Related papers: Bogolyubov Measure in Quantum Equilibrium Statisti…
As is well-known, in the conventional formulation of Bogoliubov's theory of an interacting Bose gas, the Hamiltonian $\hat{H}$ is written as a decoupled sum of contributions from different momenta of the form $\hat{H} = \sum_{k\neq…
A mean-density description of spatially-inhomogeneous Bose-condensed gases based on Bogoliubov's method is introduced. The description assumes only a large mean atomic density and so remains valid when the mean field collapses due to phase…
Strongly correlated quantum matter -- such as interacting electron systems or interacting quantum fluids -- possesses properties that cannot be understood in terms of linear fluctuations and free quasi-particles. Quantum fluctuations in…
We propose a method to measure the normal fraction of a two-dimensional Bose gas, a quantity that generally differs from the non-condensed fraction. The idea is based on applying a spatially oscillating artificial gauge field to the atoms.…
The calculation of work distributions in a quantum many-body system is of significant importance and also of formidable difficulty in the field of nonequilibrium quantum statistical mechanics. To solve this problem, inspired by…
The notion of a measure on the space of connections modulo gauge transformations that is invariant under diffeomorphisms of the base manifold is important in a variety of contexts in mathematical physics and topology. At the formal level,…
We investigate Gibbs measures relative to Brownian motion in the case when the interaction energy is given by a double stochastic integral. In the case when the double stochastic integral is originating from the Pauli-Fierz model in…
The path integral is calculated for the statistical sum of the microcanonical ensemble in a generic time-parametrization invariant gravitational model with the Friedman-Robertson-Walker (FRW) metric. This represents the first example of a…
A quantum field-theoretical model, which describes spatially non-homogeneous repulsive Bose gas in an external harmonic potential is considered. Two-point thermal correlation functions of the Bose gas are calculated in the framework of the…
This paper deals with the quantitative normal approximation of non-linear functionals of Poisson random measures, where the quality is measured by the Kolmogorov distance. Combining Stein's method with the Malliavin calculus of variations…
The structure of the thermal equilibrium state of a weakly interacting Bose gas is of current interest. We calculate the density matrix of that state in two ways. The most effective method, in terms of yielding a simple, explicit answer, is…
BRST-invariant action of general relativity in the unimodular gauge proposed by Baulieu is studied without using perturbative expansions. The expression for the path integral in the unimodular gauge is reduced to a form in which a…
We analyze the dynamics of a Bose-Einstein condensate undergoing a continuous dispersive imaging by using a Lindblad operator formalism. Continuous strong measurements drive the condensate out of the coherent state description assumed…
We demonstrate that not all generalized Bogoliubov transformations lead to $\cal D$-pseudo-bosons and prove that a correspondence between the two can only be achieved with the imposition of specific constraints on the parameters defining…
In this paper we study several inequalities of log-Sobolev type for Dunkl operators. After proving an equivalent of the classical inequality for the usual Dunkl measure $\mu_k$, we also study a number of inequalities for probability…
In this article, we will first introduce a class of Gaussian processes, and prove the quasi-invariant theorem with respect to the Gaussian Wiener measure, which is the law of the associated Gaussian process. In particular, it includes the…
We consider an inviscid 3-layer quasi-geostrophic model with stochastic forcing in a 2D bounded domain. After establishing well-posedness of such system under natural regularity assumptions on the initial condition and the (additive) noise,…
The problem of statistics of molecular random walks in a classical fluid is analyzed by means of the BBGKY hierarchy of equations reformulated in terms of the Bogolyubov evolution equation for generating functional of many-particle…
The derivation of mean-field limits for quantum systems at zero temperature has attracted many researchers in the last decades. Recent developments are the consideration of pair correlations in the effective description, which lead to a…
We consider equations describing a barotropic inviscid flow in a channel with topography effects and beta-plane approximation of Coriolis force, in which a large-scale mean flow interacts with smaller scales. Gibbsian measures associated to…