Phase transitions with finite atom number in the Dicke Model

Two-level atoms interacting with a one mode cavity field at zero temperature have order parameters which reflect the presence of a quantum phase transition at a critical value of the atom-cavity coupling strength. Two popular examples are the number of photons inside the cavity and the number of excited atoms. Coherent states provide a mean field description, which becomes exact in the thermodynamic limit. Employing symmetry adapted (SA) SU(2) coherent states (SACS) the critical behavior can be described for a finite number of atoms. A variation after projection treatment, involving a numerical minimization of the SA energy surface, associates the finite number phase transition with a discontinuity in the order parameters, which originates from a competition between two local minima in the SA energy surface.Comment: 8 pages, 10 figures, Conference Proceedings of CEWQO-2012, to be published as a Topical Issue of the journal Physica Script

Generalized Pseudo-SU(3) Model and Pairing

The pseudo-SU(3) model is extended to explicitly include the spin and proton-neutron degrees of freedom. A general formalism for evaluating matrix elements of one-body and two-body tensor operators within this framework is presented. The pairing interaction, which couples different irreducible representations of SU(3), is expressed in terms of pseudo-space tensors and a general result is given for calculating its matrix elements. The importance of pairing correlations in pseudo-SU(3) model calculations is demonstrated by examining the dependence of wavefunctions, low-energy collective excitation spectra, and moments of inertia on the strength of the pairing interaction.Comment: 21 Pages, 7 Figures (available upon request), Nucl. Phys. A in pres

Effects of Pairing in the Pseudo-SU(3) Model

An extended version of the pseudo-SU(3) model which includes both spin and proton-neutron degrees of freedom is used to study the influence of the pairing interaction on K-band mixing, B(E2) values and quadrupole moments. Using the asymmetric rotor model as a backdrop, specific consequences of a many-particle shell-model based description of these collective properties are demonstrated and fundamental limits of the collective model's approach are investigated. Finally, the pseudo-SU(3) model, including representation mixing induced by pairing, is used to calculate the energies of 140Ce and the results are compared to experimental data and other theories.Comment: 21 pages, Latex, 11 figures available on request via mail or fax, accepted by Nucl. Phys.

Inter-band B(E2) transition strengths in odd-mass heavy deformed nuclei

Inter-band B(E2) transition strengths between different normal parity bands in 163Dy and 165Er are described using the pseudo-SU(3) model. The Hamiltonian includes Nilsson single-particle energies, quadrupole-quadrupole and pairing interactions with fixed, parametrized strengths, and three extra rotor terms used to fine tune the energy spectra. In addition to inter-band transitions, the energy spectra and the ground state intra-band B(E2) strengths are reported. The results show the pseudo-SU(3) shell model to be a powerful microscopic theory for a description of the normal parity sector in heavy deformed odd-A nuclei.Comment: 4 figures, 2 table

Distances between quantum states in the tomographic-probability representation

Distances between quantum states are reviewed within the framework of the tomographic-probability representation. Tomographic approach is based on observed probabilities and is straightforward for data processing. Different states are distinguished by comparing corresponding probability-distribution functions. Fidelity as well as other distance measures are expressed in terms of tomograms.Comment: 10 pages, Contribution to the 16th Central European Workshop on Quantum Optics (CEWQO'09), May 23-27, 2009, Turku, Finlan

Shell model description of normal parity bands in odd-mass heavy deformed nuclei

The low-energy spectra and B(E2) electromagnetic transition strengths of 159Eu, 159Tb and 159Dy are described using the pseudo SU(3) model. Normal parity bands are built as linear combinations of SU(3) states, which are the direct product of SU(3) proton and neutron states with pseudo spin zero (for even number of nucleons) and pseudo spin 1/2 (for odd number of nucleons). Each of the many-particle states have a well-defined particle number and total angular momentum. The Hamiltonian includes spherical Nilsson single-particle energies, the quadrupole-quadrupole and pairing interactions, as well as three rotor terms which are diagonal in the SU(3) basis. The pseudo SU(3) model is shown to be a powerful tool to describe odd-mass heavy deformed nuclei.Comment: 11 pages, 2 figures, Accepted to be published in Phys. Rev.

Lipidomic features of honey bee and colony health during limited supplementary feeding

Honey bee nutritional health depends on nectar and pollen, which provide the main source of carbohydrates, proteins and lipids to individual bees. During malnutrition, insect metabolism accesses fat body reserves. However, this process in bees and its repercussions at the colony level are poorly understood. Using untargeted lipidomics and gene expression analysis, we examined the effects of different feeding treatments (starvation, sugar feeding and sugar + pollen feeding) on bees and correlated them with colony health indicators. We found that nutritional stress led to an increase in unsaturated triacylglycerols and diacylglycerols, as well as a decrease in free fatty acids in the bee fat body. Here, we hypothesise that stored lipids are made available through a process where unsaturations change lipid\u27s structure. Increased gene expression of three lipid desaturases in response to malnutrition supports this hypothesis, as these desaturases may be involved in releasing fatty acyl chains for lipolysis. Although nutritional stress was evident in starving and sugar-fed bees at the colony and physiological level, only starved colonies presented long-term effects in honey production

Nonperturbative and perturbative treatments of parametric heating in atom traps

We study the quantum description of parametric heating in harmonic potentials both nonperturbatively and perturbatively, having in mind atom traps. The first approach establishes an explicit connection between classical and quantum descriptions; it also gives analytic expressions for properties such as the width of fractional frequency parametric resonances. The second approach gives an alternative insight into the problem and can be directly extended to take into account nonlinear effects. This is specially important for shallow traps.Comment: 12 pages, 2 figure

Supersymmetry and superalgebra for the two-body system with a Dirac oscillator interaction

Some years ago, one of the authors~(MM) revived a concept to which he gave the name of single-particle Dirac oscillator, while another~(CQ) showed that it corresponds to a realization of supersymmetric quantum mechanics. The Dirac oscillator in its one- and many-body versions has had a great number of applications. Recently, it included the analytic expression for the eigenstates and eigenvalues of a two-particle system with a new type of Dirac oscillator interaction of frequency~$\omega$. By considering the latter together with its partner corresponding to the replacement of~$\omega$ by~$-\omega$, we are able to get a supersymmetric formulation of the problem and find the superalgebra that explains its degeneracy.Comment: 21 pages, LaTeX, 1 figure (can be obtained from the authors), to appear in J. Phys.