arXiv subjects

Marcus A. M. de Aguiar

Publications and source records attributed to Marcus A. M. de Aguiar.

71 records · Page 4Linked to original sources

arXiv2015

Semiclassical Propagator in the Generalized Coherent-State Representation

A detailed derivation of the semiclassical propagator in the generalized coherent-state representation is performed by applying the saddle-point method to a path integral over the classical phase space. With the purpose of providing greater accessibility and applicability to the developed formalism, a brief review of the generalized concept of coherent states is presented, in which three examples of coherent-state sets are examined, namely, the canonical, spin, and SU(n) bosonic coherent states.

quant-ph↗

arXiv2015

Topological structures in the Husimi flow

We study the topological properties of the quantum phase space current in the Husimi representation, focusing on the dynamical differences, induced by these properties, between the quantum and the classical flows. We show that the zeros of the Husimi function are stagnation points of the current and have a nonzero topological charge. Due to overall charge conservation, new stagnation points with opposite charge appear in pairs in the Husimi current and they have important roles in dynamical processes. As an example we show the topological effect of the zeros in the transmission rate of particle through a potential barrier.

quant-ph↗

arXiv2014

The $500.00 AAPL close: Manipulation or hedging? A quantitative analysis

Why do a market's prices move up or down? Claims about causes are made without actual information, and accepted or dismissed based upon poor or non-existent evidence. Here we investigate the price movements that ended with Apple stock closing at \$500.00 on January 18, 2013. There is a ready explanation for this price movement: market manipulation by those who sold stock options, who stood to directly benefit from this closing price. Indeed, one web commentator predicted this otherwise unlikely event publicly. This explanation was subsequently dismissed by press articles that claim that stock prices end near such round numbers based upon legitimate hedging activity. But how can we know? We show that the accepted model that points to hedging as the driving cause of prices is not quantitatively consistent with the price movement on that day. The price moved upward too quickly over a period in which the hedgers' position would require selling rather than buying. Under these conditions hedgers would have driven the price away from the strike price rather than toward it. We also show that a long published theory of the role of hedging is incomplete mathematically, and that the correct theory results in much weaker price movements. This evidence substantially weakens the case of those who claim hedging as cause of anomalous market price movements. The explanation that market manipulation is responsible for the final close cannot be dismissed based upon unsubstantiated, even invalid, hedging claims. Such proffered explanations shield potential illegal activity from further inquiry even though the claims behind those explanations have not been demonstrated.

q-fin.GN↗

arXiv2013

Evolutionary consequences of assortativeness in haploid genotypes

We study the evolution of allele frequencies in a large population where random mating is violated in a particular way that is related to recent works on speciation. Specifically, we consider non-random encounters in haploid organisms described by biallelic genes at two loci and assume that individuals whose alleles differ at both loci are incompatible. We show that evolution under these conditions leads to the disappearance of one of the alleles and substantially reduces the diversity of the population. The allele that disappears, and the other allele frequencies at equilibrium, depend only on their initial values, and so does the time to equilibration. However, certain combinations of allele frequencies remain constant during the process, revealing the emergence of strong correlation between the two loci promoted by the epistatic mechanism of incompatibility. We determine the geometrical structure of the haplotype frequency space and solve the dynamical equations, obtaining a simple rule to determine equilibrium solution from the initial conditions. We show that our results are equivalent to selection against double heterozigotes for a population of diploid individuals and discuss the relevance of our findings to speciation.

q-bio.PE↗

arXiv2012

Robustness Against Extinction by Stochastic Sex Determination in Small Populations

Sexually reproducing populations with small number of individuals may go extinct by stochastic fluctuations in sex determination, causing all their members to become male or female in a generation. In this work we calculate the time to extinction of isolated populations with fixed number $N$ of individuals that are updated according to the Moran birth and death process. At each time step, one individual is randomly selected and replaced by its offspring resulting from mating with another individual of opposite sex; the offspring can be male or female with equal probability. A set of $N$ time steps is called a generation, the average time it takes for the entire population to be replaced. The number k of females fluctuates in time, similarly to a random walk, and extinction, which is the only asymptotic possibility, occurs when k=0 or k=N. We show that it takes only one generation for an arbitrary initial distribution of males and females to approach the binomial distribution. This distribution, however, is unstable and the population eventually goes extinct in 2^N/N generations. We also discuss the robustness of these results against bias in the determination of the sex of the offspring, a characteristic promoted by infection by the bacteria Wolbachia in some arthropod species or by temperature in reptiles.

q-bio.PE↗

arXiv2011

The role of sex separation in neutral speciation

Neutral speciation mechanisms based on isolation by distance and sexual selection, termed topopatric, have recently been shown to describe the observed patterns of abundance distributions and species-area relationships. Previous works have considered this type of process only in the context of hermaphrodic populations. In this work we extend a hermaphroditic model of topopatric speciation to populations where individuals are explicitly separated into males and females. We show that for a particular carrying capacity speciation occurs under similar conditions, but the number of species generated decreases as compared to the hermaphroditic case. Evolution results in fewer species having more abundant populations.

q-bio.PE↗

arXiv2011

The Moran model as a dynamical process on networks and its implications for neutral speciation

In genetics the Moran model describes the neutral evolution of a bi-allelic gene in a population of haploid individuals subjected to mutations. We show in this paper that this model can be mapped into an influence dynamical process on networks subjected to external influences. The panmictic case considered by Moran corresponds to fully connected networks and can be completely solved in terms of hypergeometric functions. Other types of networks correspond to structured populations, for which approximate solutions are also available. This new approach to the classic Moran model leads to a relation between regular networks based on spatial grids and the mechanism of isolation by distance. We discuss the consequences of this connection for topopatric speciation and the theory of neutral speciation and biodiversity. We show that the effect of mutations in structured populations, where individuals can mate only with neighbors, is greatly enhanced with respect to the panmictic case. If mating is further constrained by genetic proximity between individuals, a balance of opposing tendencies take place: increasing diversity promoted by enhanced effective mutations versus decreasing diversity promoted by similarity between mates. Stabilization occurs with speciation via pattern formation. We derive an explicit relation involving the parameters characterizing the population that indicates when speciation is possible.

q-bio.PE↗

arXiv2011

Initial value representation for the SU(n) semiclassical propagator

The semiclassical propagator in the representation of SU(n) coherent states is characterized by isolated classical trajectories subjected to boundary conditions in a doubled phase space. In this paper we recast this expression in terms of an integral over a set of initial-valued trajectories. These trajectories are monitored by a filter that collects only the appropriate contributions to the semiclassical approximation. This framework is suitable for the study of bosonic dynamics in n modes with fixed total number of particles. We exemplify the method for a Bose-Einstein condensate trapped in a triple-well potential, providing a detailed discussion on the accuracy and efficiency of the procedure.

quant-ph↗

arXiv2011

Semiclassical propagator for SU(n) coherent states

We present a detailed derivation of the semiclassical propagator in the SU(n) coherent state representation. In order to provide support for immediate physical applications, we restrict this work to the fully symmetric irreducible representations, which are suitable for the treatment of bosonic dynamics in n modes, considering systems with conservation of total particle number. The derivation described here can be easily extended to other classes of coherent states, thus representing an alternative approach to previously published methods.

math-ph↗

arXiv2011

Energy Dissipation Via Coupling With a Finite Chaotic Environment

We study the flow of energy between a harmonic oscillator (HO) and an external environment consisting of N two-degrees of freedom non-linear oscillators, ranging from integrable to chaotic according to a control parameter. The coupling between the HO and the environment is bilinear in the coordinates and scales with system size with the inverse square root of N. We study the conditions for energy dissipation and thermalization as a function of N and of the dynamical regime of the non-linear oscillators. The study is classical and based on single realization of the dynamics, as opposed to ensemble averages over many realizations. We find that dissipation occurs in the chaotic regime for a fairly small N, leading to the thermalization of the HO and environment a Boltzmann distribution of energies for a well defined temperature. We develop a simple analytical treatment, based on the linear response theory, that justifies the coupling scaling and reproduces the numerical simulations when the environment is in the chaotic regime.

physics.class-ph↗

arXiv2011

Predicting economic market crises using measures of collective panic

Predicting panic is of critical importance in many areas of human and animal behavior, notably in the context of economics. The recent financial crisis is a case in point. Panic may be due to a specific external threat, or self-generated nervousness. Here we show that the recent economic crisis and earlier large single-day panics were preceded by extended periods of high levels of market mimicry --- direct evidence of uncertainty and nervousness, and of the comparatively weak influence of external news. High levels of mimicry can be a quite general indicator of the potential for self-organized crises.

q-fin.ST↗

arXiv2009

An Initial Value Representation with Complex Trajectories

We present an Initial Value Representation for the semiclassical coherent state propagator based on complex trajectories. We map the complex phase space into a real phase space with twice as many dimensions and use a simple procedure to automatically eliminate non-contributing trajectories. The resulting semiclassical formulas do not show divergences due to caustics and provide accurate results.

quant-ph↗

arXiv2007

Dynamical Response of Networks under External Perturbations: Exact Results

We introduce and solve a general model of dynamic response under external perturbations. This model captures a wide range of systems out of equilibrium including Ising models of physical systems, social opinions, and population genetics. The distribution of states under perturbation and relaxation process reflects two regimes -- one driven by the external perturbation, and one driven by internal ordering. These regimes parallel the disordered and ordered regimes of equilibrium physical systems driven by thermal perturbations but here are shown to be relevant for non-thermal and non-equilibrium external influences on complex biological and social systems. We extend our results to a wide range of network topologies by introducing an effective strength of external perturbation by analytic mean-field approximation. Simulations show this generalization is remarkably accurate for many topologies of current interest in describing real systems.

nlin.SI↗

arXiv2004

Semiclassical Husimi functions for spin systems

We derive a semiclassical approximation to the Husimi functions of stationary states of spin systems. We rederive the Bohr-Sommerfeld quantization for spin by locating the poles of the corresponding local Green function. The residues correspond to the Husimi functions, which are seen to agree very well with exact calculations.

quant-ph↗

arXiv2004

Resonant helical deformations in nonhomogeneous Kirchhoff filaments

We study the three-dimensional static configurations of nonhomogeneous Kirchhoff filaments with periodically varying Young's modulus. This type of variation may occur in long tandemly repeated sequences of DNA. We analyse the effects of the Young's modulus frequence and amplitude of oscillation in the stroboscopic maps, and in the regular (non chaotic) spatial configurations of the filaments. Our analysis shows that the tridimensional conformations of long filaments may depend critically on the Young's modulus frequence in case of resonance with other natural frequencies of the filament. As expected, far from resonance the shape of the solutions remain very close to that of the homogeneous case. In the case of biomolecules, it is well known that various other elements, besides sequence-dependent effects, combine to determine their conformation, like self-contact, salt concentration, thermal fluctuations, anisotropy and interaction with proteins. Our results show that sequence-dependent effects alone may have a significant influence on the shape of these molecules, including DNA. This could, therefore, be a possible mechanical function of the ``junk'' sequences.

physics.bio-ph↗

arXiv2002

Solving the boundary value problem for finite Kirchhoff rods

The Kirchhoff model describes the statics and dynamics of thin rods within the approximations of the linear elasticity theory. In this paper we develop a method, based on a shooting technique, to find equilibrium configurations of finite rods subjected to boundary conditions and given load parameters. The method consists in making a series of small changes on a {\it trial} solution satisfying the Kirchhoff equations but not necessarily the boundary conditions. By linearizing the differential equations around the trial solution we are able to push its end point to the desired position, step by step. The method is also useful to obtain configurations of rods with fixed end points but different mechanical parameters, such as tension, components of the moment or inhomogeneities.

physics.bio-ph↗

arXiv2000

Scars of the Wigner function

We propose a picture of Wigner function scars as a sequence of concentric rings along a two-dimensional surface inside a periodic orbit. This is verified for a two-dimensional plane that contains a classical orbit of a Hamiltonian system with two degrees of freedom. The orbit is hyperbolic and the classical Hamiltonian is ``softly chaotic'' at the energies considered. The stationary wave functions are the familiar mixture of scarred and random waves, but the spectral average of the Wigner functions in part of the plane is nearly that of a harmonic oscillator and individual states are also remarkably regular. These results are interpreted in terms of the semiclassical picture of chords and centres, which leads to a qualitative explanation of the interference effects that are manifest in the other region of the plane. The qualitative picture is robust with respect to a canonical transformation that bends the orbit plane.

nlin.CD↗