Detection of coherent light in an incoherent background

The change in position of the self-coherence function minimum is used to detect the presence of a coherent source, rather than the change in strength of the self-coherence function at the reference path difference. The system uses both optical and digital signal processing with MATLAB algorithm. An experimental system was built in the visible band, employing a Michelson interferometer, an interference filter centered in the red, and a silicon photodetector. The results were averaged over up to 50 scans, depending on the relative visibility of the white light and laser fringes, to reduce the scan to scan variability. Amplifier gain was introduced to reduce quantization noise

Topological Approach to Microcanonical Thermodynamics and Phase Transition of Interacting Classical Spins

We propose a topological approach suitable to establish a connection between thermodynamics and topology in the microcanonical ensemble. Indeed, we report on results that point to the possibility of describing {\it interacting classical spin systems} in the thermodynamic limit, including the occurrence of a phase transition, using topology arguments only. Our approach relies on Morse theory, through the determination of the critical points of the potential energy, which is the proper Morse function. Our main finding is to show that, in the context of the studied classical models, the Euler characteristic $\chi(E)$ embeds the necessary features for a correct description of several magnetic thermodynamic quantities of the systems, such as the magnetization, correlation function, susceptibility, and critical temperature. Despite the classical nature of the studied models, such quantities are those that do not violate the laws of thermodynamics [with the proviso that Van der Waals loop states are mean field (MF) artifacts]. We also discuss the subtle connection between our approach using the Euler entropy, defined by the logarithm of the modulus of $\chi(E)$ per site, and that using the {\it Boltzmann} microcanonical entropy. Moreover, the results suggest that the loss of regularity in the Morse function is associated with the occurrence of unstable and metastable thermodynamic solutions in the MF case. The reliability of our approach is tested in two exactly soluble systems: the infinite-range and the short-range $XY$ models in the presence of a magnetic field. In particular, we confirm that the topological hypothesis holds for both the infinite-range ($T_c \neq 0$) and the short-range ($T_c = 0$) $XY$ models. Further studies are very desirable in order to clarify the extension of the validity of our proposal

Dirac's hole theory versus quantum field theory

Dirac's hole theory and quantum field theory are usually considered equivalent to each other. For models of a certain type, however, the equivalence may not hold as we discuss in this Letter. This problem is closely related to the validity of the Pauli principle in intermediate states of perturbation theory.Comment: No figure

Doped AB_2 Hubbard Chain: Spiral, Nagaoka and RVB States, Phase Separation and Luttinger Liquid Behavior

We present an extensive numerical study of the Hubbard model on the doped AB$_2$ chain, both in the weak coupling and the infinite-U limit. Due to the special unit cell topology, this system displays a rich variety of phases as function of hole doping ($\delta$) away from half-filling. Near half-filling, spiral states develop in the weak coupling regime, while Nagaoka itinerant ferromagnetism is observed in the infinite-U limit. For higher doping the system phase-separates before reaching a Mott insulating phase of short-range RVB states at $\delta=1/3$. Moreover, for $\delta>1/3$ we observe a crossover, which anticipates the Luttinger liquid behavior for $\delta > 2/3$.Comment: 11 pages, 13 figure

Magnetism and Electronic Correlations in Quasi-One-Dimensional Compounds

In this contribution on the celebration of the 80th birthday anniversary of Prof. Ricardo Ferreira, we present a brief survey on the magnetism of quasi-one-dimensional compounds. This has been a research area of intense activity particularly since the first experimental announcements of magnetism in organic and organometallic polymers in the mid 80s. We review experimental and theoretical achievements on the field, featuring chain systems of correlated electrons in a special AB2 unit cell structure present in inorganic and organic compounds