Advanced Bogolyubov model of imperfect bose gas and superfluidity

The equilibrium properties of a system of interacting bosons are studied from a microscopic point of view. We calculate the superfluid density in the Bogolyubov model of imperfect Bose gas. The model superstable Hamiltonian is considered. We examine the case of some pair potential and find the estimate for temperature and density in the λ-point.С микроскопической точки зрения изучены равновесные свойства системы взаимодействующих бозонов. Мы вычисляем плотность сверхтекучей компоненты в модели Боголюбова неидеального бозе-газа. Рассмотрен модельный суперстабильный гамильтониан. Мы изучаем случай некоторого парного потенциала и получаем оценку для температуры и плотности в λ-точке.З мікроскопічної точки зору вивчені рівноважні властивості системи взаємодіючих бозонів. Ми обчислюємо густину надплинної компоненти в моделі Боголюбова неідеального бозе-газу. Розглянуто модельний суперстабільний гамільтоніан. Ми вивчаємо випадок деякого парного потенціалу і одержуємо оцінку для температури і густини в λ-точці

Asymptotic exactness of c-number substitution in Bogolyubov's theory of superfluidity

The Bogolyubov model of liquid helium is considered. The validity of substituting a c-number for the k=0 mode operator â0 is established rigorously. The domain of stability of the Bogolyubov's Hamiltonian is found. We derive sufficient conditions which ensure the appearance of the Bose condensate in the model. For some temperatures and some positive values of the chemical potential, there is a gapless Bogolyubov spectrum of elementary excitations, leading to a proper microscopic interpretation of superfluidity

Bogolyubov’s Approximation for Bosons

We analyze the approximating Hamiltonian method for Bose systems. Within the framework of this method, the pressure for the mean field model of an imperfect boson gas is calculated. The problem is considered by the systematic application of the Bogolyubov–Ginibre approximation.Проаналiзовано метод апроксимуючого гамiльтонiана для бозе-систем. У межах цього методу знайдено тиск для моделi середнього поля неiдеального бозе-газу. Задачу розглянуто за допомогою послiдовного застосування апроксимацiї Боголюбова–Жiнiбра

Asymptotic exactness of c-number substitution in Bogolyubov's theory of superfluidity

The Bogolyubov model of liquid helium is considered. The validity of substituting a c-number for the k=0 mode operator â0 is established rigorously. The domain of stability of the Bogolyubov's Hamiltonian is found. We derive sufficient conditions which ensure the appearance of the Bose condensate in the model. For some temperatures and some positive values of the chemical potential, there is a gapless Bogolyubov spectrum of elementary excitations, leading to a proper microscopic interpretation of superfluidity

Quantum Field Kinetics

Using the general framework of quantum field theory, we derive basic equations of quantum field kinetics. The main goal of this approach is to compute the observables associated with a quark-gluon plasma at different stages of its evolution. We start by rewriting the integral equations for the field correlators in different forms, depending on the relevant dynamical features at each different stage. Next, two versions of perturbation expansion are considered. The first is best suited for the calculation of electromagnetic emission from chaotic, but not equilibrated, strongly interacting matter. The second version allows one to derive evolution equations, which are generalizations of the familiar QCD evolution equations, and provide a basis for the calculation of the initial quark and gluon distributions after the first hard interaction of the heavy ions.Comment: 13 pages, REVTeX, 2 postscript figures appende

Method of intermediate problems in the theory of Gaussian quantum dots placed in a magnetic field

Applicability of the method of intermediate problems to the investigation of the energy eigenvalues and eigenstates of a quantum dot (QD) formed by a Gaussian confining potential in the presence of an external magnetic field is discussed. Being smooth at the QD boundaries and of finite depth and range, this potential can only confine a finite number of excess electrons thus forming a realistic model of a QD with smooth interface between the QD and its embedding environment. It is argued that the method of intermediate problems, which provides convergent improvable lower bound estimates for eigenvalues of linear half-bound Hermitian operators in Hilbert space, can be fused with the classical Rayleigh-Ritz variational method and stochastic variational method thus resulting in an efficient tool for analytical and numerical studies of the energy spectrum and eigenstates of the Gaussian quantum dots, confining small-to-medium number of excess electrons, with controllable or prescribed precision

On phenomenon of scattering on resonances associated with discretisation of systems with fast rotating phase

Numerical integration of ODEs by standard numerical methods reduces a continuous time problems to discrete time problems. Discrete time problems have intrinsic properties that are absent in continuous time problems. As a result, numerical solution of an ODE may demonstrate dynamical phenomena that are absent in the original ODE. We show that numerical integration of system with one fast rotating phase lead to a situation of such kind: numerical solution demonstrate phenomenon of scattering on resonances that is absent in the original system.Comment: 10 pages, 5 figure

Geometric approach to asymptotic expansion of Feynman integrals

We present an algorithm that reveals relevant contributions in non-threshold-type asymptotic expansion of Feynman integrals about a small parameter. It is shown that the problem reduces to finding a convex hull of a set of points in a multidimensional vector space.Comment: 6 pages, 2 figure

An approach to solve Slavnov-Taylor identities in nonsupersymmetric non-Abelian gauge theories

We present a way to solve Slavnov--Taylor identities in a general nonsupersymmetric theory. The solution can be parametrized by a limited number of functions of spacetime coordinates, so that all the effective fields are dressed by these functions via integral convolution. The solution restricts the ghost part of the effective action and gives predictions for the physical part of the effective action.Comment: revised version, section 3 is enlarged, 24 pages, Latex2e, no figures, version accepted by Phys. Rev.

Conditions for the emergence of spatial asymmetric states in attractor neural network

In this paper we show that during the retrieval process in a binary symmetric Hebb neural network, spatial localized states can be observed when the connectivity of the network is distance-dependent and when a constraint on the activity of the network is imposed, which forces different levels of activity in the retrieval and learning states. This asymmetry in the activity during the retrieval and learning is found to be sufficient condition in order to observe spatial localized states. The result is confirmed analytically and by simulation.Comment: 14