7,825 research outputs found

### 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

### 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

### 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

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