Tests of the envelope theory for three-body forces

Many-body forces, and specially three-body forces, are sometimes a relevant ingredient in various fields, such as atomic, nuclear or hadronic physics. As their precise structure is generally difficult to uncover or to implement, phenomenological effective forces are often used in practice. A form commonly used for a many-body variable is the square-root of the sum of two-body variables. Even in this case, the problem can be very difficult to treat numerically. But this kind of many-body forces can be handled at the same level of difficulty than two-body forces by the envelope theory. The envelope theory is a very efficient technique to compute approximate, but reliable, solutions of many-body systems, specially for identical particles. The quality of this technique is tested here for various three-body forces with non-relativistic systems composed of three identical particles. The energies, the eigenfunctions, and some observables are compared with the corresponding accurate results computed with a numerical variational method.Comment: 13 page

A large-NcN_c PNJL model with explicit ZNc_{N_c} symmetry

A PNJL model is built, in which the Polyakov-loop potential is explicitly Z$_{N_c}$-symmetric in order to mimic a Yang-Mills theory with gauge group SU($N_c$). The physically expected large-$N_c$ and large-$T$ behaviours of the thermodynamic observables computed from the Polyakov-loop potential are used to constrain its free parameters. The effective potential is eventually U(1)-symmetric when $N_c$ is infinite. Light quark flavours are added by using a Nambu-Jona-Lasinio (NJL) model coupled to the Polyakov loop (the PNJL model), and the different phases of the resulting PNJL model are discussed in 't Hooft's large-$N_c$ limit. Three phases are found, in agreement with previous large-$N_c$ studies. When the temperature $T$ is larger than some deconfinement temperature $T_d$, the system is in a deconfined, chirally symmetric, phase for any quark chemical potential $\mu$. When $T<T_d$ however, the system is in a confined phase in which chiral symmetry is either broken or not. The critical line $T_\chi(\mu)$, signalling the restoration of chiral symmetry, has the same qualitative features than what can be obtained within a standard $N_c=3$ PNJL model.Comment: To appear in Phys Rev

A minimal quasiparticle approach for the QGP and its large-NcN_c limits

We propose a quasiparticle approach allowing to compute the equation of state of a generic gauge theory with gauge group SU($N_c$) and quarks in an arbitrary representation. Our formalism relies on the thermal quasiparticle masses (quarks and gluons) computed from Hard-Thermal-Loop techniques, in which the standard two-loop running coupling constant is used. Our model is minimal in the sense that we do not allow any extra ansatz concerning the temperature-dependence of the running coupling. We first show that it is able to reproduce the most recent equations of state computed on the lattice for temperatures higher than 2 $T_c$. In this range of temperatures, an ideal gas framework is indeed expected to be relevant. Then we study the accuracy of various inequivalent large-$N_c$ limits concerning the description of the QCD results, as well as the equivalence between the QCD$_{AS}$ limit and the ${\cal N}=1$ SUSY Yang-Mills theory. Finally, we estimate the dissociation temperature of the $\Upsilon$-meson and comment on the estimations' stability regarding the different considered large-$N_c$ limits.Comment: 19 pages, 6 figure

Tests of the envelope theory for three-body forces

peer reviewedMany-body forces, and specially three-body forces, are sometimes a relevant ingredient in various fields, such as atomic, nuclear or hadronic physics. As their precise structure is generally difficult to uncover or to implement, phenomenological effective forces are often used in practice. A form commonly used for a many-body variable is the square-root of the sum of two-body variables. Even in this case, the problem can be very difficult to treat numerically. But this kind of many-body forces can be handled at the same level of difficulty than two-body forces by the envelope theory. The envelope theory is a very efficient technique to compute approximate, but reliable, solutions of many-body systems, specially for identical particles. The quality of this technique is tested here for various three-body forces with non-relativistic systems composed of three identical particles. The energies, the eigenfunctions, and some observables are compared with the corresponding accurate results computed with a numerical variational method

Combined effects of changing hydroclimate and human activity on coastal ecosystem health - AMORE III: Final report phase I - Summary

AMORE (Advanced Modeling and Research on Eutrophication) is an interdisciplinary consortium composed of biologists, bioengineers, biostatisticians and physical and ecological modelers aiming to the development of Sustainability Science for the management of coastal zones in the Channel and the Southern Bight of the North Sea with a focus on the Belgian coastal zone (BCZ)