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 $\Lambda$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) $D_5$.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