Correlations between the nuclear matter symmetry energy, its slope, and curvature from a nonrelativistic solvable approach and beyond

By using point-coupling versions of finite range nuclear relativistic mean field models containing cubic and quartic self interactions in the scalar field $\sigma$, a nonrelativistic limit is achieved. This approach allows an analytical expression for the symmetry energy ($J$) as a function of its slope ($L$) in a unified form, namely, $\,L\,=\,3J\,+f(m^{*},\rho_{o},B_{o},K_{o})$, where the quantities $m^{*}$, $\rho_{o}$, $B_{o}$ and $K_{o}$ are bulk parameters at the nuclear matter saturation density $\rho_{o}$. This result establishes a linear correlation between $L$ and $J$ which is reinforced by exact relativistic calculations. An analogous analytical correlation is also found for $J$, $L$ and the symmetry energy curvature ($K_{sym}$). Based on these results, we propose graphic constraints in $L\times J$ and $K_{sym}\times L$ planes which finite range models must satisfy.Comment: 9 pages, 9 figure

Phase transition of the nucleon-antinucleon plasma at different ratios

We investigate phase transitions for the Walecka model at very high temperatures. As is well known, depending on the parametrization of this model and for the particular case of a zero chemical potential ($\mu$), a first order phase transition is possible \cite{theis}. We investigate this model for the case in which $\mu \ne 0$. It turns out that, in this situation, phases with different values of antinucleon-nucleon ratios and net baryon densities may coexist. We present the temperature versus antinucleon-nucleon ratio as well as the temperature versus the net baryon density for the coexistence region. The temperature versus chemical potential phase diagram is also presented.Comment: 5 pages, 8 figure

Photon propagation through linearly active dimers

We provide an analytic propagator for non-Hermitian dimers showing linear gain or losses in the quantum regime. In particular, we focus on experimentally feasible realizations of the $\mathcal{PT}$-symmetric dimer and provide their mean photon number and second order two-point correlation. We study the propagation of vacuum, single photon spatially-separable, and two-photon spatially-entangled states. We show that each configuration produces a particular signature that might signal their possible uses as photon switches, semi-classical intensity-tunable sources, or spatially entangled sources to mention a few possible applications.Comment: 15 pages, 5 figure

Form factors in the Bullough-Dodd related models: The Ising model in a magnetic field

We consider particular modification of the free-field representation of the form factors in the Bullough-Dodd model. The two-particles minimal form factors are excluded from the construction. As a consequence, we obtain convenient representation for the multi-particle form factors, establish recurrence relations between them and study their properties. The proposed construction is used to obtain the free-field representation of the lightest particles form factors in the $\Phi_{1,2}$ perturbed minimal models. As a significant example we consider the Ising model in a magnetic field. We check that the results obtained in the framework of the proposed free-field representation are in agreement with the corresponding results obtained by solving the bootstrap equations.Comment: 20 pages; v2: some misprints, textual inaccuracies and references corrected; some references and remarks adde

Finite temperature results on the 2d Ising model with mixed perturbation

A numerical study of finite temperature features of thermodynamical observables is performed for the lattice 2d Ising model. Our results support the conjecture that the Finite Size Scaling analysis employed in the study of integrable perturbation of Conformal Field Theory is still valid in the present case, where a non-integrable perturbation is considered.Comment: 9 pages, Latex, added references and improved introductio

Universal Ratios in the 2-D Tricritical Ising Model

We consider the universality class of the two-dimensional Tricritical Ising Model. The scaling form of the free-energy naturally leads to the definition of universal ratios of critical amplitudes which may have experimental relevance. We compute these universal ratios by a combined use of results coming from Perturbed Conformal Field Theory, Integrable Quantum Field Theory and numerical methods.Comment: 4 pages, LATEX fil

Form factors of descendant operators in the massive Lee-Yang model

The form factors of the descendant operators in the massive Lee-Yang model are determined up to level 7. This is first done by exploiting the conserved quantities of the integrable theory to generate the solutions for the descendants starting from the lowest non-trivial solutions in each operator family. We then show that the operator space generated in this way, which is isomorphic to the conformal one, coincides, level by level, with that implied by the $S$-matrix through the form factor bootstrap. The solutions we determine satisfy asymptotic conditions carrying the information about the level that we conjecture to hold for all the operators of the model.Comment: 23 page