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).
Links are to the Los Alamos eprint
server:
- 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
- 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
- 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
- The Quantum Emergence of Chaos, Salman Habib, Kurt Jacobs,
and Kosuke Shizume, Phys. Rev. Lett. (in press) quant-ph/0412159
- 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
- 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
- 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
- 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
- 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
- The Emergence of Classical Dynamics in a Quantum World,
Tanmoy Bhattacharya, Salman Habib, and Kurt Jacobs, Los Alamos
Science 27, 110 (2002)
- 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
- 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
- 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
- Decoherence, Chaos, and the Correspondence Principle, Salman
Habib, Kosuke Shizume, and Wojciech H. Zurek, Phys. Rev. Lett. 80,
4361 (1998) quant-ph/9803042
- 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
- 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
- Quantum Diffusion, Salman Habib, Proceedings 4th Drexel
Symposium on Quantum Nonintegrability hep-th/9410181
- Coherent States via Decoherence, Wojciech H. Zurek, Salman Habib,
and Juan Pablo Paz, Phys. Rev. Lett. 70, 1187 (1993)
- Reduction of the Wavepacket: Preferred Observable and Decoherence
Time, Juan Pablo Paz, Salman Habib, and Wojciech H. Zurek, Phys. Rev.
D 47, 488 (1993)
- Wigner Function and Decoherence in Quantum Cosmology, Salman Habib
and Raymond Laflamme, Phys. Rev. D 42, 4056 (1990)
- Classical Limit in Quantum Cosmology: Quantum Mechanics and the
Wigner Function, Salman Habib, Phys. Rev. D 42, 2566 (1990)
Salman Habib / LANL / revised February 2005 |
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