Sandra Denise Prado

Semiclassical structure of chaotic resonance eigenfunctions

We study the resonance (or Gamow) eigenstates of open chaotic systems in the semiclassical limit, distinguishing between left and right eigenstates of the nonunitary quantum propagator and also between short-lived and long-lived states. The long-lived left (right) eigenstates are shown to concentrate as variant Plancks over 2pi-->0 on the forward (backward) trapped set of the classical dynamics. The limit of a sequence of eigenstates [psi(variant Plancks over)] 2pi-->0 is found to exhibit a remarkably rich structure in phase space that depends on the corresponding limiting decay rate. These results are illustrated for the open bakers map, for which the probability density in position space is observed to have self-similarity properties.

Orbit bifurcations and the scarring of wave functions

We extend the semiclassical theory of scarring of quantum eigenfunctions ψn(q) by classical periodic orbits to include situations where these orbits undergo generic bifurcations. It is shown that |ψn(q)|2, averaged locally with respect to position q and the energy spectrum {En}, has structure around bifurcating periodic orbits with an amplitude and length-scale whose ℏ dependence is determined by the bifurcation in question. Specifically, the amplitude scales as ℏα and the length-scale as ℏω, and values of the scar exponents, α and ω, are computed for a variety of generic bifurcations. In each case, the scars are semiclassically wider than those associated with isolated and unstable periodic orbits; moreover, their amplitude is at least as large, and in most cases larger. In this sense, bifurcations may be said to give rise to superscars. The competition between the contributions from different bifurcations to determine the moments of the averaged eigenfunction amplitude is analysed. We argue that there is a resulting universal ℏ scaling in the semiclassical asymptotics of these moments for irregular states in systems with mixed phase-space dynamics. Finally, a number of these predictions are illustrated by numerical computations for a family of perturbed cat maps.

Universal quantum signature of mixed dynamics in antidot lattices

We investigate phase coherent ballistic transport through antidot lattices in the generic case where the classical phase space has both regular and chaotic components. It is shown that the conductivity fluctuations have a non-Gaussian distribution, and that their moments have a power-law dependence on a semiclassical parameter, with fractional exponents. These exponents are obtained from bifurcating periodic orbits in the semiclassical approximation. They are universal in situations where sufficiently long orbits contribute.

Interpretações da mecânica quântica em um interferômetro virtual de Mach-Zehnder

The problem of quantum interference phenomena is analyzed on the Mach-Zehnder Interferometer - an experimental setup similar to double slits device, but much simpler - under the light of the main schools of interpretations of Quantum Mechanics. Although this is a work very based on Pessoa Jr [1]-[3], special emphasis is given to Many Worlds Interpretation due to its recent growing of interests within scientific community as much as within general public. The Many-Worlds Interpretation is an approach to Quantum Mechanics according to which, in addition to the world we are aware of directly, there are many other similar worlds that exist in parallel at the same space and time. The existence of the other worlds makes it possible to remove randomness and action at a distance from quantum theory. A basic introduction of an interpretation like Many Worlds that have been extensively present in the media is an important contribution to the initial and continued education for Physics Teachers, mainly when a more conceptual approach to the subject is aimed.

Light with Tunable Non-Markovian Phase Imprint

We introduce a simple and flexible method to generate spatially non-Markovian light with tunable coherence properties in one and two dimensions. The unusual behavior of this light is demonstrated experimentally by probing the far field and by recording its diffraction pattern after a double slit: In both cases we observe, instead of a central intensity maximum, a line- or cross-shaped dark region, whose width and profile depend on the non-Markovian coherence properties. Because these properties can be controlled and easily reproduced in experiment, the presented approach lends itself to serving as a test bed to study and gain a deeper understanding of non-Markovian processes.

TEMPORAL NETWORK ANALYSIS OF LITERARY TEXTS

We study temporal networks of characters in literature focussing on Alice’s Adventures in Wonderland (1865) by Lewis Carroll and the anonymous La Chanson de Roland (around 1100). The former, one of the most influential pieces of nonsense literature ever written, describes the adventures of Alice in a fantasy world with logic plays interspersed along the narrative. The latter, a song of heroic deeds, depicts the Battle of Roncevaux in 778 A.D. during Charlemagne’s campaign on the Iberian Peninsula. We apply methods recently developed by Taylor et al. [Taylor, D., Myers, S. A., Clauset, A., Porter, M. A. and Mucha, P. J., Eigenvector-based centrality measures for temporal networks, CoRR (2015).] to find time-averaged eigenvector centralities, Freeman indices and vitalities of characters. We show that temporal networks are more appropriate than static ones for studying stories, as they capture features that the time-independent approaches fail to yield.

A simple non-Markovian computational model of the statistics of soccer leagues: Emergence and scaling effects

Abstract We propose a novel probabilistic model that outputs the final standings of a soccer league, based on a simple dynamics that mimics a soccer tournament. In our model, a team is created with a defined potential (ability) which is updated during the tournament according to the results of previous games. The updated potential modifies a team future winning/losing probabilities. We show that this evolutionary game is able to reproduce the statistical properties of final standings of actual editions of the Brazilian tournament (Brasileirao) if the starting potential is the same for all teams. Other leagues such as the Italian (Calcio) and the Spanish (La Liga) tournaments have notoriously non-Gaussian traces and cannot be straightforwardly reproduced by this evolutionary non-Markovian model with simple initial conditions. However, we show that by setting the initial abilities based on data from previous tournaments, our model is able to capture the stylized statistical features of double round robin system (DRRS) tournaments in general. A complete understanding of these phenomena deserves much more attention, but we suggest a simple explanation based on data collected in Brazil: here several teams have been crowned champion in previous editions corroborating that the champion typically emerges from random fluctuations that partly preserve the Gaussian traces during the tournament. On the other hand, in the Italian and Spanish cases, only a few teams in recent history have won their league tournaments. These leagues are based on more robust and hierarchical structures established even before the beginning of the tournament. For the sake of completeness, we also elaborate a totally Gaussian model (which equalizes the winning, drawing, and losing probabilities) and we show that the scores of the Brazilian tournament “Brasileirao” cannot be reproduced. This shows that the evolutionary aspects are not superfluous and play an important role which must be considered in other alternative models. Finally, we analyze the distortions of our model in situations where a large number of teams is considered, showing the existence of a transition from a single to a double peaked histogram of the final classification scores. An interesting scaling is presented for different sized tournaments.

O tratamento clássico do interferômetro de Mach-Zehnder: uma releitura mais moderna do experimento da fenda dupla na introdução da física quântica

In this paper, the optical Mach-Zehnder Interferometer (MZI) in classical regime is fully analysed. One of our main goals is to supply the basis for future transpositions to the quantum regime. The MZI is a device totally analogous to the double-slit experiment [1] but a more modern version in technological terms. It has been used extensively in papers related to quantum computation and quantum cryptography [2]. Those are fields grounded on quantum superposition and quantum interference phenomena. It has also appeared in papers related to the teaching of introductory quantum physics where the conceptual problem of which path a given photon goes through arises more naturally [3-10]. The analytical results shown here were used in the production of an educational software to simulate the classical and quantum interference phenomena. The software has been widely used in introductory quantum physics courses in IF-UFRGS.

Orbit bifurcations and wavefunction autocorrelations

It was recently shown (Keating J P and Prado S D 2001 Proc. R. Soc. A 457 1855–72) that, in the semiclassical limit, the scarring of quantum eigenfunctions by classical periodic orbits in chaotic systems may be dramatically enhanced when the orbits in question undergo bifurcation. Specifically, a bifurcating orbit gives rise to a scar with an amplitude that scales as α and a width that scales as ω, where α and ω are bifurcation-dependent scar exponents whose values are typically smaller than those (α = ω = ½) associated with isolated and unstable periodic orbits. We here analyse the influence of bifurcations on the autocorrelation function of quantum eigenstates, averaged with respect to energy. It is shown that the length-scale of the correlations around a bifurcating orbit scales semiclassically as 1−α, where α is the corresponding scar amplitude exponent. This imprint of bifurcations on quantum autocorrelations is illustrated by numerical computations for a family of perturbed cat maps.

Periodic orbit bifurcations and scattering time delay fluctuations

We study fluctuations of the Wigner time delay for open (scattering) systems which exhibit mixed dynamics in the classical limit. It is shown that in the semiclassical limit the time delay fluctuations have a distribution that differs markedly from those which describe fully chaotic (or strongly disordered) systems: their moments have a power law dependence on a semiclassical parameter, with exponents that are rational fractions. These exponents are obtained from bifurcating periodic orbits trapped in the system. They are universal in situations where sufficiently long orbits contribute. We illustrate the influence of bifurcations on the time delay numerically using an open quantum map.