The focus of this research proposal is the interplay of stochasticity and nonlinearity in physics and biology. Two projects are in physics and have their origin in earlier studies by the Principal Investigator on the amplification of intrinsic noise by chaos. Two projects are in biology and concern the fundamental constructive role of noise in molecular and cellular mechanisms. Each project involves a combination of methods. Analytic and numerical methods will be used, and contact with experiments will be made wherever possible. One project of each type is described below. 1) The classical Lyapunov exponent has been shown by the Principal Investigator to be a quantum signature of classical chaos. This realization depends on the use of Husimi-Wigner distributions that have direct classical analogues as non-negative ensemble densities. Husimi-Wigner wave packets are most easily constructed using generalized coherent states. In this proposal, a new class of coherent states called Klauder states will be studied. Especially interesting are the Klauder states for the Coulomb problem. This work will impact research on quantum-classical correspondence and on experiments with Rydberg atom traps. 2) Rectified Brownian movement is a mechanism by which metabolic Gibbs free energy is converted into useful mechanical work inside cells. Rather than a direct chemo-mechanical conversion in which chemical energy is transduced into work, an indirect mechanism is proposed. In this alternative mechanism, work is done by heat, but not in violation of the second law of thermodynamics. Instead, a diffusion regime is applicable in which the boundary conditions are asymmetric. The asymmetry is paid for with metabolic free energy. The impact of this work will be to potentially provide a unified mechanism for a great many basic cellular processes.
