Localization properties of a tight-binding electronic model on the Apollonian network

An investigation on the properties of electronic states of a tight-binding Hamiltonian on the Apollonian network is presented. This structure, which is defined based on the Apollonian packing problem, has been explored both as a complex network, and as a substrate, on the top of which physical models can defined. The Schrodinger equation of the model, which includes only nearest neighbor interactions, is written in a matrix formulation. In the uniform case, the resulting Hamiltonian is proportional to the adjacency matrix of the Apollonian network. The characterization of the electronic eigenstates is based on the properties of the spectrum, which is characterized by a very large degeneracy. The $2\pi /3$ rotation symmetry of the network and large number of equivalent sites are reflected in all eigenstates, which are classified according to their parity. Extended and localized states are identified by evaluating the participation rate. Results for other two non-uniform models on the Apollonian network are also presented. In one case, interaction is considered to be dependent of the node degree, while in the other one, random on-site energies are considered.Comment: 7pages, 7 figure

Constraint on the chemical potentials of hydrogen and proton in recombination

In this paper, we revisit the hydrogen recombination history from a novel perspective: the evolution of chemical potentials. We derive expressions for the chemical potentials, which depend on the thermal bath temperature and the ionization degree of the universe. Our main finding reveals a constraint between the chemical potentials of hydrogen and proton at $z\approx 1200$ when the free electron fraction is $X_e\approx 1/3$. Furthermore, we present important data on the chemical potentials during recombination, highlighting the differences between the predictions of the Peebles' and CosmoRec code solutions. Finally, we discuss a particular case related to the chemical potential of hydrogen.Comment: 5 pages, 3 figure

Optimal estimation of losses at the ultimate quantum limit with non-Gaussian states

We address the estimation of the loss parameter of a bosonic channel probed by arbitrary signals. Unlike the optimal Gaussian probes, which can attain the ultimate bound on precision asymptotically either for very small or very large losses, we prove that Fock states at any fixed photon number saturate the bound unconditionally for any value of the loss. In the relevant regime of low-energy probes, we demonstrate that superpositions of the first low-lying Fock states yield an absolute improvement over any Gaussian probe. Such few-photon states can be recast quite generally as truncations of de-Gaussified photon-subtracted states.Comment: 4 pages, 3 figure

Dimensionality effects in the LDOS of ferromagnetic hosts probed via STM: spin-polarized quantum beats and spin filtering

We theoretically investigate the local density of states (LDOS) probed by a STM tip of ferromagnetic metals hosting a single adatom and a subsurface impurity. We model the system via the two-impurity Anderson Hamiltonian. By using the equation of motion with the relevant Green functions, we derive analytical expressions for the LDOS of two host types: a surface and a quantum wire. The LDOS reveals Friedel-like oscillations and Fano interference as a function of the STM tip position. These oscillations strongly depend on the host dimension. Interestingly, we find that the spin-dependent Fermi wave numbers of the hosts give rise to spin-polarized quantum beats in the LDOS. While the LDOS for the metallic surface shows a damped beating pattern, it exhibits an opposite behavior in the quantum wire. Due to this absence of damping, the wire operates as a spatially resolved spin filter with a high efficiency.Comment: revised tex

Efeito de uma geração adicional de recombinação sobre a resposta à seleção recorrente em milho (Zea mays L.).

O presente trabalho foi conduzido com o objetivo de avaliar se uma geração adicional de recombinação liberaria mais variabilidade genética do que uma única geração, além de verificar se a resposta esperada à seleção após duas gerações de recombinação seria de magnitude tal que compensasse a realização do ciclo adicional

ANALYSIS OF DISPERSION ERRORS IN ACOUSTIC WAVE SIMULATIONS

The governing equations of the acoustic problem are the compressible Euler equations. The discretization of these equations has to ensure that the acoustic waves are transported with non-dispersive and non-dissipative characteristics. In the present study numerical simulations of a standing acoustic wave are performed. Four different space discretization schemes are tested, namely, a second order finite-differences, a fourth order finitedifferences, a fourth order finite-differences compact scheme and a sixth order finite-differences compact scheme. The time integration is done with a fourth order Runge-Kutta scheme. The results obtained are compared with linearized analytical solutions. The influence of the dispersion on the simulation of a standing wave is analyzed. The results confirm that high order accuracy schemes can be more efficient for simulation of acoustic waves, especially the waves with high frequency