Stochastic phenomena, the dynamical effects of thermal and molecular fluctuations, are of continuing interest in physics and biology. Our approach involves theory, numerical simulations and contact with experiments. In one part of the research, quantum mechanical consequences of chaotic dynamics in classical systems will be studied. Classical measures of fluctuation amplification by chaos, such as Lyapunov exponents, can be related to the growth rate of quantum variances in systems that can be described both classically and quantally. This connection will be explored in the context of magneto-optically trapped cesium atom experiments. This work leads to a reevaluation of fundamental classical concepts such as point and trajectory that turn out to be unstable characteristics of chaotic systems. In another part of the research, stochastic properties of the propagation of action potentials along neurons is explored. These studies provide a first principles account of ion channel fluctuations and their affects on action potential propagation, timing, and interspike statistics, each of which has been recently highlighted as of importance for the information coding problem in neuronal signals. The fluctuations cause spontaneous firing patterns that have been measured and which will be compared with numerical simulations of a stochastic theory.
