Topological monodromy as an obstruction to Hamiltonization of nonholonomic systems: pro or contra?

The phenomenon of a topological monodromy in integrable Hamiltonian and nonholonomic systems is discussed. An efficient method for computing and visualizing the monodromy is developed. The comparative analysis of the topological monodromy is given for the rolling ellipsoid of revolution problem in two cases, namely, on a smooth and on a rough plane. The first of these systems is Hamiltonian, the second is nonholonomic. We show that, from the viewpoint of monodromy, there is no difference between the two systems, and thus disprove the conjecture by Cushman and Duistermaat stating that the topological monodromy gives a topological obstruction for Hamiltonization of the rolling ellipsoid of revolution on a rough plane.Comment: 31 pages, 11 figure

Spiral attractors as the root of a new type of "bursting activity" in the Rosenzweig-MacArthur model

We study the peculiarities of spiral attractors in the Rosenzweig-MacArthur model, that describes dynamics in a food chain "prey-predator-superpredator". It is well-known that spiral attractors having a "teacup" geometry are typical for this model at certain values of parameters for which the system can be considered as slow-fast system. We show that these attractors appear due to the Shilnikov scenario, the first step in which is associated with a supercritical Andronov-Hopf bifurcation and the last step leads to the appearance of a homoclinic attractor containing a homoclinic loop to a saddle-focus equilibrium with two-dimension unstable manifold. It is shown that the homoclinic spiral attractors together with the slow-fast behavior give rise to a new type of bursting activity in this system. Intervals of fast oscillations for such type of bursting alternate with slow motions of two types: small amplitude oscillations near a saddle-focus equilibrium and motions near a stable slow manifold of a fast subsystem. We demonstrate that such type of bursting activity can be either chaotic or regular

The first data on the infestation of the parti-coloured bat, Vespertilio murinus (Chiroptera, Vespertilionidae), with gamasid mites, Steatonyssus spinosus (Mesostigmata, Gamasina, Macronyssidae)

This article presents one of the very few records of a macronyssid mite (Mesostigmata, Gamasina, Macronyssidae) infestation of vesper bats (Chiroptera, Vespertilionidae). It is the first report of the influence of host parameters on the infestation of the parti-coloured bat, Vespertilio murinus, by the mite Steatonyssus spinosus. It has been shown that the infestation varies considerably throughout the host's occupation of summer roosts and the highest infestation was observed in the post-lactation period. Female bats are infested significantly more intensively than male bats due to changes in their immune status during pregnancy and lactation. The infestation decreases in the period when the breeding colony disbands due to both roost switching and the intensification of grooming during this period. © Russian Journal Of Theriology, 2017

On the Bethe Ansatz for the Jaynes-Cummings-Gaudin model

We investigate the quantum Jaynes-Cummings model - a particular case of the Gaudin model with one of the spins being infinite. Starting from the Bethe equations we derive Baxter's equation and from it a closed set of equations for the eigenvalues of the commuting Hamiltonians. A scalar product in the separated variables representation is found for which the commuting Hamiltonians are Hermitian. In the semi classical limit the Bethe roots accumulate on very specific curves in the complex plane. We give the equation of these curves. They build up a system of cuts modeling the spectral curve as a two sheeted cover of the complex plane. Finally, we extend some of these results to the XXX Heisenberg spin chain.Comment: 16 page

Spectral form factor in a random matrix theory

In the theory of disordered systems the spectral form factor $S(\tau)$, the Fourier transform of the two-level correlation function with respect to the difference of energies, is linear for $\tau<\tau_c$ and constant for $\tau>\tau_c$. Near zero and near $\tau_c$ its exhibits oscillations which have been discussed in several recent papers. In the problems of mesoscopic fluctuations and quantum chaos a comparison is often made with random matrix theory. It turns out that, even in the simplest Gaussian unitary ensemble, these oscilllations have not yet been studied there. For random matrices, the two-level correlation function $\rho(\lambda_1,\lambda_2)$ exhibits several well-known universal properties in the large N limit. Its Fourier transform is linear as a consequence of the short distance universality of $\rho(\lambda_1,\lambda_2)$. However the cross-over near zero and $\tau_c$ requires to study these correlations for finite N. For this purpose we use an exact contour-integral representation of the two-level correlation function which allows us to characterize these cross-over oscillatory properties. The method is also extended to the time-dependent case.Comment: 36P, (+5 figures not included

A Review of Symmetry Algebras of Quantum Matrix Models in the Large-N Limit

This is a review article in which we will introduce, in a unifying fashion and with more intermediate steps in some difficult calculations, two infinite-dimensional Lie algebras of quantum matrix models, one for the open string sector and one for the closed string sector. Physical observables of quantum matrix models in the large-N limit can be expressed as elements of these Lie algebras. We will see that both algebras arise as quotient algebras of a larger Lie algebra. We will also discuss some properties of these Lie algebras not published elsewhere yet, and briefly review their relationship with well-known algebras like the Cuntz algebra, the Witt algebra and the Virasoro algebra. We will also review how Yang--Mills theory, various low energy effective models of string theory, quantum gravity, string-bit models, and quantum spin chain models can be formulated as quantum matrix models. Studying these algebras thus help us understand the common symmetry of these physical systems.Comment: 77 pages, 21 eps figures, 1 table, LaTeX2.09; an invited review articl

The experimental evidence of the amplified spontaneous emission of Yb³⁺ ions in LiYbF<inf>4</inf> crystal

© 2017 Elsevier B.V.The experimental evidence of the amplified spontaneous emission of Yb3+ ions in LiYbF4 crystal, which partially stipulates up-conversion processes in Yb-sensitized phosphors, doped by rare-earth ions are presented for the first time. To do that the spatial distributions and the spectra of Yb3+ ions luminescence along the excitation radiation propagation through the sample were studied simultaneously. The laser diode radiation (1 W, λ=932 nm) was used for the luminescence excitation and its surface power density was varied by shifting of the position of the laser beam waist within the sample (similar to Z-scanning)