Grupo de Análisis Matemático Aplicado (GAMA)
http://hdl.handle.net/10016/5857
2016-06-29T14:33:28ZSimple proof of Page’s conjecture on the average entropy of a subsystem
http://hdl.handle.net/10016/6583
Simple proof of Page’s conjecture on the average entropy of a subsystem
Sánchez-Ruiz, Jorge
It is shown that Page’s formula for the average entropy S(m,n) of a subsystem of dimension m ≤ n of a quantum system of Hilbert space dimension mn in a pure state [Phys. Rev. Lett. 71, 1291 (1993)] can be written in terms of the one-point correlation function of a Laguerre ensemble of random matrices. This leads to a proof of Page’s conjecture, Sm,n = tsum(k=n+1)mn1/k-m-1/2n, which is simpler than that given by Foong and Kanno [Phys. Rev. Lett. 72, 1148 (1994)].
1995-11-01T00:00:00ZLearning dynamics explains human behavior in Prisoner's Dilemma on networks
http://hdl.handle.net/10016/21441
Learning dynamics explains human behavior in Prisoner's Dilemma on networks
Cimini, Giulio; Sánchez, Angel
Cooperative behavior lies at the very basis of human societies, yet its evolutionary origin remains a key unsolved puzzle. Whereas reciprocity or conditional cooperation is one of the most prominent mechanisms proposed to explain the emergence of cooperation in social dilemmas, recent experimental findings on networked Prisoner's Dilemma games suggest that conditional cooperation also depends on the previous action of the player—namely on the 'mood' in which the player currently is. Roughly, a majority of people behave as conditional cooperators if they cooperated in the past, while they ignore the context and free-ride with high probability if they did not. However, the ultimate origin of this behavior represents a conundrum itself. Here we aim specifically at providing an evolutionary explanation of moody conditional cooperation. To this end, we perform an extensive analysis of different evolutionary dynamics for players' behavioral traits—ranging from standard processes used in game theory based on payoff comparison to others that include non-economic or social factors. Our results show that only a dynamic built upon reinforcement learning is able to give rise to evolutionarily stable moody conditional cooperation, and at the end to reproduce the human behaviors observed in the experiments.
The proceeding at: DPG-Frühjahrstagung (SOE: Fachverband Physik sozio-ökonomischer Systeme) = DPG Spring Meeting (Physics of Socio-Economic Systems), took place 2014 31- March, 04-April, in Dresden (Germany).
2014-03-31T00:00:00ZAsymptotic formula for the quantum entropy of position in energy eigenstates
http://hdl.handle.net/10016/6590
Asymptotic formula for the quantum entropy of position in energy eigenstates
Sánchez-Ruiz, Jorge
The asymptotic formula $S_Q\sim S_C -1 + \ln 2$ is obtained for the information entropy in position space S$_Q$ of one-dimensional quantum systems in energy eigenstates, where $S_C$ is the position entropy corresponding to a microcanonical ensemble of analogous classical systems having the same energy. This result is analytically and numerically verified for several simple systems.
1997-02-10T00:00:00ZDemixing behavior in two-dimensional mixtures of anisotropic hard bodies
http://hdl.handle.net/10016/7012
Demixing behavior in two-dimensional mixtures of anisotropic hard bodies
Martínez-Ratón, Yuri; Velasco, Enrique; Mederos, Luis
Scaled particle theory for a binary mixture of hard discorectangles and for a binary mixture of hard rectangles is used to predict possible liquid-crystal demixing scenarios in two dimensions. Through a bifurcation analysis from the isotropic phase, it is shown that isotropic-nematic demixing is possible in two-dimensional liquid-crystal mixtures composed of hard convex bodies. This bifurcation analysis is tested against exact calculations of the phase diagrams in the framework of the restricted-orientation two-dimensional model (Zwanzig model). Phase diagrams of a binary mixture of hard discorectangles are calculated through the parametrization of the orientational distribution functions. The results show not only isotropic-nematic, but also nematic-nematic demixing ending in a critical point, as well as an isotropic-nematic-nematic triple point for a mixture of hard disks and hard discorectangles.
11 pages, 9 figures.-- PACS nrs.: 64.70.Md, 64.75.+g, 61.20.Gy.-- ArXiv pre-print available at: http://arxiv.org/abs/cond-mat/0509213
2005-09-01T00:00:00Z