A Photoreceptor Model that Replicates Human Light Adaptation Characteristics

Whitehall (593-24); Office of Naval Research (N00014-95-1-0409); Universidad Nacional Autonoma de Mexico (Graduate Fellowship

Heat Transport in Quantum Spin Chains: Stochastic Baths vs Quantum Trajectories

We discuss the problem of heat conduction in quantum spin chain models. To investigate this problem it is necessary to consider the finite open system connected to heat baths. We describe two different procedures to couple the system with the reservoirs: a model of stochastic heat baths and the quantum trajectories solution of the quantum master equation. The stochastic heat bath procedure operates on the pure wave function of the isolated system, so that it is locally and periodically collapsed to a quantum state consistent with a boundary nonequilibrium state. In contrast, the quantum trajectories procedure evaluates ensemble averages in terms of the reduced density matrix operator of the system. We apply these procedures to different models of quantum spin chains and numerically show their applicability to study the heat flow.Comment: 13 pages, 5 figures, submitted to European Physics Journal Special Topic

Wages and Industrial Clusters in Rio Grande Do Sul (Brazil)

The paper estimates the effects of agglomeration economies on wages of industrial workers in the state of Rio Grande do Sul, Brazil. The techniques of Exploratory Analysis of Spatial Data are used to locate the clusters of the states’ industry in 2000. Then, this information was combined to census microdata in order to run wage regressions inspired by the empirical tests of New Economic Geography models (HANSON, 1998, specially). The results were statistically and economically significant: even when controlled by demographic variables, the individual wages of industrial workers were higher on the cities with larger population, more urbanized, higher market potential and closer to the economic centre of the Rio Grande do Sul. These findings indicate how intense the economic forces that shape the spatial structure of the state are, and suggest changes in current regional policies.

Magnetically Induced Thermal Rectification

We consider far from equilibrium heat transport in chaotic billiard chains with non-interacting charged particles in the presence of non-uniform transverse magnetic field. If half of the chain is placed in a strong magnetic field, or if the strength of the magnetic field has a large gradient along the chain, heat current is shown to be asymmetric with respect to exchange of the temperatures of the heat baths. Thermal rectification factor can be arbitrarily large for sufficiently small temperature of one of the baths.Comment: 4 pages, 5 figure

Transport properties of a modified Lorentz gas

We present a detailed study of the first simple mechanical system that shows fully realistic transport behavior while still being exactly solvable at the level of equilibrium statistical mechanics. The system under consideration is a Lorentz gas with fixed freely-rotating circular scatterers interacting with point particles via perfectly rough collisions. Upon imposing a temperature and/or a chemical potential gradient, a stationary state is attained for which local thermal equilibrium holds for low values of the imposed gradients. Transport in this system is normal, in the sense that the transport coefficients which characterize the flow of heat and matter are finite in the thermodynamic limit. Moreover, the two flows are non-trivially coupled, satisfying Onsager's reciprocity relations to within numerical accuracy as well as the Green-Kubo relations . We further show numerically that an applied electric field causes the same currents as the corresponding chemical potential gradient in first order of the applied field. Puzzling discrepancies in higher order effects (Joule heating) are also observed. Finally, the role of entropy production in this purely Hamiltonian system is shortly discussed.Comment: 16 pages, 16 figures, submitted to J. Stat. Phy

First passages for a search by a swarm of independent random searchers

In this paper we study some aspects of search for an immobile target by a swarm of N non-communicating, randomly moving searchers (numbered by the index k, k = 1, 2,..., N), which all start their random motion simultaneously at the same point in space. For each realization of the search process, we record the unordered set of time moments \{\tau_k\}, where \tau_k is the time of the first passage of the k-th searcher to the location of the target. Clearly, \tau_k's are independent, identically distributed random variables with the same distribution function \Psi(\tau). We evaluate then the distribution P(\omega) of the random variable \omega \sim \tau_1/bar{\tau}, where bar{\tau} = N^{-1} \sum_{k=1}^N \tau_k is the ensemble-averaged realization-dependent first passage time. We show that P(\omega) exhibits quite a non-trivial and sometimes a counterintuitive behaviour. We demonstrate that in some well-studied cases e.g., Brownian motion in finite d-dimensional domains) the \textit{mean} first passage time is not a robust measure of the search efficiency, despite the fact that \Psi(\tau) has moments of arbitrary order. This implies, in particular, that even in this simplest case (not saying about complex systems and/or anomalous diffusion) first passage data extracted from a single particle tracking should be regarded with an appropriate caution because of the significant sample-to-sample fluctuations.Comment: 35 pages, 18 figures, to appear in JSTA

Negative response to an excessive bias by a mixed population of voters

We study an outcome of a vote in a population of voters exposed to an externally applied bias in favour of one of two potential candidates. The population consists of ordinary individuals, that are in majority and tend to align their opinion with the external bias, and some number of contrarians --- individuals who are always hostile to the bias but are not in a conflict with ordinary voters. The voters interact among themselves, all with all, trying to find an opinion reached by the community as a whole. We demonstrate that for a sufficiently weak external bias, the opinion of ordinary individuals is always decisive and the outcome of the vote is in favour of the preferential candidate. On the contrary, for an excessively strong bias, the contrarians dominate in the population's opinion, producing overall a negative response to the imposed bias. We also show that for sufficiently strong interactions within the community, either of two subgroups can abruptly change an opinion of the other group.Comment: 11 pages, 6 figure