Correlations for the Dyson Brownian motion model with Poisson initial conditions

The circular Dyson Brownian motion model refers to the stochastic dynamics of the log-gas on a circle. It also specifies the eigenvalues of certain parameter-dependent ensembles of unitary random matrices. This model is considered with the initial condition that the particles are non-interacting (Poisson statistics). Jack polynomial theory is used to derive a simple exact expression for the density-density correlation with the position of one particle specified in the initial state, and the position of one particle specified at time $\tau$, valid for all $\beta > 0$. The same correlation with two particles specified in the initial state is also derived exactly, and some special cases of the theoretical correlations are illustrated by comparison with the empirical correlations calculated from the eigenvalues of certain parameter-dependent Gaussian random matrices. Application to fluctuation formulas for time displaced linear statistics in made.Comment: 17 pgs., 2 postscript fig

Beginner Modeling Exercises

The goal of this paper written as part of the MIT Systems Dynamics in Education Project is to teach the reader how to distinguish between stocks and flows. A stock is an accumulation that is changed over time by inflows and outflows. The reader will gain intuition about stocks and flow through and extensive list of different examples and will practice modeling simple systems with constant flows. STELLA modeling examples include, but are not restricted to, skunks populations, landfills, a bank account and nuclear weapons. Educational levels: High school, Middle school, Undergraduate lower division, Undergraduate upper division

Exact calculation of the ground state single-particle Green's function for the 1/r21/r^2 quantum many body system at integer coupling

The ground state single particle Green's function describing hole propagation is calculated exactly for the $1/r^2$ quantum many body system at integer coupling. The result is in agreement with a recent conjecture of Haldane.Comment: Late