Variational wave functions for homogenous Bose systems

We study variational wave functions of the product form, factorizing according to the wave vectors k, for the ground state of a system of bosons interacting via positive pair interactions with a positive Fourier transform. Our trial functions are members of different orthonormal bases in Fock space. Each basis contains a quasiparticle vacuum state and states with an arbitrary finite number of quasiparticles. One of the bases is that of Valatin and Butler (VB), introduced fifty years ago and parametrized by an infinite set of variables determining Bogoliubov's canonical transformation for each k. In another case, inspired by Nozi\`eres and Saint James the canonical transformation for k=0 is replaced by a shift in the creation/annihilation operators. For the VB basis we prove that the lowest energy is obtained in a state with ~sqrt{volume} quasiparticles in the zero mode. The number of k=0 physical particles is of the order of the volume and its fluctuation is anomalously large, resulting in an excess energy. The same fluctuation is normal in the second type of optimized bases, the minimum energy is smaller and is attained in a vacuum state. Associated quasiparticle theories and questions about the gap in their spectrum are also discussed

Phases of a polar spin-1 Bose gas in a magnetic field

The two Bose--Einstein condensed phases of a polar spin-1 gas at nonzero magnetizations and temperatures are investigated. The Hugenholtz--Pines theorem is generalized to this system. Crossover to a quantum phase transition is also studied. Results are discussed in a mean field approximation.Comment: 6 pages, 3 figures, revised versio

Fázisátalakulások és szimmetriasértő fázisok dinamikája = Dynamics of Phase Transitions and Symmetry Breaking Phases

A pályázat célja szimmetriasértő fázisok kialakulásának és tulajdonságainak elméleti vizsgálata volt. Fontos területek voltak az alábbiak. Erősen kölcsönható anyag fázisdiagramjának meghatározása effektív mezon-kvark modellekből felösszegzett perturbációszámítással. A kozmológiai inflációt lezáró egyensúlytól távoli folyamatok dinamikája. Univerzalitási osztályok és skálatörvények egyensúlytól távoli rendszerek kritikus jelenségeinél. Spinor Bose-gázok mágneses tulajdonságai, különböző mágneses fázisok, és ezekben a kvázirészek dinamikája. Szuperfolyékony Fermi-gázok univerzális tulajdonságai a Feshbach-rezonancián. Bose-kondenzáció dinamikája és kontrollparaméter függése üregrezonátorba helyezett gázban. Matematikai fizikai vizsgálatok a Bose-Einstein-kondenzációval és a kristályszerkezet kialakulásával kapcsolatban. | The aim of the research has been the theoretical investigation of the development and properties of symmetry breaking phases. Important fields of the study have been as follows. Determination of the phase diagram of strongly interacting matter from effective meson-quark models with resummation of perturbative series. Investigation of the far from equilibrium dynamical processes characterizing the exit of the universe from the stage of cosmological inflation. Universality classes and scaling laws describing critical phenomena in systems far from equilibrium. Magnetic features of spinor Bose gases, specification of different magnetic phases and the calculation of quasiparticle dynamics in them. Universal properties of inhomogeneous Fermi gases at the Feshbach resonance. The dynamics and control parameter dependence of a Bose-Einstein condensate in an optical cavity. Investigation of the properties of Bose-Einstein condensation and of its competition with crystallization by the methods of mathemetical physics

Static properties and spin dynamics of the ferromagnetic spin-1 Bose gas in magnetic field

Properties of spin-1 Bose gases with ferromagnetic interaction in the presence of a nonzero magnetic field are studied. The equation of state and thermodynamic quantities are worked out with the help of a mean-field approximation. The phase diagram besides Bose-Einstein condensation contains a first order transition where two values of the magnetization coexist. The dynamics is investigated with the help of the Random Phase Approximation. The soft mode corresponding to the critical point of the magnetic phase transition is found to behave like in conventional theory.Comment: 8 pages and 3 figures included in text, submitted to Physical Review

The Kohn mode for trapped Bose gases within the dielectric formalism

The presence of undamped harmonic center of mass oscillations of a weakly interacting Bose gas in a harmonic trap is demonstrated within the dielectric formalism for a previously introduced finite temperature approximation including exchange. The consistency of the approximation with the Kohn theorem is thereby demonstrated. The Kohn modes are found explicitly, generalizing an earlier zero-temperature result found in the literature. It is shown how the Kohn mode disappears from the single-particle spectrum, while remaining in the density oscillation spectrum, when the temperature increases from below to above the condensation temperature.Comment: 6 pages revte

Three fluid hydrodynamics of spin-1 Bose-Einstein condensates

We study excitations of the spin-1 Bose gas at finite temperatures and in the presence of a not so strong magnetic field, or equivalently, when the gas sample is partially polarized. Motivated by the success of two-fluid hydrodynamics of scalar superfluids we develop a three-fluid hydrodynamic description to treat the low frequency and long wavelength excitations of the spin-1 Bose gas. We derive the coupled linear hydrodynamic equations of the three sounds and evaluate them numerically in a self-consistent mean field approximation valid for the dilute gas at the intermediate and critical temperature regions. In this latter region we identify the critical mode

Clustering of Fermi particles with arbitrary spin

A single l-shell model is investigated for a system of fermions of spin s and an attractive s-wave, spin channel independent, interaction. The spectra and eigenvectors are determined exactly for different l, s values and particle numbers N. As a generalization of Cooper pairing it is shown that when N=mu(2s+1), mu=1,2,...,2l+1, the ground state consists of clusters of (2s+1) particles. The relevance of the results for more general situations including the homogeneous system is briefly discussed.Comment: Submitted for publication, 4 pages, 1 figur

Energies and damping rates of elementary excitations in spin-1 Bose-Einstein condensed gases

Finite temperature Green's function technique is used to calculate the energies and damping rates of elementary excitations of the homogeneous, dilute, spin-1 Bose gases below the Bose-Einstein condensation temperature both in the density and spin channels. For this purpose the self-consistent dynamical Hartree-Fock model is formulated, which takes into account the direct and exchange processes on equal footing by summing up certain classes of Feynman diagrams. The model is shown to fulfil the Goldstone theorem and to exhibit the hybridization of one-particle and collective excitations correctly. The results are applied to the gases of ^{23}Na and ^{87}Rb atoms.Comment: 26 pages, 21 figures. Added 2 new figures, detailed discussio