Fishing out collective memory of migratory schools

Animals form groups for many reasons but there are costs and benefit associated with group formation. One of the benefits is collective memory. In groups on the move, social interactions play a crucial role in the cohesion and the ability to make consensus decisions. When migrating from spawning to feeding areas fish schools need to retain a collective memory of the destination site over thousand of kilometers and changes in group formation or individual preference can produce sudden changes in migration pathways. We propose a modelling framework, based on stochastic adaptive networks, that can reproduce this collective behaviour. We assume that three factors control group formation and school migration behaviour: the intensity of social interaction, the relative number of informed individuals and the preference that each individual has for the particular migration area. We treat these factors independently and relate the individuals preferences to the experience and memory for certain migration sites. We demonstrate that removal of knowledgable individuals or alteration of individual preference can produce rapid changes in group formation and collective behavior. For example, intensive fishing targeting the migratory species and also their preferred prey can reduce both terms to a point at which migration to the destination sites is suddenly stopped. The conceptual approaches represented by our modelling framework may therefore be able to explain large-scale changes in fish migration and spatial distribution.

Path integration and perturbation theory with complex Euclidean actions

The Euclidean path integral quite often involves an action that is not completely real {it i.e.} a complex action. This occurs when the Minkowski action contains $t$-odd CP-violating terms. Analytic continuation to Euclidean time yields an imaginary term in the Euclidean action. In the presence of imaginary terms in the Euclidean action, the usual method of perturbative quantization can fail. Here the action is expanded about its critical points, the quadratic part serving to define the Gaussian free theory and the higher order terms defining the perturbative interactions. For a complex action, the critical points are generically obtained at complex field configurations. Hence the contour of path integration does not pass through the critical points and the perturbative paradigm cannot be directly implemented. The contour of path integration has to be deformed to pass through the complex critical point using a generalized method of steepest descent, in order to do so. Typically, what is done is that only the real part of the Euclidean action is considered, and its critical points are used to define the perturbation theory. In this article we present a simple 0+1-dimensional example, of $N$ scalar fields interacting with a U(1) gauge field, in the presence of a Chern-Simons term, where alternatively, the path integral can be done exactly, the procedure of deformation of the contour of path integration can be done explicitly and the standard method of only taking into account the real part of the action can be followed. We show explicitly that the standard method does not give a correct perturbative expansion.

Validity of the Adiabatic Approximation

We analyze the validity of the adiabatic approximation, and in particular the reliability of what has been called the standard criterion for validity of this approximation. Recently, this criterion has been found to be insufficient. We will argue that the criterion is sufficient only when it agrees with the intuitive notion of slowness of evolution of the Hamiltonian. However, it can be insufficient in cases where the Hamiltonian varies rapidly but only by a small amount. We also emphasize the distinction between the adiabatic {em theorem} and the adiabatic {em approximation}, two quite different although closely related ideas.