Quantum Phase Transitions in the U(5)-O(6) Large N limit

The U(5)-O(6) transitional behavior of the Interacting Boson Model in the large N limit is revisited. Some low-lying energy levels, overlaps of the ground state wavefunctions, B(E2) transition rate for the decay of the first excited energy level to the ground state, and the order parameters are calculated for different total numbers of bosons. The results show that critical behaviors of these quantities are greatly enhanced with increasing of the total number of bosons N, especially fractional occupation probability for d bosons in the ground state, the difference between the expectation value of n_d in the first excited 0^+ state and the ground state, and another quantity related to the isomer shift behave similarly in both the O(6)-U(5) large N and U(5)-SU(3) phase transitions.Comment: 7 Pages LaTeX, 3 figure

Using ion beams to tune the nanostructure and optical response of co-deposited Ag : BBBN thin films

The present study is devoted to co-deposited Ag : BN nanocermet thin films and is focused on the influence of ion irradiation conditions on their structural and linear optical properties. Ion irradiation was performed in situ during the growth of the nanocermets using a 50 eV assistance beam (nitrogen/argon or nitrogen-ion assistance) and ex situ on as-grown films using a 120 keV argon-ion beam (post-irradiation). Grazing incidence small-angle x-ray scattering measurements show that (i) as-grown N-assisted films contain prolate spheroidal clusters (height-to-diameter ratio H/D ≈ 1.8), (ii) N/Ar-ion assistance leads to the formation of more elongated clusters (H/D ≈ 2.1) and (iii) post-irradiation leads to a decrease of H/D to a value close to 1. These results are discussed on the basis of atomic diffusion processes involved during the growth of the nanocermets and during the post-irradiation. The optical transmittance spectra of these films measured at normal incidence display one absorption band, due to the excitation of the (1,1) plasmon mode of the clusters. In the case of the as-grown films, an additional band appears at oblique incidence for P-polarized light, as a consequence of the excitation of the (1,0) plasmon mode of the clusters. Our results show that the spectral position of the absorption bands (which can be tuned in the 400-600 nm range) depends on the H/D ratio of the clusters, in good agreement with calculations of optical transmittance considering the nanocomposite layer as a uniaxial anisotropic medium whose dielectric tensor is described by an anisotropic Maxwell-Garnett model. © 2007 IOP Publishing Ltd.The authors would like to thank CNRS-CSIC and Picasso programmes for financial support which permitted the collaboration between the Instituto de Ciencia de Materiales de Sevilla (Spain) and the Laboratoire de Metallurgie Physique ´ de Poitiers (France). The authors also thank J P Simon and the D2AM staff at the ESRF for their support during the GISAXS measurements.Peer Reviewe

The excitation spectrum for weakly interacting bosons in a trap

We investigate the low-energy excitation spectrum of a Bose gas confined in a trap, with weak long-range repulsive interactions. In particular, we prove that the spectrum can be described in terms of the eigenvalues of an effective one-particle operator, as predicted by the Bogoliubov approximation.Comment: LaTeX, 32 page

The Second Order Upper Bound for the Ground Energy of a Bose Gas

Consider $N$ bosons in a finite box $\Lambda= [0,L]^3\subset \mathbf R^3$ interacting via a two-body smooth repulsive short range potential. We construct a variational state which gives the following upper bound on the ground state energy per particle $$\bar\lim_{\rho\to0} \bar \lim_{L \to \infty, N/L^3 \to \rho} (\frac{e_0(\rho)- 4 \pi a \rho}{(4 \pi a)^{5/2}(\rho)^{3/2}})\leq \frac{16}{15\pi^2},$$ where $a$ is the scattering length of the potential. Previously, an upper bound of the form $C 16/15\pi^2$ for some constant $C > 1$ was obtained in \cite{ESY}. Our result proves the upper bound of the the prediction by Lee-Yang \cite{LYang} and Lee-Huang-Yang \cite{LHY}.Comment: 62 pages, no figure

Generalized Bose-Einstein Condensation

Generalized Bose-Einstein condensation (GBEC) involves condensates appearing simultaneously in multiple states. We review examples of the three types in an ideal Bose gas with different geometries. In Type I there is a discrete number of quantum states each having macroscopic occupation; Type II has condensation into a continuous band of states, with each state having macroscopic occupation; in Type III each state is microscopically occupied while the entire condensate band is macroscopically occupied. We begin by discussing Type I or "normal" BEC into a single state for an isotropic harmonic oscillator potential. Other geometries and external potentials are then considered: the {}"channel" potential (harmonic in one dimension and hard-wall in the other), which displays Type II, the {}"cigar trap" (anisotropic harmonic potential), and the "Casimir prism" (an elongated box), the latter two having Type III condensations. General box geometries are considered in an appendix. We particularly focus on the cigar trap, which Van Druten and Ketterle first showed had a two-step condensation: a GBEC into a band of states at a temperature $T_{c}$ and another "one-dimensional" transition at a lower temperature $T_{1}$ into the ground state. In a thermodynamic limit in which the ratio of the dimensions of the anisotropic harmonic trap is kept fixed, $T_{1}$ merges with the upper transition, which then becomes a normal BEC. However, in the thermodynamic limit of Beau and Zagrebnov, in which the ratio of the boundary lengths increases exponentially, $T_{1}$ becomes fixed at the temperature of a true Type I phase transition. The effects of interactions on GBEC are discussed and we show that there is evidence that Type III condensation may have been observed in the cigar trap.Comment: 17 pages; 6 figures. Intended for American Journal of Physic