Classical and Quantum Nonlinear Dynamics      

My interests in this area cover topics such as novel methods for the computation of Lyapunov exponents [with Robert Ryne (LBNL) and Govindan Rangarajan (IISc), both of whom I've known since graduate school], the effect of noise on transport in mixed phase spaces [with the late Henry Kandrup and Elaine Mahon (Florida)], continuous measurement and decoherence in nonlinear quantum systems [with Ben Greenbaum (student at Columbia), Kurt Jacobs (ex-LANL postdoc, now at Griffith), regular visitor from Japan, Kosuke Shizume (Tsukuba), and Bala Sundaram (CUNY/Courant)], mean field approximations to quantum dynamics and possible improvements [largely with Fred Cooper (T-8) and John Dawson (UNH), and Bogdan Mihaila (T-6)], the relationship between chaos and statistical mechanics, and realistic modeling of quantum chaos experiments. This last effort involves a large group of people including Andrew Doherty (Queensland) and Hideo Mabuchi (Caltech), Bala Sundaram, as well as Kurt Jacobs and Kosuke Shizume. Tanmoy Bhattacharya (T-8) has provided inestimable help on all of the above topics. Finally, a collaboration with Ivan Deutsch's group at UNM, especially with his student Shohini Ghosh, was stimulating and productive.

Papers

Links are to the Los Alamos eprint server:

  1. Emergence of Chaos in Quantum Systems Far from the Classical Limit, Salman Habib, Kurt Jacobs, and Kosuke Shizume, Phys. Rev. Lett. 96, 010403 (2006) quant-ph/0412159
  2. Chaos and Quantum Mechanics, Salman Habib, Tanmoy Bhattacharya, Benjamin Greenbaum, Kurt Jacobs, Kosuke Shizume, and Bala Sundaram, in Nonlinear Dynamics in Astronomy and Physics, Proceedings of the 16th Florida Workshop in Nonlinear Astronomy and Physics, dedicated to the memory of Henry Kandrup (November, 2004, Gainesville), edited by Stephen Gottesman, J.-R. Buchler, and M.E. Mahon, Ann. N.Y. Acad. Sci. 1045, 308 (2005); quant-ph/0505085
  3. Nonlinear Quantum Dynamics, Salman Habib, Tanmoy Bhattacharya, Andrew Doherty, Benjamin Greenbaum, Asa Hopkins, Kurt Jacobs, Hideo Mabuchi, Keith Schwab, Kosuke Shizume, Daniel Steck, and Bala Sundaram, Proceedings of the NATO Advanced Workshop, Nonlinear Dynamics and Fundamental Interactions, Tashkent, October, 2004, edited by Faqir Khanna and Davron Matrasulov (Springer, 2006) quant-ph/0505046
  4. Gaussian Dynamics is Classical Dynamics, Salman Habib quant-ph/0406011
  5. The Delta-Function-Kicked Rotor: Momentum Diffusion and the Quantum-Classical Boundary, Tanmoy Bhattacharya, Salman Habib, Kurt Jacobs, and Kosuke Shizume, Phys. Rev. A 65, 032115 (2002) quant-ph/0105086
  6. Quantum And Classical Dynamics Of Atoms in a Magneto-Optical Lattice, Shohini Ghose, Paul M. Alsing, Ivan H. Deutsch, Poul S. Jessen, David L. Haycock, Tanmoy Bhattacharya, Salman Habib, and Kurt Jacobs, Proceedings, 7th Experimental Chaos Conference (San Diego, August 2002) quant-ph/0210131
  7. The Quantum-Classical Transition in Nonlinear Dynamical Systems, Salman Habib, Kurt Jacobs, Hideo Mabuchi, Robert Ryne, Kosuke Shizume, and Bala Sundaram, Phys. Rev. Lett. 88, 040402 (2002) quant-ph/0010093
  8. No Mere Anarchy, Salman Habib, Science 293, 221 (2001)
  9. Continuous Quantum Measurement and the Emergence of Classical Chaos, Tanmoy Bhattacharya, Salman Habib, and Kurt Jacobs, Phys. Rev. Lett. 85, 4852 (2000) quant-ph/9906092
  10. Exact and Approximate Dynamics of the Quantum Mechanical O(N) Model, Bogdan Mihaila, Tara Athan, Fred Cooper, John Dawson, and Salman Habib, Phys. Rev. D 62, 125015 (2000) hep-ph/0003105
  11. Computation of Lyapunov Spectrum for Continuous-Time Dynamical Systems and Discrete Maps, T.M. Janaki, Govindan Rangarajan, Salman Habib, and Robert D. Ryne, Phys. Rev. E 60, 6614 (1999)
  12. The Quantum Roll in d-Dimensions and the Large-d Expansion, Bogdan Mihaila, John F. Dawson, Fred Cooper, Mary Brewster, and Salman Habib hep-ph/9808234
  13. How Wigner Functions Transform Under Symplectic Maps, Alex J. Dragt and Salman Habib, to appear in Proceedings of the Advanced Beam Dynamics Workshop on Quantum Aspects of Beam Physics (Monterey, CA 1998) quant-ph/9806056
  14. Decoherence, Chaos, and the Correspondence Principle, Salman Habib, Kosuke Shizume, and Wojciech H. Zurek, Phys. Rev. Lett. 80, 4361 (1998) quant-ph/9803042
  15. Lyapunov Exponents without Rescaling and Reorthogonalization, Govindan Rangarajan, Salman Habib, and Robert D. Ryne, Phys. Rev. Lett. 80, 3747 (1998) chao-dyn/9803017
  16. Chaos in Time Dependent Variational Approximations to Quantum Dynamics, Fred Cooper, John Dawson, Salman Habib, and Robert D. Ryne, Phys. Rev. E 57, 1489 (1998) quant-ph/9610013
  17. Chaos and Noise in Galactic Potentials, Salman Habib, Henry E. Kandrup, and M. Elaine Mahon, Ap. J. 480, 155 (1997) astro-ph/9409050
  18. Chaos and Noise in a Truncated Toda Potential, Salman Habib, Henry E. Kandrup, and M. Elaine Mahon, Phys. Rev. E 53, 5473 (1996) chao-dyn/9406011
  19. Semiquantum Chaos and the Large N Expansion, Fred Cooper, John Dawson, Salman Habib, Yuval Kluger, Dawn Meredith, and Harvey Shepard, Physica D 83, 74 (1995) chao-dyn/9411004
  20. Symplectic Calculation of Lyapunov Exponents, Salman Habib and Robert D. Ryne, Phys. Rev. Lett. 74, 70 (1995) chao-dyn/9406010
  21. Symplectic Computation of Lyapunov Exponents, Salman Habib and Robert D. Ryne, Proceedings, NEEDS'94 acc-phys/9411001
  22. Quantum Diffusion, Salman Habib, Proceedings 4th Drexel Symposium on Quantum Nonintegrability hep-th/9410181
Related Links

T-Division Research Highlights for 2005: Nonlinear Quantum Dynamics [PDF].

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Salman Habib / LANL / revised March 2005
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