6,645 research outputs found
Spectra of Field Fluctuations in Braneworld Models with Broken Bulk Lorentz Invariance
We investigate five-dimensional braneworld setups with broken Lorentz
invariance continuing the developments of our previous paper (arXiv:0712.1136),
where a family of static self-tuning braneworld solutions was found. We show
that several known braneworld models can be embedded into this family. Then we
give a qualitative analysis of spectra of field fluctuations in backgrounds
with broken Lorentz invariance. We also elaborate on one particular model and
study spectra of scalar and spinor fields in it. It turns out that the spectra
we have found possess very peculiar and unexpected properties.Comment: 30 pages, 8 figures, minor corrections, references added, note adde
Calculation of some determinants using the s-shifted factorial
Several determinants with gamma functions as elements are evaluated. This
kind of determinants are encountered in the computation of the probability
density of the determinant of random matrices. The s-shifted factorial is
defined as a generalization for non-negative integers of the power function,
the rising factorial (or Pochammer's symbol) and the falling factorial. It is a
special case of polynomial sequence of the binomial type studied in
combinatorics theory. In terms of the gamma function, an extension is defined
for negative integers and even complex values. Properties, mainly composition
laws and binomial formulae, are given. They are used to evaluate families of
generalized Vandermonde determinants with s-shifted factorials as elements,
instead of power functions.Comment: 25 pages; added section 5 for some examples of application
Helical, Angular and Radial Ordering in Narrow Capillaries
To enlighten the nature of the order-disorder and order-order transitions in
block copolymer melts confined in narrow capillaries we analyze peculiarities
of the conventional Landau weak crystallization theory of systems confined to
cylindrical geometry. This phenomenological approach provides a quantitative
classification of the cylindrical ordered morphologies by expansion of the
order parameter spatial distribution into the eigenfunctions of the Laplace
operator. The symmetry of the resulting ordered morphologies is shown to
strongly depend both on the boundary conditions (wall preference) and the ratio
of the cylinder radius and the wave length of the critical order parameter
fluctuations, which determine the bulk ordering of the system under
consideration. In particular, occurrence of the helical morphologies is a
rather general consequence of the imposed cylindrical symmetry for narrow
enough capillaries. We discuss also the ODT and OOT involving some other
simplest morphologies. The presented results are relevant also to other
ordering systems as charge-density waves appearing under addition of an ionic
solute to a solvent in its critical region, weakly charged polyelectrolyte
solutions in poor solvent, microemulsions etc.Comment: 6 pages, 3 figure
Partial order and a -topology in a set of finite quantum systems
A `whole-part' theory is developed for a set of finite quantum systems
with variables in . The partial order `subsystem'
is defined, by embedding various attributes of the system (quantum
states, density matrices, etc) into their counterparts in the supersystem
(for ). The compatibility of these embeddings is studied. The
concept of ubiquity is introduced for quantities which fit with this structure.
It is shown that various entropic quantities are ubiquitous. The sets of
various quantities become -topological spaces with the divisor topology,
which encapsulates fundamental physical properties. These sets can be converted
into directed-complete partial orders (dcpo), by adding `top elements'. The
continuity of various maps among these sets is studied
Analytical solutions of the Schr\"{o}dinger equation with the Woods-Saxon potential for arbitrary state
In this work, the analytical solution of the radial Schr\"{o}dinger equation
for the Woods-Saxon potential is presented. In our calculations, we have
applied the Nikiforov-Uvarov method by using the Pekeris approximation to the
centrifugal potential for arbitrary states. The bound state energy
eigenvalues and corresponding eigenfunctions are obtained for various values of
and quantum numbers.Comment: 14 page
The functional integral with unconditional Wiener measure for anharmonic oscillator
In this article we propose the calculation of the unconditional Wiener
measure functional integral with a term of the fourth order in the exponent by
an alternative method as in the conventional perturbative approach. In contrast
to the conventional perturbation theory, we expand into power series the term
linear in the integration variable in the exponent. In such a case we can
profit from the representation of the integral in question by the parabolic
cylinder functions. We show that in such a case the series expansions are
uniformly convergent and we find recurrence relations for the Wiener functional
integral in the - dimensional approximation. In continuum limit we find
that the generalized Gelfand - Yaglom differential equation with solution
yields the desired functional integral (similarly as the standard Gelfand -
Yaglom differential equation yields the functional integral for linear harmonic
oscillator).Comment: Source file which we sent to journa
Relativistic phase space: dimensional recurrences
We derive recurrence relations between phase space expressions in different
dimensions by confining some of the coordinates to tori or spheres of radius
and taking the limit as . These relations take the form of
mass integrals, associated with extraneous momenta (relative to the lower
dimension), and produce the result in the higher dimension.Comment: 13 pages, Latex, to appear in J Phys
Green's function of a finite chain and the discrete Fourier transform
A new expression for the Green's function of a finite one-dimensional lattice
with nearest neighbor interaction is derived via discrete Fourier transform.
Solution of the Heisenberg spin chain with periodic and open boundary
conditions is considered as an example. Comparison to Bethe ansatz clarifies
the relation between the two approaches.Comment: preprint of the paper published in Int. J. Modern Physics B Vol. 20,
No. 5 (2006) 593-60
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