Ronald F. Fox
Regents' Professor Emeritus
Honors & Awards
stochastic processes, nonlinear dynamics, quantum chaos, and biophysics
- Contributions to the Theory of Nonequilibrium Thermodynamics
- Advisors: Mark Kac and George Uhlenbeck
- Postdoctoral Fellow, Miller Institute for Basic research in Science and Department of Physics, University of California at Berkeley, 1969-1971
- Assistant Professor of Physics, Georgia Tech 1971-1974
- Associate Professor of Physics, Georgia Tech 1974-1979
- Professor of Physics, Georgia Tech 1979-1991
- Regents Professor of Physics, Georgia Tech 1991-
- Assistant Director, School of Physics 1982-1984
- Associate Director, School of Physics 1986-1989
- Associate Chair, School of Physics 1997-1999
- Member, Sigma Xi, Rockefeller University
- Member, American Physical Society
- Member, New York Academy of Sciences
- Acting Chair, School of Physics 1999-2000
- Chairman, School of Physics 2001-June, 2005
- Regents' Professor Emeritus, 2007-Present
Professor Fox's research includes stochastic processes, nonlinear dynamics, quantum chaos, and biophysics.
Stochastic processes arise from the study of fluctuations in physical systems. Professor Fox has looked at the mathematical formulation of such processes (especially multiplicative processes and colored noise), the numerical simulation of stochastic differential equations (novel algorithms have been published), and the application of stochastic processes to experimental studies of physical systems. Applications include magnetic relaxation, the theory of spectra, noise in lasers, and hydrodynamic turbulence.
The primary focus of Professor Fox's work in nonlinear dynamics has been on the exponential amplification of intrinsic, molecular fluctuations by chaotic dynamics. Amplification by several orders of magnitude has been predicted for fluid systems, and in laser systems the expectation is that amplification will be over many orders of magnitude. This effect has repercussions for the physical reality of fractal attractors and for the feasibility of control of chaos by feedback. It also forces a rethinking of the relationship between the microscopic description of physical processes and macroscopic descriptions of the same. A particularly tantalizing connection involves the difference in behavior between point-wise trajectories and densities for chaotic iterated maps.
The work on quantum chaos has dealt with an appropriate definition of the term and with the hallmark of classical chaos in a system treated quantum mechanically. Studies on the periodically kicked pendulum and on the periodically kicked top have shown that Husimi-Wigner wave packets and their corresponding classical ensembles exhibit exponential growth of variable covariances with growth rates determined by the largest classical Lyapunov exponent. Consequently, a quantum measurement of the variance growth rate yields the classical Lyapunov exponent. The wave packets and ensembles are constructed using coherent states; in the case of the top, generalized su(2) coherent states. This method permits a direct connection between wave packets and phase space concepts including the Lyapunov exponent.
The biophysics work has covered energy transduction, especially chemosmosis, the origin of protein biosynthesis, and the origin of energy metabolism. Two monographs on these ideas have been published. Recent work covers ion channel fluctuations, and the mechanism of molecular motors. The ion channel fluctuation work provides a first principles account of the noise in voltage gated potassium and sodium channels in nerve membrane as described by the Hodgkin-Huxley equations. Both small patches and spatially dependent action potential propagation have been considered. The molecular motor work covers ubiquinone energy transduction, rotary enzyme complexes, ion transporters and the mechanism of actin-myosin dynamics in muscle fibers. The central idea is the distinction between chemo-mechanical energy conversion and energy driven rectification of Brownian motion.
- "An exact value for Avogadro's number: untangling this constant from Le Gran K could provide a new definition of the gram", R.F. Fox and T. P. Hill, American Scientist, 95 104-107 (March 2007).
- "Coherent State Analysis of the Quantum Bouncing Ball", William Mather and R.F. Fox, Physical Review A, 73 032109 (2006), 9 pages.
- "Kinesin's Biased Stepping Mechanism: Amplification of Neck Linker Zippering", William Mather and R.F. Fox, Biophysical Journal, 91 2416-2426 (2006)
- Luz V. Vela-Arevalo and R. F. Fox, "Coherent states of the driven Rydberg atom: Quantum-classical correspondence of periodically driven systems", Physical Review A 71, 063403 (2005), 12 pages.
- R.F. Fox, "Origin of Life and Energy", Encyclopedia of Energy, Volume 4 (2004).
- Luz V. Vela-Arevalo and R.F. Fox, "Semiclassical Analysis of Long-Wavelength Multiphoton Processes: The Rydberg atom", Physical Review A 69, 063409 (2004).
- M. H. Choi and R. F. Fox, "Evolution of Escape Processes with Time Varying Load", Physical Review E 66, 031103 (2002), 6 pages.
- M.H. Choi and R.F. Fox, "Quasiadiabatic Analysis for Ionization of a particle in a Perturbed Potential", Physical Review E 66, 046124 (2002), 5 pages.
- R.F. Fox and L.V. Vela-Arevalo, "Semiclassical Analysis of Long Wavelength, Multiphoton Processes: The Periodically Driven Harmonic Oscillator", Physical Review A 66, 053402 (2002), 10 pages.
- R. F. Fox and M. H. Choi, "Rectified Brownian motion and kinesin motion along microtubules", Physical Review E, Vol. 63, 051901. (2001), 12 pages.
- R.F. Fox and M.H. Choi, "Generalized Coherent States for Systems with Degenerate Energy Spectra", "Physical Review A 64, 042104 (2001).
- R.F. Fox and M. H. Choi, "Generalized Coherent States and Quantum-Classical Correspondence", Physical Review A 61, 032107 (2000), 11 pages.
- R.F. Fox, "Generalized Coherent States", Physical Review A, 59, 3241-3255(1999).
- R.F. Fox, "Rectified Brownian Movement in Molecular and Cell Biology", Physical Review E 57, 2177-2203 (1998).
- R.F. Fox and P. Jung, "Quasi-adiabatic Time Evolution, Avoided Level Crossings and Berry's Phase", Physical Review A 57, 2339-2346 (1998)
- M. H. Choi, R.F. Fox and P. Jung, "Quantifying Stochastic Resonance in Bistable Systems: Response vs Residence Time Distribution Functions", Physical Review E 57, 6335-6344 (1998).
- R.F. Fox, "Entropy Evolution for the Baker Map", Chaos 8, 462-465 (1998)
- R. F. Fox, "Stochastic Versions of the Hodgkin-Huxley Equations", Biophysical Journal 72, 2068-2074 (1997).
- R. F. Fox, "Construction of the Jordan Basis for the Baker Map", Chaos 7, 254-269 (1997).
- R.F. Fox, "Unstable Evolution of Point-Wise Trajectory Solutions to Chaotic Maps", Chaos 5, 619 (1995).
- R. F. Fox and Y. Lu, "Emergent Collective Behavior in Large Numbers of Globally Coupled Independently Stochastic Ion Channels", Physical Review E 49, 3421 (1994).
- R. F. Fox and T. C. Elston, "Chaos and Quantum-Classical Correspondence in the Kicked Pendulum", Physical Review E 49, 3683 (1994).
- R. F. Fox and T. C. Elston, "Chaos and Quantum-Classical Correspondence in the Kicked Top", Physical Review E 50, 2553 (1994).
- R.F. Fox and Y. Lu, "Analytic and Numerical Study of Stochastic Resonance", Physical Review E 48, 3390 (1993).
- R.F. Fox and J.E. Keizer, "Amplification of Intrinsic Fluctuations by Chaotic Dynamics", Physical Review A 43, 1709 (1991).
- R.F. Fox, "Second Order Algorithm for the Numerical Integration of Colored Noise Problems", Physical Review A 43, 2649 (1991).
- R.F. Fox, "Generalized Coherent State Analysis of Semi-Classical Quantum Chaos for an Angular Momentum J in a Resonant Cavity", Physical Review A 44, 6193 (1991).
- R. F. Fox, Energy and the Evolution of Life, W. H. Freeman and Co., New York (1988).