Quantum-Classical Transition      

The treatment of the boundary between quantum and classical physics has been controversial ever since the early days of quantum mechanics. Nevertheless, the resolution of this problem is very important for several fundamental issues in cosmology, in understanding certain low temperature experiments in condensed matter physics, in quantum and atomic optics, and in quantum measurement theory, more generally. The issue of when classical methods may be applied in nonequilibrium quantum field theory remains murky. Quantum decoherence, which is the dynamical suppression of quantum interference effects, allows for a smooth classical limit to exist in certain cases. Although decoherence does not resolve the quantum measurement problem as it is usually stated, it, along with the statistical interpretation of quantum mechanics, leads to a self-consistent formalism which can be safely applied to all physical situations.

Aside from studies of decoherence I carried out with Raymond Laflamme (Perimeter), Juan Pablo Paz (IAFE/LANL), Wojciech Zurek (T-DO), and Kosuke Shizume (Tsukuba), more recently I have become interested in obtaining the classical limit from quantum mechanics via the theory of continuous measurements. This approach is more fine-grained than the decoherence methodology mentioned above and allows the consideration of conditioned state evolution which takes into account the results from measurements as they become known. Work with Tanmoy Bhattacharya (T-8) and Kurt Jacobs (Griffith) -- extended to more general systems with Paul Alsing, Ivan Deutsch, and Shohini Ghosh (UNM) -- has succeeded in the extraction of the classical Lyapunov exponent using this formalism. More recently we have established that chaos exists in the quantum regime far from the classical limit. Research on different topics in this subfield continues with a subset of the above as well as with Bala Sundaram (CUNY) and Ben Greenbaum (Columbia).

Papers

Links are to the Los Alamos eprint server:

  1. Semiclassics of the Chaotic Quantum-Classical Transition, Benjamin Greenbaum, Salman Habib, Kosuke Shizume, and Bala Sundaram, Phys. Rev. E 76, 046215 (2007) quant-ph/0610004v2
  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 F. Khanna quant-ph/0505046
  4. The Quantum Emergence of Chaos, Salman Habib, Kurt Jacobs, and Kosuke Shizume, Phys. Rev. Lett. (in press) quant-ph/0412159
  5. The Semiclassical Regime of the Chaotic Quantum-Classical Transition, Benjamin D. Greenbaum, Salman Habib, Kosuke Shizume, and Bala Sundaram, Chaos 15, 033302 (2005) quant-ph/0401174
  6. The Transition to Classical Chaos in a Coupled Quantum System through Continuous Measurement, Shohini Ghose, Paul Alsing, Ivan Deutsch, Tanmoy Bhattacharya, and Salman Habib, Phys. Rev. A 69, 052116 (2004) quant-ph/0309093
  7. Recovering Classical Dynamics from Coupled Quantum Systems through Continuous Measurement, Shohini Ghose, Paul M. Alsing, Ivan H. Deutsch, Tanmoy Bhattacharya, Salman Habib, and Kurt Jacobs, Phys. Rev. A 67, 052102 (2003) quant-ph/0208064
  8. Continuous Quantum Measurement and the Quantum to Classical Transition, Tanmoy Bhattacharya, Salman Habib, and Kurt Jacobs, Phys. Rev. A 67, 042103 (2003) quant-ph/0211036
  9. 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
  10. The Emergence of Classical Dynamics in a Quantum World, Tanmoy Bhattacharya, Salman Habib, and Kurt Jacobs, Los Alamos Science 27, 110 (2002)
  11. 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
  12. 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
  13. 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
  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. Classical Dynamics for Linear Systems: The Case of Quantum Brownian Motion, James Anglin and Salman Habib, Mod. Phys. Lett. A 11, 2655 (1996) quant-ph/9507011
  16. Dissipation and Decoherence in Mean Field Theory, Salman Habib, Yuval Kluger, Emil Mottola, and Juan Pablo Paz, Phys. Rev. Lett. 76, 4660 (1996) hep-ph/9509413
  17. Quantum Diffusion, Salman Habib, Proceedings 4th Drexel Symposium on Quantum Nonintegrability hep-th/9410181
  18. Coherent States via Decoherence, Wojciech H. Zurek, Salman Habib, and Juan Pablo Paz, Phys. Rev. Lett. 70, 1187 (1993)
  19. Reduction of the Wavepacket: Preferred Observable and Decoherence Time, Juan Pablo Paz, Salman Habib, and Wojciech H. Zurek, Phys. Rev. D 47, 488 (1993)
  20. Wigner Function and Decoherence in Quantum Cosmology, Salman Habib and Raymond Laflamme, Phys. Rev. D 42, 4056 (1990)
  21. Classical Limit in Quantum Cosmology: Quantum Mechanics and the Wigner Function, Salman Habib, Phys. Rev. D 42, 2566 (1990)
Related Links

T-Division Research Highlights for 2005: Semiclassics and Topological Aspects of the Quantum-Classical Transition [PDF].

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Salman Habib / LANL / revised February 2005
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