Renormalization Group Treatment of Nonrenormalizable Interactions

The structure of the UV divergencies in higher dimensional nonrenormalizable theories is analysed. Based on renormalization operation and renormalization group theory it is shown that even in this case the leading divergencies (asymptotics) are governed by the one-loop diagrams the number of which, however, is infinite. Explicit expression for the one-loop counter term in an arbitrary D-dimensional quantum field theory without derivatives is suggested. This allows one to sum up the leading asymptotics which are independent of the arbitrariness in subtraction of higher order operators. Diagrammatic calculations in a number of scalar models in higher loops are performed to be in agreement with the above statements. These results do not support the idea of the na\"ive power-law running of couplings in nonrenormalizable theories and fail (with one exception) to reveal any simple closed formula for the leading terms.Comment: LaTex, 11 page

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

Verification of CPT-invariance of QED bound states for the production of muonium or antimuonium in scattering of electrons or positrons by nuclei

A possibility of a verification of CPT-invariance of QED for bound states by example of muonium or antimuonium produced in reactions of scattering of electrons or positrons by nuclei is considered. The number of events of the muonium production is estimated for contemporary accelerators. The method of the detection of muonium by measuring of oscillations of the decay curve caused by the interference between the ground and excited state of muonium is suggested. The admixture of the excited muonium to the final state is calculated.Comment: 7 pages, 3 figures, Latex, published in JETP 74, 196 (2001), corrected mistypes in eqs. (2.2), (2.4), (2.7

Gauge and parametrization dependence in higher derivative quantum gravity

The structure of counterterms in higher derivative quantum gravity is reexamined. Nontrivial dependence of charges on the gauge and parametrization is established. Explicit calculations of two-loop contributions are carried out with the help of the generalized renormgroup method demonstrating consistency of the results obtained.Comment: 22 pages, Latex, no figure

The Dressing Factor and Crossing Equations

We utilize the DHM integral representation for the BES dressing factor of the world-sheet S-matrix of the AdS_5xS^5 light-cone string theory, and the crossing equations to fix the principal branch of the dressing factor on the rapidity torus. The results obtained are further used, in conjunction with the fusion procedure, to determine the bound state dressing factor of the mirror theory. We convincingly demonstrate that the mirror bound state S-matrix found in this way does not depend on the internal structure of a bound state solution employed in the fusion procedure. This welcome feature is in perfect parallel to string theory, where the corresponding bound state S-matrix has no bearing on bound state constituent particles as well. The mirror bound state S-matrix we found provides the final missing piece in setting up the TBA equations for the AdS_5xS^5 mirror theory.Comment: LaTex, 48 pages, 10 figures; v2: a new section added where the dressing factor of the mirror theory is found; v3: formula (6.12) is corrected, a new figure is added, accepted for publication in J.Phys.

Prospects for measuring the 229Th isomer energy using a metallic magnetic microcalorimeter

The Thorium-229 isotope features a nuclear isomer state with an extremely low energy. The currently most accepted energy value, 7.8 +- 0.5 eV, was obtained from an indirect measurement using a NASA x-ray microcalorimeter with an instrumental resolution 26 eV. We study, how state-of-the-art magnetic metallic microcalorimeters with an energy resolution down to a few eV can be used to measure the isomer energy. In particular, resolving the 29.18 keV doublet in the \gamma-spectrum following the \alpha-decay of Uranium-233, corresponding to the decay into the ground and isomer state, allows to measure the isomer transition energy without additional theoretical input parameters, and increase the energy accuracy. We study the possibility of resolving the 29.18 keV line as a doublet and the dependence of the attainable precision of the energy measurement on the signal and background count rates and the instrumental resolution.Comment: 32 pages, 8 figures, eq. (3) correcte

Note About Integrability and Gauge Fixing for Bosonic String on AdS(5)xS(5)

This short note is devoted to the study of the integrability of the bosonic string on AdS(5)xS(5) in the uniform light-cone gauge. We construct Lax connection for gauge fixed theory and we argue that it is flat.Comment: 17 page

Two-point phase correlations of a one-dimensional bosonic Josephson junction

We realize a one-dimensional Josephson junction using quantum degenerate Bose gases in a tunable double well potential on an atom chip. Matter wave interferometry gives direct access to the relative phase field, which reflects the interplay of thermally driven fluctuations and phase locking due to tunneling. The thermal equilibrium state is characterized by probing the full statistical distribution function of the two-point phase correlation. Comparison to a stochastic model allows to measure the coupling strength and temperature and hence a full characterization of the system