1,749 research outputs found
The Cauchy-Schlomilch transformation
The Cauchy-Schl\"omilch transformation states that for a function and , the integral of and over the
interval are the same. This elementary result is used to evaluate
many non-elementary definite integrals, most of which cannot be obtained by
symbolic packages. Applications to probability distributions is also given
Coulomb Interactions via Local Dynamics: A Molecular--Dynamics Algorithm
We derive and describe in detail a recently proposed method for obtaining
Coulomb interactions as the potential of mean force between charges which are
dynamically coupled to a local electromagnetic field. We focus on the Molecular
Dynamics version of the method and show that it is intimately related to the
Car--Parrinello approach, while being equivalent to solving Maxwell's equations
with freely adjustable speed of light. Unphysical self--energies arise as a
result of the lattice interpolation of charges, and are corrected by a
subtraction scheme based on the exact lattice Green's function. The method can
be straightforwardly parallelized using standard domain decomposition. Some
preliminary benchmark results are presented.Comment: 8 figure
Lattice Green functions in all dimensions
We give a systematic treatment of lattice Green functions (LGF) on the
-dimensional diamond, simple cubic, body-centred cubic and face-centred
cubic lattices for arbitrary dimensionality for the first three
lattices, and for for the hyper-fcc lattice. We show that there
is a close connection between the LGF of the -dimensional hypercubic lattice
and that of the -dimensional diamond lattice. We give constant-term
formulations of LGFs for all lattices and dimensions. Through a still
under-developed connection with Mahler measures, we point out an unexpected
connection between the coefficients of the s.c., b.c.c. and diamond LGFs and
some Ramanujan-type formulae for Comment: 30 page
Diffusion-Limited One-Species Reactions in the Bethe Lattice
We study the kinetics of diffusion-limited coalescence, A+A-->A, and
annihilation, A+A-->0, in the Bethe lattice of coordination number z.
Correlations build up over time so that the probability to find a particle next
to another varies from \rho^2 (\rho is the particle density), initially, when
the particles are uncorrelated, to [(z-2)/z]\rho^2, in the long-time asymptotic
limit. As a result, the particle density decays inversely proportional to time,
\rho ~ 1/kt, but at a rate k that slowly decreases to an asymptotic constant
value.Comment: To be published in JPCM, special issue on Kinetics of Chemical
Reaction
FIBONACCI SUPERLATTICES OF NARROW-GAP III-V SEMICONDUCTORS
We report theoretical electronic structure of Fibonacci superlattices of
narrow-gap III-V semiconductors. Electron dynamics is accurately described
within the envelope-function approximation in a two-band model.
Quasiperiodicity is introduced by considering two different III-V semiconductor
layers and arranging them according to the Fibonacci series along the growth
direction. The resulting energy spectrum is then found by solving exactly the
corresponding effective-mass (Dirac-like) wave equation using tranfer-matrix
techniques. We find that a self-similar electronic spectrum can be seen in the
band structure. Electronic transport properties of samples are also studied and
related to the degree of spatial localization of electronic envelope-functions
via Landauer resistance and Lyapunov coefficient. As a working example, we
consider type II InAs/GaSb superlattices and discuss in detail our results in
this system.Comment: REVTeX 3.0, 16 pages, 8 figures available upon request. To appear in
Semiconductor Science and Technolog
Shear modulus of the hadron-quark mixed phase
Robust arguments predict that a hadron-quark mixed phase may exist in the
cores of some "neutron" stars. Such a phase forms a crystalline lattice with a
shear modulus higher than that of the crust due to the high density and charge
separation, even allowing for the effects of charge screening. This may lead to
strong continuous gravitational-wave emission from rapidly rotating neutron
stars and gravitational-wave bursts associated with magnetar flares and pulsar
glitches. We present the first detailed calculation of the shear modulus of the
mixed phase. We describe the quark phase using the bag model plus first-order
quantum chromodynamics corrections and the hadronic phase using relativistic
mean-field models with parameters allowed by the most massive pulsar. Most of
the calculation involves treating the "pasta phases" of the lattice via
dimensional continuation, and we give a general method for computing
dimensionally continued lattice sums including the Debye model of charge
screening. We compute all the shear components of the elastic modulus tensor
and angle average them to obtain the effective (scalar) shear modulus for the
case where the mixed phase is a polycrystal. We include the contributions from
changing the cell size, which are necessary for the stability of the
lower-dimensional portions of the lattice. Stability also requires a minimum
surface tension, generally tens of MeV/fm^2 depending on the equation of state.
We find that the shear modulus can be a few times 10^33 erg/cm^3, two orders of
magnitude higher than the first estimate, over a significant fraction of the
maximum mass stable star for certain parameter choices.Comment: 22 pages, 12 figures, version accepted by Phys. Rev. D, with the
corrections to the shear modulus computation and Table I given in the erratu
Second Order Darboux Displacements
The potentials for a one dimensional Schroedinger equation that are displaced
along the x axis under second order Darboux transformations, called 2-SUSY
invariant, are characterized in terms of a differential-difference equation.
The solutions of the Schroedinger equation with such potentials are given
analytically for any value of the energy. The method is illustrated by a
two-soliton potential. It is proven that a particular case of the periodic
Lame-Ince potential is 2-SUSY invariant. Both Bloch solutions of the
corresponding Schroedinger equation equation are found for any value of the
energy. A simple analytic expression for a family of two-gap potentials is
derived
- …