308 research outputs found
Principle of maximum force and holographic principle: two principles or one?
We show how the maximum force principle can be derived from the holographic
principle and vice versa, thus demonstrating equivalence of the two principles.Comment: 3 pages, minor corrections, text slightly extended, results and
conclusions unchange
A Thousand Problems in Cosmology: Horizons
This is one chapter of the collection of problems in cosmology, in which we
assemble the problems, with solutions, that concern one of the most distinctive
features of general relativity and cosmology---the horizons.
The first part gives an elementary introduction into the concept in the
cosmological context, then we move to more formal exposition of the subject and
consider first simple, and then composite models, such as CDM. The
fourth section elevates the rigor one more step and explores the causal
structure of different simple cosmological models in terms of conformal
diagrams. The section on black holes relates the general scheme of constructing
conformal diagrams for stationary black hole spacetimes. The consequent parts
focus on more specific topics, such as the various problems regarding the
Hubble sphere, inflation and holography.
The full collection is available in the form of a wiki-based resource at
universeinproblems.com. The cosmological community is welcome to contribute to
its development.Comment: 61 pages, 44 figures; a new chapter of a collection of problems
arXiv:0904.0382; full collection at http://universeinproblems.com ; v2: added
solutions; v3: added re
Over-barrier decay of the mixed state
Classical escape in 2D Hamiltonian systems with the mixed state has been
studied numerically and analytically. The wide class of potentials with the
mixed state is presented by polinomial potentials. In potentials, where the
mixed state could be realized, i.e. the phase space contains regions of both
regular and chaotic motion, escape problem has a number of new features. In
particular, some local minima become a trap with number of particles depending
on energy and other values that characterize the ensemble of particles.
Choosing the form of initial ensemble one chooses the set of parameters that
determine the number of trapped particles.Comment: 17pages, 13 figure
Expanding Universe: slowdown or speedup?
The kinematics and dynamic interpretation of the cosmological expansion is
reviewed in a widely accessible manner with emphasis on the acceleration
aspect. Virtually all the approaches that can in principle account for the
accelerated expansion of the Universe are reviewed, including dark energy as an
item in the energy budget of the Universe; modified Einstein equations; and, on
a fundamentally new level, the use of the holographic principle.Comment: 70 pages, 16 figures, 1 tables. corrected some error
New Cosmographic Constraints on the Dark Energy and Dark Matter Coupling
We consider three cosmological models with linear interaction between the
dark components and obtain restrictions on the coupling constant in terms of
the cosmographic parameters. It enables us to find constraints on the coupling
constant directly based on observational data and to restrict number of
numerous models describing interaction in the dark sector.Comment: 7 pages, 3 figures, preprint submitted to JCA
Signatures of Quantum Chaos in Wave Functions Structure for Multi-well 2D Potentials
We propose a new approach to investigation of quantum manifestations of
classical stochasticity (QMCS) in wave functions structure, which can be
realized in potentials with two and more local minima. The main advantage of
the proposed approach is the possibility to detect QMCS in comparison not
different wave functions, but different parts of the same wave function.
Efficiency of the approach is demonstrated for two potentials: surface
quadrupole oscillations (QO) and lower umbillic catastrophe (UC) .Comment: 5 pages, 4 figures, to be submitted to "Pis'ma v ZhETF
Cosmography of Cardassian model
The parameters of any model that satisfies the cosmological principle (the
universe is homogeneous and isotropic on large scale), can be expressed through
cosmographic parameters. In this paper, we perform this procedure for the
Cardassian model. We demonstrate a number of advantages of the approach used
before traditional methods.Comment: 3 figures. corrected some error
Quadrupole Oscillations as Paradigm of the Chaotic Motion in Nuclei. Part 1
We have presented a complete description of classical dynamics generated by
the Hamiltonian of quadrupole nuclear oscillations and identified those
peculiarities of quantum dynamics that can be interpreted as quantum
manifestations of classical stochasticity. Particular attention has been given
to investigation of classical dynamics in the potential energy surface with a
few local minima. A new technique is suggested for determination of the
critical energy of the transition to chaos. It is simpler than criteria of
transition to chaos connected with one or another version of overlap resonances
criterion. We have numerically demonstrated that for potential with a localized
unstable region motion becomes regular at the high energy again, i.e.
transition regularity-chaos-regularity {R - C - R} takes place for these
potentials. The variations of statistical properties of energy spectrum in the
process of {R - C - R) transition have been studied in detail. We proved that
the type of the classical motion is correlated with the structure of the
eigenfunctions of highly excited states in the (R - C - R) transition. Shell
structure destruction induced by the increase of nonintegrable perturbation was
analyzed.Comment: 47 pages, LaTex, 17 figure
An ideal quantum clock and Principle of maximum force
We show that the space-time uncertainty relation for the quantum clock can be
derived from the maximum force principle.Comment: 2 page
Regular and Chaotic Classical and Quantum Dynamics in Multi-Well Potentials
We present a detailed review of the topics listed in the title, in particular
using recent results of the authors.Comment: 180 pages, 159 figure
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