David Farrelly

Professor of Physical Chemistry

Department of Chemistry and Biochemistry
Utah State University
Logan, UT 84322-0300 USA

Office Phone: (435) 797-1608; FAX (435) 797-3390

E-mail: davidfarrelly@yahoo.com

B.S., 1977, University of Manchester

Ph.D., 1980, University of Manchester

Research Interests

Theory of intramolecular energy flow

Non-linear dynamics of highly excited molecules

Chaotics dynamics

Dynamics of atoms interacting with intense electromagnetic fields

Theory of scanning tunneling microscopy and atomic force microscopy

Theories of gas-surface scattering

Dynamics of chemical reactions at surfaces

My research is in theoretical chemical physics and is primarily directed to studying the dynamics of microscopic and mesoscopic systems (e.g., quantum dots) in the classical limit of quantum mechanics, i. e., when h is small. Examples of such systems are ultrahigh atomic and molecular Rydberg states and electrons in quantum dots, sometimes called artificial atoms. The sensitivity of these systems to external electric and/or magnetic fields makes them ideal candidates to study the dynamical effects of symmetry-breaking perturbations. Practical aplications include ZEKE spectroscopy that relies on the preparation and stabilization of ultrahigh Rydberg molecules (principle quantum number n > 200) and the development of quantum electronics in which the wavelength and localization of individual electrons in a quantum dot need to be controlled. These systems all exist at the boundary of quantum and classical mechanics and display a range of novel dynamical properties such as chaos and Arnold diffusion. We investigate these systems using a variety of theoretical and numerical methods ranging from classical trajectory simulations to direct integration of the time dependent Schrödinger equation. A good review of work in this area is contained in an article in Science (vol. 273, p. 307, 1996) that features some of our research. The titles in the following list of publications provide an overview of some of our recent research activities.

Selected Publications

K. Krantzman and D. Farrelly, "Semiclassical mechanics of the quadratic Zeeman effect in hydrogen,"Phys. Rev. A., (1992).

D. Farrelly and J.A. Milligan, "Action-angle variables for the diamagnetic Kepler problem." Phys. Rev. A., 45, 8277, (1992).

D. Farrelly, T. Uzer, P.E. Raines, J.P. Skelton, and J.A. Milligan, "Electronic structure of Rydberg atoms in parallel electric and magnetic fields." Phys. Rev. A., 45, 4738, (1992).

J.A. Griffiths and D. Farrelly, "Ionization of atoms by elliptically and circularly polarized microwave fields." Phys. Rev. A., 45, 2678, (1992).

D. Farrelly and R.D. Levine, "Optical model of dissociative chemisorption: H2 on the (111), (110), and (100) faces of copper." J. Chem. Phys., 97, 2139, (1992).

"Controlling tunneling in a driven double well system." D. Farrelly and J.A. Milligan: In J. Broeckhove and L. Lathouwers, editors, Time-Dependent Quantum Molecular Quantum Molecular Dynamics: Theory and Experiment, page 45. Plenum Press, New York, (1992).

"Complex angular momentum theory of heavy- ion elastic scattering: Semiclassical calculation of Regge poles for complex optical nuclear potentials." J.N.L. Connor and D. Farrelly, Phys. Rev. C., 48, 2419, (1993).

"Assymetric top description of Rydberg electron dynamics in crossed external fields," M.J. Gourlay, T. Uzer, and D. Farrelly, Phys. Rev. A., 47,3113, (1993).

"Atomic Analogs of Local and normal modes: D. Farrelly and J.A. Milligan, "The Hydrogen atom in a generalized van der Waals potential," Phys. Rev. A., 47, 3137, (1993).

D. Farelly and J.E. Howard, "Comment on þRegular and chaotic motion in ion traps: A nonlinear analysis of trap equations." Phys. Rev. A., 48, 851, (1993).

J.E. Howard and D. Farrelly, "Integrability of the Paul Trap Generalized van der Waals and Hamillonians." Phys. Lett. A., 48, 62, (1993).

D. Farrelly and J.A. Milligan, "Two-frequency control and suppression of tunneling in the driven double well." Phys. Rev. E., 47, R2225, (1993)

D. Farrelly and J.E. Howard , "Double well dynamics of two ions in a Paul and Penning Traps." Phys. Rev. A., 49, 1494 (1994).

D. Farrelly and M. Emmel, "Semiclassical quantization of doubly excited intrashell resonances of the helium atom." Chem. Phys. Letts., 217, 520 (1994).

D. Farrelly, J. Humphreys, "Normalization of resonant Hamiltonians," (proceedings of NATO Advanced Research Workshop on Integrability and Chaotic Behaviour held in Torun, Poland, 1994, p. 189.

D. Farrelly and J.E. Howard. "Integrable and chaotic behaviour in the Paul trap and the Hydrogen atom in a generalized van der Waals potential," (proceedings of NATO Advanced Research Workshop on Integrability and Chaotic Behaviour held in Torun, Poland, 1994, p. 237.

D. Farrelly, "Motional Stark effect on Rydberg States in Crossed Electric and Magnetic Fields." Phys. Letts. A., 191, 265 (1994).

E. Lee, D. Farrelly, and T. Uzer, "Core Induced Stabilization and Ionization of Molecular Rydberg States." Chem. Phys. Letts., 231, 241 (1994).

D. Farrelly and T. Uzer, "Normalization and the Detection of Integrability." Celest. Mech. and Dynam. Astronon., 61, 71 (1995).

D. Farrelly and T. Uzer, "Ionization Mechanism of Rydberg Atoms in a Circularly Polarized Microwave Field." Phys. Rev. Letts., 74, 1720 (1995).

D. Farrelly, P. Bellomo and T. Uzer, "Comment on 'Chaotic Autoionization of Molecular Rydberg States." Phys. Rev. Letts., 74, 3495 (1995).

T. Uzer and D. Farrelly, “Threshold Ionization Dynamics of the Hydrogen Atom in Crossed Electric and Magnetic Fields,” Phys Rev. A., 52, R2501 (1995).

D. Farrelly and T. Uzer, "Ionization Mechanism of Rydberg Atoms in a Circularly Polarized Microwave Field," Phys. Rev. Letts., 74, 1720(1995).

D. Farrelly, E. Lee, and T. Uzer, "Comment on 'Lagrange Equilibrium Points in Celestial Mechanics and Nonspreading Wavepackets for Strongly driven Rydberg Electrons'," Phys. Rev. Letts, 75, 972 (1995).

A. Smew, D. Farrelly, and T. Uzer, "Comment on 'Circular Rydberg Orbits in Circularly Polarized Microwave Radiation'," Phys. Rev. A, 51, 4293(1995).

D. Farrelly, 'Comment on "Saddle Point Ionization and the Runge-Lenz Invariant,"' Phys. Rev. A., 55, 1550 (1997).

A. Brunello, T. Uzer and D. Farrelly. “Nonstationary, Nondispersive Wavepackets in a Rydberg Atom,” Phys. Rev. Letts., 76, 2874 (1997).

J. von Milczewski, D. Farrelly and T. Uzer. “Frequency Analysis of 3D Electronic 1/r Dynamics, Tuning Between Order and Chaos,” Phys. Rev. Letts., 78, 1436 (1997).

J. von Milczewski, D. Farrelly and T. Uzer. “1/r Dynamics in External Fields: 2D or 3D?” Phys. Rev. Lett., 78, 2349 (1997).

E. Lee, A.F. Brunello and D. Farrelly. “Coherent States in a Rydberg Atom: Classical Mechanics,” Phys. Rev. A (Atomic, Molecular, and Optical Physics), 55, 2203 (1997).

C.Cerjan, E. Lee, D. Farrelly and T. Uzer. “Coherent States in a Rydberg Atom: Quantum Mechanics,” Phys. Rev. A. 55, 2222 (1997).

J. von Milczewski, D. Farrelly and T. Uzer. “Role of the Atomic Coulomb Center in Ionization and Periodic Orbit Selection,” Phys. Rev. A (Atomic, Molecular, and Optical Physics), 56, 657 (1997).

P. Bellomo, D. Farrelly and T. Uzer. “Collisional Population of Ultra-High, Ultra-Long Living Rydberg States Under ZEKE Conditions,” J. Chem Phys., 107, 2499 (1997).

D. Farrelly, E. Lee and T. Uzer. “Comment on ‘Pair Tunneling in Semiconductor Quantum Dots,” Phys. Rev. Lett., 80, 3884 (1998).

P. Bellomo, D. Farrelly and T. Uzer. “Excitation and Stability of Ultrahigh Rydberg States in Stray Electric Fields,” J. Phys. Chem., 101, 8902 (1997).

E. Lee, D. Farrelly and T. Uzer. “A Saturnian Atom,” Optics Express, 1 (1997).

A.F. Brunello, L.T. Uzer, D. Farrelly. “Hydrogen Atom in Circulary Polarized Microwaves: Chaotic Ionization Via Core Scattering,” Physical Review A (Atomic, Molecular, and Optical Physics), 55, 3730 (1997).

P.Bellomo, D. Farrelly and T. Uzer. “Anomalous Autoionization Lifetimes of Rydberg States in a Circularly Polarized Microwave Field,” J. Chem. Phys., 108, 420 (1998).

E. Lee, M. Puzder, M.Y. Chou, T. Uzer and D. Farrelly. “Pair Tunneling States in Semiconductor Quantum Dots,” Phys. Rev. B., 57, 12281 (1998).

M. Rakovic, T. Uzer and D. Farrelly. “Classical and Quantum Mechanics of an Integrable Limit of the Hydrogen Atom in Polarized and Magnetic Fields,” Phys. Rev. A., 57, 2814 (1998).

T. Uzer, E. Lee and D. Farrelly. “Ionization of Rydberg Atoms by Coriolis Forces,” Physical Review A, 58, 4761 (1998).

P. Bellomo, D. Farrelly, and T. Uzer. “Collisional Intrashell Transitions in Alkali Rydberg Atoms under ZEKE Conditions,” J. Chem. Phys., 108, 9295 (1998).

P. Bellomo, C. Stroud, D. Farrelly and T. Uzer, Quantum-classical correspondence in the hydrogen atom in weak external fields, Phys. Rev. A, 58, 3896 (1998).

E. Lee, D. Farrelly, and K.B. Whaley, Rotational Level Structure of SF6 Doped 4Hen Clusters, Phys. Rev. Lett. 83, 3812 (1999).

C. Jaffe, D. Farrelly, and T. Uzer, Transition state in atomic physics, Phys. Rev. A, 60, 3833 (1999).

C. Jaffe, D. Farrelly, and T. Uzer, Transition State Theory without Time-Reversal Symmetry: Chaotic Ionization of the Hydrogen Atom, Phys. Rev. Lett., 84, 610 (2000).

T. Uzer, E. Lee, D. Farrelly, and A. Brunello, Synthesis of a Classical Atom; Wavepacket analogues of the Trojan asteroids, Contemporary Physics, 41, 1 (2000).

From Asteroids to Atoms; Quantum Wavepackets and the Restricted Three-Body Problem of Celestial Mechanics, in The Physics and Chemistry of Wavepackets, ed. J.A. Yeazell (Wiley, New York, 2000) pp. 95-130.

E. A. lee, D. Farrelly and T. Uzer, Stabilization of Molecular Atoms, Faraday Disc., 115, 217 (2000)

A. Elipe, D. Farrelly and I. M. Wytrzyszczak, Phase space structure of the Penning trap with octupole perturbation, Phys. Rev. A., 65, 033423 (2002).

C. Chandre, D. Farrelly and T. Uzer, Thresholds to chaos and ionization of Rydberg atoms in rotating fields, Phys. Rev. A., 65, 053402 (2002).

C. Jaffe, S. Ross, M.W. Lo, J. Marsen, D. Farrelly and T. Uzer, Statistical theory of asteroid escape rates, Phys. Rev. Lett., 89, 011101 (2002).

D. Farrelly, E. A. Lee and T. Uzer, The classical atom: Stabilization of electronic Trojan wavepackets. Fortschr. Phys. 50, 636 (2002).

S. Astakhov, A. Burbanks, S. Wiggins and D. Farrelly, Chaos Assisted Capture of Irregular Moons Nature, 423, 264 (2003).

S. Astakhov, A. Burbanks, S. Wiggins and D. Farrelly, Dynamics of Capture in the Restricted Three-Body Problem, in Order and chaos in stellar and planetary systems, Astron. Soc. Pac. Conf. Series, pp. 80-85 CS-316, 2004.

S. Astakhov, E. Lee and D. Farrelly. Capture and escape in the elliptic restricted three-body problem. MNRAS, 354, 971 (2004).

S. Astakhov, E. Lee, and D. Farrelly. Formation of Kuiper-belt binaries through multiple chaotic scattering encounters with low-mass intruders. MNRAS, 360, 401 (2005)

M. Kalinski, L. Hansen, and D. Farrelly, Nondispersive two-electron wave packets in a helium atom. Phys. Rev. Lett., 95, 103001 (2005)

J. L. Cagide Fajín, B. Fernández, A. Mikosz, and D. Farrelly. Accurate computations of the rovibrational spectrum of the He-HF van der Waals complex. Mol. Phys., (2006) in press.