Integrability vs non-integrability: Hard hexagons and hard squares compared

In this paper we compare the integrable hard hexagon model with the non-integrable hard squares model by means of partition function roots and transfer matrix eigenvalues. We consider partition functions for toroidal, cylindrical, and free-free boundary conditions up to sizes $40\times40$ and transfer matrices up to 30 sites. For all boundary conditions the hard squares roots are seen to lie in a bounded area of the complex fugacity plane along with the universal hard core line segment on the negative real fugacity axis. The density of roots on this line segment matches the derivative of the phase difference between the eigenvalues of largest (and equal) moduli and exhibits much greater structure than the corresponding density of hard hexagons. We also study the special point $z=-1$ of hard squares where all eigenvalues have unit modulus, and we give several conjectures for the value at $z=-1$ of the partition functions.Comment: 46 page

Hard hexagon partition function for complex fugacity

We study the analyticity of the partition function of the hard hexagon model in the complex fugacity plane by computing zeros and transfer matrix eigenvalues for large finite size systems. We find that the partition function per site computed by Baxter in the thermodynamic limit for positive real values of the fugacity is not sufficient to describe the analyticity in the full complex fugacity plane. We also obtain a new algebraic equation for the low density partition function per site.Comment: 49 pages, IoP styles files, lots of figures (png mostly) so using PDFLaTeX. Some minor changes added to version 2 in response to referee report

Monthly and Diurnal Variability of Rain Rate and Rain Attenuation during the Monsoon Period in Malaysia

Rain is the major source of attenuation for microwave propagation above 10 GHz. In tropical and equatorial regions where the rain intensity is higher, designing a terrestrial and earth-to-satellite microwave links is very critical and challenging at these frequencies. This paper presents the preliminary results of rain effects in a 23 GHz terrestrial point-to-point communication link 1.3km long. The experimental test bed had been set up at Skudai, Johor Bahru, Malaysia. In this area, a monsoon equatorial climate prevails and the rainfall rate can reach values well above 100mm/h with significant monthly and diurnal variability. Hence, it is necessary to implement a mitigation technique for maintaining an adequate radio link performance for the action of very heavy rain. Since we now know that the ULPC (Up Link Power Control) cannot guarantee the desired performance, a solution based on frequency band diversity is proposed in this paper. Here, a secondary radio link operating in a frequency not affected by rain (C band for instance) is placed parallel with the main link. Under no rain or light rain conditions, the secondary link carries without priority radio signals. When there is an outage of the main link due to rain, the secondary link assumes the priority traffic. The outcome of the research shows a solution for higher operating frequencies during rainy events

Traps for pinning and scattering of antiferromagnetic skyrmions via magnetic properties engineering

Micromagnetic simulations have been performed to investigate the controllability of the skyrmion position in antiferromagnetic nanotracks with their magnetic properties modified spatially. In this study we have modeled magnetic defects as local variations on the material parameters, such as the exchange stiffness, saturation magnetization, perpendicular magnetocrystalline anisotropy and Dzyaloshinskii-Moriya constant. Thus, we have observed not only pinning (potential well) but also scattering (potential barrier) of antiferromagnetic skyrmions, when adjusting either a local increase or a local reduction for each material parameter. In order to control of the skyrmion motion it is very important to impose certain positions along the nanotrack where the skyrmion can stop. Magnetic defects incorporated intentionally in antiferromagnetic racetracks can be useful for such purpose. In order to provide guidelines for experimental studies, we vary both material parameters and size of the modified region. The found results show that the efficiency of skyrmion trap depends on a suitable combination of magnetic defect parameters. Furthermore, we discuss the reason why skyrmions are either attracted or repelled by a region magnetically modified.Comment: arXiv admin note: substantial text overlap with arXiv:1810.0375

Interactions of Hermitian and non-Hermitian Hamiltonians

The coupling of non-Hermitian PT-symmetric Hamiltonians to standard Hermitian Hamiltonians, each of which individually has a real energy spectrum, is explored by means of a number of soluble models. It is found that in all cases the energy remains real for small values of the coupling constant, but becomes complex if the coupling becomes stronger than some critical value. For a quadratic non-Hermitian PT-symmetric Hamiltonian coupled to an arbitrary real Hermitian PT-symmetric Hamiltonian, the reality of the ground-state energy for small enough coupling constant is established up to second order in perturbation theory.Comment: 9 pages, 0 figure

Qualidade de frutos de macieiras Eva e Princesa sob fertirrigação nitrogenada em Petrolina-PE.

O presente trabalho foi desenvolvido com o objetivo de avaliar a qualidade física e química de frutos das macieiras Eva e Princesa, em função a fertirrigação nitrogenada em Petrolina-PE

The brachistochrone problem in open quantum systems

Recently, the quantum brachistochrone problem is discussed in the literature by using non-Hermitian Hamilton operators of different type. Here, it is demonstrated that the passage time is tunable in realistic open quantum systems due to the biorthogonality of the eigenfunctions of the non-Hermitian Hamilton operator. As an example, the numerical results obtained by Bulgakov et al. for the transmission through microwave cavities of different shape are analyzed from the point of view of the brachistochrone problem. The passage time is shortened in the crossover from the weak-coupling to the strong-coupling regime where the resonance states overlap and many branch points (exceptional points) in the complex plane exist. The effect can {\it not} be described in the framework of standard quantum mechanics with Hermitian Hamilton operator and consideration of $S$ matrix poles.Comment: 18 page

Standstill Electric Charge Generates Magnetostatic Field Under Born-Infeld Electrodynamics

The Abelian Born-Infeld classical non-linear electrodynamic has been used to investigate the electric and magnetostatic fields generated by a point-like electrical charge at rest in an inertial frame. The results show a rich internal structure for the charge. Analytical solutions have also been found. Such findings have been interpreted in terms of vacuum polarization and magnetic-like charges produced by the very high strengths of the electric field considered. Apparently non-linearity is to be accounted for the emergence of an anomalous magnetostatic field suggesting a possible connection to that created by a magnetic dipole composed of two mognetic charges with opposite signals. Consistently in situations where the Born-Infeld field strength parameter is free to become infinite, Maxwell`s regime takes over, the magnetic sector vanishes and the electric field assumes a Coulomb behavior with no trace of a magnetic component. The connection to other monopole solutions, like Dirac`s, t' Hooft`s or Poliakov`s types, are also discussed. Finally some speculative remarks are presented in an attempt to explain such fields.Comment: 11 pages, 3 figures. In this version is update a permanent address of the author L.P.G. De Assis and information on submission publication. Submetted to International Journal of Theoretical Physic