Interfering resonances in a quantum billiard

We present a method for numerically obtaining the positions, widths and wavefunctions of resonance states in a two dimensional billiard connected to a waveguide. For a rectangular billiard, we study the dynamics of three resonance poles lying separated from the other ones. As a function of increasing coupling strength between the waveguide and the billiard two of the states become trapped while the width of the third one continues to increase for all coupling strengths. This behavior of the resonance poles is reflected in the time delay function which can be studied experimentally.Comment: 2 pages, 3 figure

A tree of linearisable second-order evolution equations by generalised hodograph transformations

We present a list of (1+1)-dimensional second-order evolution equations all connected via a proposed generalised hodograph transformation, resulting in a tree of equations transformable to the linear second-order autonomous evolution equation. The list includes autonomous and nonautonomous equations.Comment: arXiv version is already officia

Phase transitions in open quantum systems

We consider the behaviour of open quantum systems in dependence on the coupling to one decay channel by introducing the coupling parameter $\alpha$ being proportional to the average degree of overlapping. Under critical conditions, a reorganization of the spectrum takes place which creates a bifurcation of the time scales with respect to the lifetimes of the resonance states. We derive analytically the conditions under which the reorganization process can be understood as a second-order phase transition and illustrate our results by numerical investigations. The conditions are fulfilled e.g. for a picket fence with equal coupling of the states to the continuum. Energy dependencies within the system are included. We consider also the generic case of an unfolded Gaussian Orthogonal Ensemble. In all these cases, the reorganization of the spectrum occurs at the critical value $\alpha_{crit}$ of the control parameter globally over the whole energy range of the spectrum. All states act cooperatively.Comment: 28 pages, 22 Postscript figure

Pseudo-epsilon expansion and the two-dimensional Ising model

Starting from the five-loop renormalization-group expansions for the two-dimensional Euclidean scalar \phi^4 field theory (field-theoretical version of two-dimensional Ising model), pseudo-\epsilon expansions for the Wilson fixed point coordinate g*, critical exponents, and the sextic effective coupling constant g_6 are obtained. Pseudo-\epsilon expansions for g*, inverse susceptibility exponent \gamma, and g_6 are found to possess a remarkable property - higher-order terms in these expansions turn out to be so small that accurate enough numerical estimates can be obtained using simple Pade approximants, i. e. without addressing resummation procedures based upon the Borel transformation.Comment: 4 pages, 4 tables, few misprints avoide

Plasma dispersion of multisubband electron systems over liquid helium

Density-density response functions are evaluated for nondegenerate multisubband electron systems in the random-phase approximation for arbitrary wave number and subband index. We consider both quasi-two-dimensional and quasi-one- dimensional systems for electrons confined to the surface of liquid helium. The dispersion relations of longitudinal intrasubband and transverse intersubband modes are calculated at low temperatures and for long wavelengths. We discuss the effects of screening and two-subband occupancy on the plasmon spectrum. The characteristic absorption edge of the intersubband modes is shifted relatively to the single-particle intersubband separation and the depolarization shift correction can be significant at high electron densities

Certain features of using modified collagen-containing raw materials with prolonged shelf life in food technology

In the current circumstances, trends in nutrition of a person striving to lead a healthy life-style require intake of meat products with the reduced energy value, minimal amounts of fat, increased protein mass fraction, presence of substances improving homeostasis of the body. The synergism of the modern nutrition science and meat industry enables creating food products that satisfy consumers’ demand. Today, in the Russian Federation, a theoretical and practical base of the technology development has been collected to the full extent in the field of rational processing of secondary raw materials in the food industry, optimal use of animal secondary raw materials, study of the protein ingredients of animal and plant origin and their deep scientifically substantiated processing, improvement of technological processes and equipment, and correspondently, product range extension. The paper broadens the information about the modified collagen-containing raw materials (cattle rumen), examines physico-chemical characteristics of the collagen-containing raw material and its changes in the process of freeze-drying with a special attention paid to the study of changes in the histological structure. The presence of the relatively uniform fibrillar structure was determined, which facilitated discovering the functional potential of proteinoids that form the fibrillar matrix in the composition of products from different groups. Analysis of IR-spectra revealed several significant absorption bands linked with the state of peptide bonds. The character of bands is linked with the complex of valence and deformation vibrations of the N- and С- types. It is believed that IR-spectra reflect conformations in the protein secondary structure, which suggests preserving properties of the tropocollagen particle or collagen molecule. Freeze-dried modified collagen-containing cattle rumen was tested by the example of jellies. The obtained databank broadens information about physico-chemical properties of modified collagen-containing raw materials (cattle rumen).In the current circumstances, trends in nutrition of a person striving to lead a healthy life-style require intake of meat products with the reduced energy value, minimal amounts of fat, increased protein mass fraction, presence of substances improving homeostasis of the body. The synergism of the modern nutrition science and meat industry enables creating food products that satisfy consumers’ demand. Today, in the Russian Federation, a theoretical and practical base of the technology development has been collected to the full extent in the field of rational processing of secondary raw materials in the food industry, optimal use of animal secondary raw materials, study of the protein ingredients of animal and plant origin and their deep scientifically substantiated processing, improvement of technological processes and equipment, and correspondently, product range extension. The paper broadens the information about the modified collagen-containing raw materials (cattle rumen), examines physico-chemical characteristics of the collagen-containing raw material and its changes in the process of freeze-drying with a special attention paid to the study of changes in the histological structure. The presence of the relatively uniform fibrillar structure was determined, which facilitated discovering the functional potential of proteinoids that form the fibrillar matrix in the composition of products from different groups. Analysis of IR-spectra revealed several significant absorption bands linked with the state of peptide bonds. The character of bands is linked with the complex of valence and deformation vibrations of the N- and С- types. It is believed that IR-spectra reflect conformations in the protein secondary structure, which suggests preserving properties of the tropocollagen particle or collagen molecule. Freeze-dried modified collagen-containing cattle rumen was tested by the example of jellies. The obtained databank broadens information about physico-chemical properties of modified collagen-containing raw materials (cattle rumen)

Radiative Losses in Plasma Accelerators

We investigate the dynamics of a relativistic electron in a strongly nonlinear plasma wave in terms of classical mechanics by taking into account the action of the radiative reaction force. The two limiting cases are considered. In the first case where the energy of the accelerated electrons is low, the electron makes many betatron oscillations during the acceleration. In the second case where the energy of the accelerated electrons is high, the betatron oscillation period is longer than the electron residence time in the accelerating phase. We show that the force of radiative friction can severely limit the rate of electron acceleration in a plasma accelerator.Comment: 17 pages, 5 figure

Critical thermodynamics of three-dimensional MN-component field model with cubic anisotropy from higher-loop \epsilon expansion

The critical thermodynamics of an $MN$-component field model with cubic anisotropy relevant to the phase transitions in certain crystals with complicated ordering is studied within the four-loop \ve expansion using the minimal subtraction scheme. Investigation of the global structure of RG flows for the physically significant cases M=2, N=2 and M=2, N=3 shows that the model has an anisotropic stable fixed point with new critical exponents. The critical dimensionality of the order parameter is proved to be equal to $N_c^C=1.445(20)$, that is exactly half its counterpart in the real hypercubic model.Comment: 9 pages, LaTeX, no figures. Published versio