Hierarchical Mean-Field Theories in Quantum Statistical Mechanics

We present a theoretical framework and a calculational scheme to study the coexistence and competition of thermodynamic phases in quantum statistical mechanics. The crux of the method is the realization that the microscopic Hamiltonian, modeling the system, can always be written in a hierarchical operator language that unveils all symmetry generators of the problem and, thus, possible thermodynamic phases. In general one cannot compute the thermodynamic or zero-temperature properties exactly and an approximate scheme named ``hierarchical mean-field approach'' is introduced. This approach treats all possible competing orders on an equal footing. We illustrate the methodology by determining the phase diagram and quantum critical point of a bosonic lattice model which displays coexistence and competition between antiferromagnetism and superfluidity.Comment: 4 pages, 2 psfigures. submitted Phys. Rev.

Wavelets Applied to the Detection of Point Sources of UHECRs

In this work we analyze the effect of smoothing maps containing arrival directions of cosmic rays with a gaussian kernel and kernels of the mexican hat wavelets of orders 1, 2 and 3. The analysis is performed by calculating the amplification of the signal-to-noise ratio for several anisotropy patterns (noise) and different number of events coming from a simulated source (signal) for an ideal detector capable of observing the full sky with equal probability. We extend this analysis for a virtual detector located within the array of detectors of the Pierre Auger Observatory, considering an acceptance law.Comment: 9 pages, 8 figures. Proceedings of the Young Researchers Meeting, 2010. Available in: http://www.ifi.unicamp.br/physicae/ojs-2.1.1/index.php/physicae/article/view/191; Physicae, Proceedings of the Young Researchers Meeting, Vol 1, 201

Statistical Signs of Social Influence on Suicides

Certain currents in sociology consider society as being composed of autonomous individuals with independent psychologies. Others, however, deem our actions as strongly influenced by the accepted standards of social behavior. The later view was central to the positivist conception of society when in 1887 \'Emile Durkheim published his monograph Suicide (Durkheim, 1897). By treating the suicide as a social fact, Durkheim envisaged that suicide rates should be determined by the connections (or the lack of them) between people and society. Under the same framework, Durkheim considered that crime is bound up with the fundamental conditions of all social life and serves a social function. In this sense, and regardless of its extremely deviant nature, crime events are somehow capable to release certain social tensions and so have a purging effect in society. The social effect on the occurrence of homicides has been previously substantiated (Bettencourt et al., 2007; Alves et al., 2013), and confirmed here, in terms of a superlinear scaling relation: by doubling the population of a Brazilian city results in an average increment of 135 % in the number of homicides, rather than the expected isometric increase of 100 %, as found, for example, for the mortality due to car crashes. Here we present statistical signs of the social influence on the suicide occurrence in cities. Differently from homicides (superlinear) and fatal events in car crashes (isometric), we find sublinear scaling behavior between the number of suicides and city population, with allometric power-law exponents, $\beta = 0.836 \pm 0.009$ and $0.870 \pm 0.002$, for all cities in Brazil and US, respectively. The fact that the frequency of suicides is disproportionately small for larger cities reveals a surprisingly beneficial aspect of living and interacting in larger and more complex social networks.Comment: 7 pages, 4 figure