Instantons and radial excitations in attractive Bose-Einstein condensates

Imaginary- and real-time versions of an equation for the condensate density are presented which describe dynamics and decay of any spherical Bose-Einstein condensate (BEC) within the mean field appraoch. We obtain quantized energies of collective finite amplitude radial oscillations and exact numerical instanton solutions which describe quantum tunneling from both the metastable and radially excited states of the BEC of 7Li atoms. The mass parameter for the radial motion is found different from the gaussian value assumed hitherto, but the effect of this difference on decay exponents is small. The collective breathing states form slightly compressed harmonic spectrum, n=4 state lying lower than the second Bogolyubov (small amplitude) mode. The decay of these states, if excited, may simulate a shorter than true lifetime of the metastable state. By scaling arguments, results extend to other attractive BEC-s.Comment: 6 pages, 3 figure

Incremental, Inductive Coverability

We give an incremental, inductive (IC3) procedure to check coverability of well-structured transition systems. Our procedure generalizes the IC3 procedure for safety verification that has been successfully applied in finite-state hardware verification to infinite-state well-structured transition systems. We show that our procedure is sound, complete, and terminating for downward-finite well-structured transition systems---where each state has a finite number of states below it---a class that contains extensions of Petri nets, broadcast protocols, and lossy channel systems. We have implemented our algorithm for checking coverability of Petri nets. We describe how the algorithm can be efficiently implemented without the use of SMT solvers. Our experiments on standard Petri net benchmarks show that IC3 is competitive with state-of-the-art implementations for coverability based on symbolic backward analysis or expand-enlarge-and-check algorithms both in time taken and space usage.Comment: Non-reviewed version, original version submitted to CAV 2013; this is a revised version, containing more experimental results and some correction

Order Parameter at the Boundary of a Trapped Bose Gas

Through a suitable expansion of the Gross-Pitaevskii equation near the classical turning point, we obtain an explicit solution for the order parameter at the boundary of a trapped Bose gas interacting with repulsive forces. The kinetic energy of the system, in terms of the classical radius $R$ and of the harmonic oscillator length $a_{_{HO}}$, follows the law $E_{kin}/N \propto R^{-2} [\log (R/a_{_{HO}}) + \hbox{const.}]$, approaching, for large $R$, the results obtained by solving numerically the Gross-Pitaevskii equation. The occurrence of a Josephson-type current in the presence of a double trap potential is finally discussed.Comment: 11 pages, REVTEX, 4 figures (uuencoded-gzipped-tar file) also available at http://anubis.science.unitn.it/~dalfovo/papers/papers.htm

Effect of anharmonicities in the critical number of trapped condensed atoms with attractive two-body interaction

We determine the quantitative effect, in the maximum number of particles and other static observables, due to small anharmonic terms added to the confining potential of an atomic condensed system with negative two-body interaction. As an example of how a cubic or quartic anharmonic term can affect the maximum number of particles, we consider the trap parameters and the results given by Roberts et al. [Phys. Rev. Lett. 86, 4211 (2001)]. However, this study can be easily transferred to other trap geometries to estimate anharmonic effects.Comment: Total of 5 pages, 3 figures and 1 table. To appear in Phys. Rev.

Stability of the trapped nonconservative Gross-Pitaevskii equation with attractive two-body interaction

The dynamics of a nonconservative Gross-Pitaevskii equation for trapped atomic systems with attractive two-body interaction is numerically investigated, considering wide variations of the nonconservative parameters, related to atomic feeding and dissipation. We study the possible limitations of the mean field description for an atomic condensate with attractive two-body interaction, by defining the parameter regions where stable or unstable formation can be found. The present study is useful and timely considering the possibility of large variations of attractive two-body scattering lengths, which may be feasible in recent experiments.Comment: 6 pages, 5 figures, submitted to Physical Review

The effects of metallicity on {delta} Scuti star asteroseismology

In {delta} Scuti star seismology, most researchers use evolution and pulsation models assuming a solar element mixture and Z = 0.02 for preliminary determinations of stellar masses or evolutionary state from observed frequencies. Here the authors investigate the consequences of this assumption by considering the effects of metallicity changes in the models on their inferences of the internal structure of {delta} Scuti stars. They use the main-sequence {delta} Scuti star FG Vir, and the more evolved shell hydrogen burning star {delta} Scuti to illustrate their results

Intensive adoption as a management strategy for unowned, urban cats: A case study of 25 years of trap–assess–resolve (TAR) in Auckland, New Zealand

Globally, unowned urban cats are a major concern because they may suffer from poor welfare and cause problems, including public health risks, nuisances, and urban wildlife predation. While management options are often presented as a choice between culling or trap–neuter–return (TNR), for 25 years, the Lonely Miaow (Inc.) charity in Auckland, New Zealand (hereafter LM), has used a third strategy—intensive adoption or trap–assess–resolve (TAR). As of 2019, of 14,611 unowned cats trapped, 64.2% were adopted, 22.2% were euthanized if unsocialised or in grave ill-health, 5.7% were neutered and returned to the site, and 7.9% had other outcomes, such as being transferred to other shelters. Adoption rates increased over this time, exceeding 80.0% in 2018 and 2019. The cost of processing each cat from capture to adoption rose from NZD 58 in 1999 to NZD 234 by 2017. Approximately 80% of colonies (sites where cats were trapped) were around residential areas. Approximately 22% of cats required veterinary treatment after capture; common ailments included respiratory infections, ringworm, dental problems, and trauma. Consistently, 52% of cats were young kittens (5 years old. TAR avoids euthanasia where possible. Its effectiveness would be enhanced by fewer abandonments of owned cats and kittens, fitting within integrated strategies for the control of unowned cats involving community education. Cat adoptions improve the welfare of cats and, with appropriate husbandry, should alleviate concerns about nuisances, public health, and attacks on wildlife or the cats themselves, essentially benefitting the community and the cats. This case study is relevant to other cities around the world that are seeking to manage unowned cats

Bosons in anisotropic traps: ground state and vortices

We solve the Gross-Pitaevskii equations for a dilute atomic gas in a magnetic trap, modeled by an anisotropic harmonic potential. We evaluate the wave function and the energy of the Bose Einstein condensate as a function of the particle number, both for positive and negative scattering length. The results for the transverse and vertical size of the cloud of atoms, as well as for the kinetic and potential energy per particle, are compared with the predictions of approximated models. We also compare the aspect ratio of the velocity distribution with first experimental estimates available for $^{87}$Rb. Vortex states are considered and the critical angular velocity for production of vortices is calculated. We show that the presence of vortices significantly increases the stability of the condensate in the case of attractive interactions.Comment: 22 pages, REVTEX, 8 figures available upon request or at http://anubis.science.unitn.it/~dalfovo/papers/papers.htm

Evolution of a Bose-condensed gas under variations of the confining potential

We discuss the dynamic properties of a trapped Bose-condensed gas under variations of the confining field and find analytical scaling solutions for the evolving coherent state (condensate). We further discuss the characteristic features and the depletion of this coherent state.Comment: 4 pages, no postscript figure

Stability of Bose condensed atomic Li-7

We study the stability of a Bose condensate of atomic $^7$Li in a (harmonic oscillator) magnetic trap at non-zero temperatures. In analogy to the stability criterion for a neutron star, we conjecture that the gas becomes unstable if the free energy as a function of the central density of the cloud has a local extremum which conserves the number of particles. Moreover, we show that the number of condensate particles at the point of instability decreases with increasing temperature, and that for the temperature interval considered, the normal part of the gas is stable against density fluctuations at this point.Comment: Submitted for publication in Physical Review