arXiv subjects

Rosemary J. Harris

Publications and source records attributed to Rosemary J. Harris.

25 records · Page 2Linked to original sources

arXiv2015

Random walkers with extreme value memory: modelling the peak-end rule

Motivated by the psychological literature on the "peak-end rule" for remembered experience, we perform an analysis within a random walk framework of a discrete choice model where agents' future choices depend on the peak memory of their past experiences. In particular, we use this approach to investigate whether increased noise/disruption always leads to more switching between decisions. Here extreme value theory illuminates different classes of dynamics indicating that the long-time behaviour is dependent on the scale used for reflection; this could have implications, for example, in questionnaire design.

cond-mat.stat-mech↗

arXiv2015

Dynamics of non-Markovian exclusion processes

Driven diffusive systems are often used as simple discrete models of collective transport phenomena in physics, biology or social sciences. Restricting attention to one-dimensional geometries, the asymmetric simple exclusion process (ASEP) plays a paradigmatic role to describe noise-activated driven motion of entities subject to an excluded volume interaction and many variants have been studied in recent years. While in the standard ASEP the noise is Poissonian and the process is therefore Markovian, in many applications the statistics of the activating noise has non-standard distribution with possible memory effects resulting from internal degrees of freedom or external sources. This leads to temporal correlations and can significantly affect the shape of the current-density relation as has been studied recently for a number of scenarios. In this paper we report a general framework to derive the fundamental diagram of ASEPs driven by non-Poissonian noise by using effectively only two simple quantities, viz., the mean residual lifetime of the jump distribution and a suitably defined temporal correlation length. We corroborate our results by detailed numerical studies for various noise statistics under periodic boundary conditions and discuss how our approach can be applied to more general driven diffusive systems.

cond-mat.stat-mech↗

arXiv2014

Fluctuation relations for anisotropic systems

Currents of particles or energy in driven nonequilibrium steady states are known to satisfy certain symmetries, referred to as fluctuation relations, determining the ratio of the probabilities of positive fluctuations to negative ones. A generalization of these fluctuation relations has been proposed recently for extended nonequilibrium systems of dimension greater than one, assuming, crucially, that they are isotropic [P. I.\ Hurtado, C.\ Pérez-Espigares, J. J.\ del Pozo, and P. L.\ Garrido, Proc.\ Nat.\ Acad.\ Sci.\ (USA) \textbf{108}, 7704 (2011)]. Here we relax this assumption and derive a fluctuation relation for $d$-dimensional systems having anisotropic bulk driving rates. We illustrate this anisotropic fluctuation relation for the particle current fluctuations in the 2-$d$ anisotropic zero-range process, using both exact and fluctuating hydrodynamic approaches.

cond-mat.stat-mech↗

arXiv2012

Current loops and fluctuations in the zero-range process on a diamond lattice

We study the zero-range process on a simple diamond lattice with open boundary conditions and determine the conditions for the existence of loops in the mean current. We also perform a large deviation analysis for fluctuations of partial and total currents and check the validity of the Gallavotti-Cohen fluctuation relation for these quantities. In this context, we show that the fluctuation relation is not satisfied for partial currents between sites even if it is satisfied for the total current flowing between the boundaries. Finally, we extend our methods to study a chain of coupled diamonds and demonstrate co-existence of mean current regimes.

cond-mat.stat-mech↗

arXiv2012

Large deviation approach to nonequilibrium systems

The theory of large deviations has been applied successfully in the last 30 years or so to study the properties of equilibrium systems and to put the foundations of equilibrium statistical mechanics on a clearer and more rigorous footing. A similar approach has been followed more recently for nonequilibrium systems, especially in the context of interacting particle systems. We review here the basis of this approach, emphasizing the similarities and differences that exist between the application of large deviation theory for studying equilibrium systems on the one hand and nonequilibrium systems on the other. Of particular importance are the notions of macroscopic, hydrodynamic, and long-time limits, which are analogues of the equilibrium thermodynamic limit, and the notion of statistical ensembles which can be generalized to nonequilibrium systems. For the purpose of illustrating our discussion, we focus on applications to Markov processes, in particular to simple random walks.

cond-mat.stat-mech↗

arXiv2009

Short-time behaviour of demand and price viewed through an exactly solvable model for heterogeneous interacting market agents

We introduce a stochastic heterogeneous interacting-agent model for the short-time non-equilibrium evolution of excess demand and price in a stylized asset market. We consider a combination of social interaction within peer groups and individually heterogeneous fundamentalist trading decisions which take into account the market price and the perceived fundamental value of the asset. The resulting excess demand is coupled to the market price. Rigorous analysis reveals that this feedback may lead to price oscillations, a single bounce, or monotonic price behaviour. The model is a rare example of an analytically tractable interacting-agent model which allows us to deduce in detail the origin of these different collective patterns. For a natural choice of initial distribution the results are independent of the graph structure that models the peer network of agents whose decisions influence each other.

q-fin.GN↗

arXiv2008

Out-of-equilibrium bosons on a one-dimensional optical random lattice

We study the transport properties of a one-dimensional hard-core boson lattice gas coupled to two particle reservoirs at different chemical potentials generating a current flow through the system. In particular, the influence of random fluctuations of the underlying lattice on the stationary state properties is investigated. We show analytically that the steady-state density presents a linear profile. The local steady-state current obeys the Fourier law $j=-κ(τ)\nabla ρ$ where $τ$ is a typical timescale of the lattice fluctuations and $\nabla ρ$ the density gradient imposed %on the system by the reservoirs.

cond-mat.stat-mech↗