17,766 research outputs found
Entropy Bounds, Holographic Principle and Uncertainty Relation
A simple derivation of the bound on entropy is given and the holographic
principle is discussed. We estimate the number of quantum states inside space
region on the base of uncertainty relation. The result is compared with the
Bekenstein formula for entropy bound, which was initially derived from the
generalized second law of thermodynamics for black holes. The holographic
principle states that the entropy inside a region is bounded by the area of the
boundary of that region. This principle can be called the kinematical
holographic principle. We argue that it can be derived from the dynamical
holographic principle which states that the dynamics of a system in a region
should be described by a system which lives on the boundary of the region. This
last principle can be valid in general relativity because the ADM hamiltonian
reduces to the surface term.Comment: LaTeX, 8 pages, no figure
Cyclic Universe with an Inflationary Phase from a Cosmological Model with Real Gas Quintessence
Phase-plane stability analysis of a dynamical system describing the Universe
as a two-fraction fluid containing baryonic dust and real virial gas
quintessence is presented. Existence of a stable periodic solution experiencing
inflationary periods is shown. A van der Waals quintessence model is revisited
and cyclic Universe solution again found.Comment: 21 pages, 8 figures, to appear in Physical Review
On kaonic deuterium. Quantum field theoretic and relativistic covariant approach
We study kaonic deuterium, the bound K^-d state A_(K d). Within a quantum
field theoretic and relativistic covariant approach we derive the energy level
displacement of the ground state of kaonic deuterium in terms of the amplitude
of K^-d scattering for arbitrary relative momenta. Near threshold our formula
reduces to the well-known DGBT formula. The S-wave amplitude of K^-d scattering
near threshold is defined by the resonances Lambda(1405), Sigma(1750) and a
smooth elastic background, and the inelastic channels K^- d -> NY and K^- d ->
NY pion, with Y = Sigma^(+/-), Sigma^0 and Lambda^0, where the final-state
interactions play an important role. The Ericson-Weise formula for the S-wave
scattering length of K^-d scattering is derived. The total width of the energy
level of the ground state of kaonic deuterium is estimated using the
theoretical predictions of the partial widths of the two-body decays A_(Kd) ->
NY and experimental data on the rates of the NY-pair production in the
reactions K^-d -> NY. We obtain Gamma_{1s} = (630 +/-100) eV. For the shift of
the energy level of the ground state of kaonic deuterium we predict
epsilon_(1s) = (353 +/-60)eV.Comment: 73 pages,10 figures, Latex, We have slightly corrected the
contribution of the double scattering. The change of the S-wave scattering
length of K^-d scattering does not go beyond the theoretical uncertainty,
which is about 18
Wavelets and their use
This review paper is intended to give a useful guide for those who want to
apply discrete wavelets in their practice. The notion of wavelets and their use
in practical computing and various applications are briefly described, but
rigorous proofs of mathematical statements are omitted, and the reader is just
referred to corresponding literature. The multiresolution analysis and fast
wavelet transform became a standard procedure for dealing with discrete
wavelets. The proper choice of a wavelet and use of nonstandard matrix
multiplication are often crucial for achievement of a goal. Analysis of various
functions with the help of wavelets allows to reveal fractal structures,
singularities etc. Wavelet transform of operator expressions helps solve some
equations. In practical applications one deals often with the discretized
functions, and the problem of stability of wavelet transform and corresponding
numerical algorithms becomes important. After discussing all these topics we
turn to practical applications of the wavelet machinery. They are so numerous
that we have to limit ourselves by some examples only. The authors would be
grateful for any comments which improve this review paper and move us closer to
the goal proclaimed in the first phrase of the abstract.Comment: 63 pages with 22 ps-figures, to be published in Physics-Uspekh
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