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

Finite temperature spectral functions of the linear O(N)-model at large N applied to the π−σ\pi -\sigma system

The thermal evolution of the spectral densities derivable from the two-point functions of the elementary and the quadratic composite fields of the O(N) model is studied in the isosinglet channel and in the broken symmetry phase at infinite N. The results are applied with realistic parameter values to the N=4 case. They provide a reasonable description of the $\sigma$ meson at T=0. Threshold enhancement is observed around $T\sim 1.07m_\pi$. For higher temperatures the maximum of the spectral function in the single meson channel decreases and becomes increasingly rounded.Comment: 10 pages, 4 figures. Change in the abstract and replacement of Fig.3 due to a numerical error not influencing the physics conten

Transition from Poissonian to GOE level statistics in a modified Artin's billiard

One wall of Artin's billiard on the Poincar\'e half plane is replaced by a one-parameter ($c_p$) family of nongeodetic walls. A brief description of the classical phase space of this system is given. In the quantum domain, the continuousand gradual transition from the Poisson like to GOE level statistics due to the small perturbations breaking the symmetry responsible for the 'arithmetic chaos' at $c_p=1$ is studied. Another GOE \rightrrow Poisson transition due to the mixed phase space for large perturbations is also investigated. A satisfactory description of the intermediate level statistics by the Brody distribution was found in boh cases. The study supports the existence of a scaling region around $c_p=1$. A finite size scaling relation for the Brody-parameter as a function of $1-c_p$ and the number of levels considered can be established

Structure of the perturbation series of the spin-1 Bose gas at low temperatures

The properties of Green's functions and various correlation functions of density and spin operators are considered in a homogeneous spin-1 Bose gas in different phases. The dielectric formalism is worked out and the partial coincidence of the one-particle and collective spectra is pointed out below the temperature of Bose-Einstein condensation. As an application the formalism is used to give two approximations for the propagators and the correlation functions and the spectra of excitations including shifts and widths due to the thermal cloud.Comment: 34 pages, 17 figure

Calculation of the even-odd energy difference in superfluid Fermi systems using the pseudopotential theory

The pseudopotential theory is extended to the Bogoliubov-de Gennes equations to determine the excess energy when one atom is added to the trapped superfluid Fermi system with even number of atoms. Particular attention is paid to systems being at the Feshbach resonance point. The results for relatively small particle numbers are in harmony with the Monte Carlo calculations, but are also relevant for systems with larger particle numbers. Concerning the additional one-quasiparticle state we define and determine two new universal numbers to characterize its widths. Copyright © EPLA, 2012

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