Classification of static and homogeneous solutions in exactly solvable models of two-dimensional dilaton gravity

We give the full list of types of static (homogeneous)solutions within a wide family of exactly solvable 2D dilaton gravities with backreaction of conformal fields. It includes previously known solutions as particular cases. Several concrete examples are considered for illustration. They contain a black hole and cosmological horizon in thermal equilibrium, extremal and ultraextremal horizons, etc. In particular, we demonstrate that adS and dS geometries can be \QTR{it}{exact} solutions of semiclassical field equations for a \QTR{it}{nonconstant} dilaton field.Comment: 19 pages. To appear in Int. J. Mod. Phys.

Application of the JJ-matrix Method to Faddeev-Merkuriev equation: beyond pseudostates

A version of the $J$-matrix method for solving numerically the three-body Faddeev-Merkuriev differential equations is proposed. This version allows to take into account the full spectrum of the two-body Coulomb subsystem. As a result, a discrete analog of the Lippmann-Schwinger equation is obtained which allows to interpret correctly the three-body wave function in two-body domains. The scheme is applied to calculations of the fully resolved absolute differential cross sections for the He$(e,2e)$He$^+$ and He$(e,3e)$He$^{++}$ reactions at small energy and momentum transfers. The results are in good agreement with the experiment both in shape and in absolute value.Comment: 22 pages, 7 figure

Exactly solvable models in 2D semiclassical dilaton gravity and extremal black holes

Previously known exactly solvable models of 2D semiclassical dilaton gravity admit, in the general case, only non-extreme black holes. It is shown that there exist exceptional degenerate cases, that can be obtained by some limiting transitions from the general exact solution, which include, in particular, extremal and ultraextremal black holes. We also analyze properties of extreme black holes without demanding exact solvability and show that for such solutions quantum backreaction forbids the existence of ultraextreme black holes. The conditions,under which divergencies of quantum stresses in a free falling frame can disappear, are found. We derive the closed equation with respect to the metric as a function of the dilaton field that enables one, choosing the form of the metric, to restore corresponding Lagrangian. It is demonstrated that exactly solvable models, found earlier, can be extended to include an electric charge only in two cases: either the dilaton-gravitation coupling is proportional to the potential term, or the latter vanishes. The second case leads to the effective potential with a negative amplitude and we analyze, how this fact affects the structure of spacetime. We also discuss the role of quantum backreaction in the relationship between extremal horizons and the branch of solutions with a constant dilaton.Comment: 31 pages. In v.2 typo in Ref. [2] corrected, 4 references added. Accepted in Class. Quant. Gra

Ground state wavefunction of the quantum Frenkel-Kontorova model

The wavefunction of an incommensurate ground state for a one-dimensional discrete sine-Gordon model -- the Frenkel-Kontorova (FK) model -- at zero temperature is calculated by the quantum Monte Carlo method. It is found that the ground state wavefunction crosses over from an extended state to a localized state when the coupling constant exceeds a certain critical value. So, although the quantum fluctuation has smeared out the breaking of analyticity transition as observed in the classical case, the remnant of this transition is still discernible in the quantum regime.Comment: 5 Europhys pages, 3 EPS figures, accepted for publication in Europhys. Letter

Test beam studies of the TRD prototype filled with different gas mixtures based on Xe, Kr, and Ar

Towards the end of LHC Run1, gas leaks were observed in some parts of the Transition Radiation Tracker (TRT) of ATLAS. Due to these leaks, primary Xenon based gas mixture was replaced with Argon based mixture in various parts. Test-beam studies with a dedicated Transition Radiation Detector (TRD) prototype were carried out in 2015 in order to understand transition radiation performance with mixtures based on Argon and Krypton. We present and discuss the results of these test-beam studies with different active gas compositions.Comment: 5 pages,12 figures, The 2nd International Conference on Particle Physics and Astrophysics (ICPPA-2016); Acknowledgments section correcte

Some results of test beam studies of Transition Radiation Detector prototypes at CERN

Operating conditions and challenging demands of present and future accelerator experiments result in new requirements on detector systems. There are many ongoing activities aimed to develop new technologies and to improve the properties of detectors based on existing technologies. Our work is dedicated to development of Transition Radiation Detectors (TRD) suitable for different applications. In this paper results obtained in beam tests at SPS accelerator at CERN with the TRD prototype based on straw technology are presented. TRD performance was studied as a function of thickness of the transition radiation radiator and working gas mixture pressure

Many-body symbolic dynamics of a classical oscillator chain

We study a certain type of the celebrated Fermi-Pasta-Ulam particle chain, namely the inverted FPU model, where the inter-particle potential has a form of a quartic double well. Numerical evidence is given in support of a simple symbolic description of dynamics (in the regime of sufficiently high potential barrier between the wells) in terms of an (approximate) Markov process. The corresponding transition matrix is formally identical to a ferromagnetic Heisenberg quantum spin-1/2 chain with long range coupling, whose diagonalization yields accurate estimates for a class of time correlation functions of the model.Comment: 22 pages in LaTeX with 14 figures; submitted to Nonlinearity ; corrected page offset proble

Heat conduction in one dimensional nonintegrable systems

Two classes of 1D nonintegrable systems represented by the Fermi-Pasta-Ulam (FPU) model and the discrete $\phi^4$ model are studied to seek a generic mechanism of energy transport in microscopic level sustaining macroscopic behaviors. The results enable us to understand why the class represented by the $\phi^4$ model has a normal thermal conductivity and the class represented by the FPU model does not even though the temperature gradient can be established.Comment: 4 Revtex Pages, 4 Eps figures included, to appear in Phys. Rev. E, March 200

Heat conduction in 1D lattices with on-site potential

The process of heat conduction in one-dimensional lattice with on-site potential is studied by means of numerical simulation. Using discrete Frenkel-Kontorova, $\phi$--4 and sinh-Gordon we demonstrate that contrary to previously expressed opinions the sole anharmonicity of the on-site potential is insufficient to ensure the normal heat conductivity in these systems. The character of the heat conduction is determined by the spectrum of nonlinear excitations peculiar for every given model and therefore depends on the concrete potential shape and temperature of the lattice. The reason is that the peculiarities of the nonlinear excitations and their interactions prescribe the energy scattering mechanism in each model. For models sin-Gordon and $\phi$--4 phonons are scattered at thermalized lattice of topological solitons; for sinh-Gordon and $\phi$--4 - models the phonons are scattered at localized high-frequency breathers (in the case of $\phi$--4 the scattering mechanism switches with the growth of the temperature).Comment: 26 pages, 18 figure

Continuous selections of multivalued mappings

This survey covers in our opinion the most important results in the theory of continuous selections of multivalued mappings (approximately) from 2002 through 2012. It extends and continues our previous such survey which appeared in Recent Progress in General Topology, II, which was published in 2002. In comparison, our present survey considers more restricted and specific areas of mathematics. Note that we do not consider the theory of selectors (i.e. continuous choices of elements from subsets of topological spaces) since this topics is covered by another survey in this volume