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

Kekule-distortion-induced Exciton instability in graphene

Effects of a Kekule distortion on exciton instability in single-layer graphene are discussed. In the framework of quantum electrodynamics the mass of the electron generated dynamically is worked out using a Schwinger-Dyson equation. For homogeneous lattice distortion it is shown that the generated mass is independent of the amplitude of the lattice distortion at the one-loop approximation. Formation of excitons induced by the homogeneous Kekule distortion could appear only through direct dependence of the lattice distortion.Comment: 6 pages, 1 figur

Running couplings in equivariantly gauge-fixed SU(N) Yang--Mills theories

In equivariantly gauge-fixed SU(N) Yang--Mills theories, the gauge symmetry is only partially fixed, leaving a subgroup $H\subset SU(N)$ unfixed. Such theories avoid Neuberger's nogo theorem if the subgroup $H$ contains at least the Cartan subgroup $U(1)^{N-1}$, and they are thus non-perturbatively well defined if regulated on a finite lattice. We calculate the one-loop beta function for the coupling $\tilde{g}^2=\xi g^2$, where $g$ is the gauge coupling and $\xi$ is the gauge parameter, for a class of subgroups including the cases that $H=U(1)^{N-1}$ or $H=SU(M)\times SU(N-M)\times U(1)$. The coupling $\tilde{g}$ represents the strength of the interaction of the gauge degrees of freedom associated with the coset $SU(N)/H$. We find that $\tilde{g}$, like $g$, is asymptotically free. We solve the renormalization-group equations for the running of the couplings $g$ and $\tilde{g}$, and find that dimensional transmutation takes place also for the coupling $\tilde{g}$, generating a scale $\tilde{\Lambda}$ which can be larger than or equal to the scale $\Lambda$ associated with the gauge coupling $g$, but not smaller. We speculate on the possible implications of these results.Comment: 14 pages, late

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