On the Anandan-Stodolsky effect

Partha Ghose, Dipankar Home

Pierre-Louis Giscard

Robert A. Harris, Leo Stodolsky

In a Search and Discovery news item (Physics Today, September 2009, page 16), we are faulted for not couching our work of the early 1980s “in terms of the then-nascent decoherence theory.” Well, we’re sorry about that, and can only offer the excuse that the term “decoherence” hadn’t yet been coined. We called it “quantum damping” and “tunneling friction.” The reader may agree that those are perhaps not such bad descriptions.Anyone bothering to read the articles 1 , 2 2. R. A. Harris, R. Silbey, J. Chem. Phys. 78, 7330 (1983). 1. R. A. Harris, L. Stodolsky, J. Chem. Phys. 74, 2145 (1981) Phys. Lett. B 116, 464 (1982). or those we have written since 3 3. L. Stodolsky, in Quantum Coherence: University of South Carolina , Columbia, USA , 14-16 December 1989 J. S. Anandan, ed., World Scientific , Hackensack, NJ (1990), p. 320; in Time and Matter: Proceedings of the International Colloquium on the Science of Time, I. I. Bigi, M. Faessler, eds., World Scientific, Hackensack, NJ (2006), p. 117, also available at http://arxiv.org/abs/quant-ph/0303024v2. will find the solutions to Hund’s paradox and the ideas presently in circulation concerning decoherence, like “decoherence by the environment,” clearly and quantitatively explicated.The situation is amusingly reminiscent of the case of Ramses II. Apparently, some people claim the pharaoh couldn’t have died of tuberculosis 4 4. J. R. Searle, N. Y. Rev. Books 56(14), 88 (2009). because the disease wasn’t discovered until the 19th century.REFERENCESSection:ChooseTop of pageREFERENCES <<1. R. A. Harris, L. Stodolsky, J. Chem. Phys. 74, 2145 (1981) Google ScholarCrossref, ISI Phys. Lett. B 116, 464 (1982). , Google ScholarCrossref, ISI2. R. A. Harris, R. Silbey, J. Chem. Phys. 78, 7330 (1983). Google ScholarCrossref, ISI3. L. Stodolsky, in Quantum Coherence: University of South Carolina , Columbia, USA , 14-16 December 1989 , Google Scholar J. S. Anandan, ed., World Scientific , Hackensack, NJ (1990), p. 320; Google Scholarin Time and Matter: Proceedings of the International Colloquium on the Science of Time, I. I. Bigi, M. Faessler, eds., World Scientific, Hackensack, NJ (2006), p. 117, also available at http://arxiv.org/abs/quant-ph/0303024v2. Google Scholar4. J. R. Searle, N. Y. Rev. Books 56(14), 88 (2009). Google Scholar© 2010 American Institute of Physics.

J. Anandan, Yakir Aharonov

The geometric phase in quantum mechanics is formulated for charged particles in a gauge-invariant, geometric manner. It is then extended to an evolution resulting from a sequence of measurements as in the work of Pancharatnam and Aharonov and Vardi. Its close connection to the Feynman formulation of quantum mechanics is pointed out. The geometric angles, which are generalizations of the classical, adiabatic angles introduced by Hannay and the quantum, adiabatic angles introduced by Anandan and Stodolsky in their group-theoretic treatment of Berry's phase, are studied in quantum and classical physics. The geometric phase for a quantum spin in a magnetic field due to a second particle is obtained using the quantum reference frame defined by the latter. The question of whether the geometric phase and angles are local or nonlocal and their relationship to the electromagnetic and gravitational phases are also discussed.

S. Chaturvedi, Narasimhaiengar Mukunda, R. Simon

Zhaoyan Wu, Jingxia Wang