×
Belot, Gordon; Earman, John

Chaos out of order: quantum mechanics, the correspondence principle and chaos. (English) Zbl 1222.81181

Stud. Hist. Philos. Sci., Part B, Stud. Hist. Philos. Mod. Phys. 28, No. 2, 147-182 (1997).

Cited in 14 Documents

MSC:

81Q50 Quantum chaos
00A30 Philosophy of mathematics
00A79 Physics
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
70K50 Bifurcations and instability for nonlinear problems in mechanics
Cite Review PDF
Full Text: DOI

References:

[1] Albert, D. Z., The Foundations of Quantum Mechanics and the Approach to Thermodynamic Equilibrium, British Journal for Philosophy of Science, 45, 669-677 (1994)
[2] Alekseev, V. M.; Yakobson, M. V., Symbolic Dynamics and Hyperbolic Dynamic Systems, Physics Reports, 75, 287-325 (1981)
[3] Balazs, N. L.; Voros, A., Chaos on the Pseudosphere, Physics Reports, 143, 109-240 (1986)
[4] Ballentine, L. E., The Emergence of Classical Properties from Quantum Mechanics: New Problems from Old, (Ferraro, M.; Merwe, A.van der, Fundamental Problems in Quantum Physics (1995), Kluwer: Kluwer Dordrecht), 15-28
[5] Batterman, R., Chaos, Quantization, and the Correspondence Principle, Synthese, 89, 189-227 (1991)
[6] Batterman, R., Quantum Chaos and Semiclassical Mechanics, (PSA 1992, Vol. 2 (1993), Philosophy of Science Association: Philosophy of Science Association East-Lansing, MI), 50-65
[7] Batterman, R., Chaos:Algorithmic Complexity vs Dynamical Instability (1994), preprint
[8] Batterman, R.; White, H., Chaos and Algorithmic Complexity, Foundations of Physics, 26, 307-336 (1996)
[9] Benatti, F., Deterministic Chaos in Infinite Quantum Systems (1993), Springer: Springer New York · Zbl 0771.60098
[10] Berman, G. P.; Rubaev, V. Y.; Zaslavsky, G. M., The Problem of Quantum Chaos in a Kicked Harmonic Oscillator, Nonlinearity, 4, 543-566 (1991) · Zbl 0721.60124
[11] Berry, M. V., Random Renormalization in the Semiclassical Long-Time Limit of a Precessing Spin, Physica D, 33, 26-33 (1988) · Zbl 0667.10026
[12] Berry, M. V., Some Quantum-to-Classical Asymptotics, (Giannoni; etal. (1991)), 255-303, (1991)
[13] Blank, J.; Exner, P.; Miloslow, H., Hilbert Space Operators in Quantum Mechanics (1994), American Institute of Physics: American Institute of Physics New York · Zbl 0873.46038
[14] Carruthers, P.; Nieto, M. M., Phase and Angle Variables in Quantum Mechanics, Reviews of Modern Physics, 40, 411-440 (1968)
[15] Casati, G., Chaotic Behavior in Quantum Systems: Theory and Applications (1985), Plenum Press: Plenum Press New York
[16] Casati, G.; Chirikov, B. V., The Legacy of Chaos in Quantum Mechanics, (Casati, G.; Chirikov, B. V., Quantum Chaos: Between Order and Chaos (1995), Cambridge University Press: Cambridge University Press Cambridge), 3-53
[17] (Casati, G.; Guarneri, I.; Similansky, U., Quantum Chaos. Quantum Chaos, Proceedings of the International School of Physics, ‘Enrico Fermi’ Course CXIX (1993), North-Holland: North-Holland Amsterdam)
[18] (Cerdeira, H. A.; Ramaswamy, R.; Gutzwiller, M. C.; Casati, G., Quantum Chaos (1991), World Scientific: World Scientific Singapore)
[19] Chirikov, B. V., The Problem of Quantum Chaos, (Heiss (1992)), 1-56, (1992)
[20] Cornfeld, I. P.; Fomin, S. V.; Sinai, Y. G., Ergodic Theory (1982), Springer: Springer New York · Zbl 0493.28007
[21] Cushing, J. T., Quantum Mechanics: Historical Contingency and the Copenhagen Hemgemony (1994), University of Chicago Press: University of Chicago Press Chicago · Zbl 0828.00005
[22] (Cvitanovic, P.; Percival, I.; Wirzba, A., Quantum Chaos—Quantum Measurement (1992), Kluwer: Kluwer Dordrecht)
[23] Degli Esposti, M.; Graffi, S.; Isola, S., Classical Limit of Quantized Hyperbolic Toral Automorphisms, Communications in Mathematical Physics, 167, 471-507 (1995) · Zbl 0822.58022
[24] Earman, J., A Primer on Determinism (1986), Reidel: Reidel Dordrecht
[25] Earman, J.; Rédei, M., Why Ergodic Theory Does Not Explain the Success of Equilibrium Statistical Mechanics, British Journal for the Philosophy of Science, 47, 63-78 (1996) · Zbl 1133.82300
[26] Emch, G. G., Algebraic Methods in Statistical and Quantum Mechanics (1972), Wiley Interscience: Wiley Interscience New York · Zbl 0235.46085
[27] Emch, G. G., Quantum and Classical Mechanics in Homogeneous Riemannian Manifolds, Journal of Mathematical Physics, 23, 1785-1791 (1982) · Zbl 0514.70022
[28] Emch, G. G.; Narnhofer, H.; Thirring, W.; Sewell, G. L., Anosov Actions on Noncommutative Algebras, Journal of Mathematical Physics, 35, 5582-5599 (1994) · Zbl 0817.58028
[29] Ford, J., Quantum Chaos. Is There Any?, (Bai-Lin, H., Directions in Chaos, Vol. 2 (1988), World Scientific: World Scientific Singapore), 128-147
[30] Ford, J., What is Chaos that We Should be Mindful of It, (Davies, P., The New Physics (1989), Cambridge University Press: Cambridge University Press Cambridge), 348-371
[31] Ford, J.; Ilg, M., Eigenfunctions, Eigenvalues, and Time Evolution of Finite, Bounded, Undriven, Quantum Systems are Not Chaotic, Physical Review A, 45, 6165-6173 (1992)
[32] Ford, J.; Mantica, G., Does Quantum Mechanics Obey the Correspondence Principle? Is it Complete?, American Journal of Physics, 60, 1071-1086 (1992)
[33] Ford, J.; Mantica, G.; Ristow, G. H., The Arnold Cat: Failure of the Correspondence Principle, Physica D, 50, 493-520 (1991) · Zbl 0742.58024
[34] Fox, R. F.; Lan, B. L., Chaos and Correspondence Limit in the Periodically Kicked Pendulum, Physical Review A, 41, 2952-2968 (1990)
[35] Gaspard, P., Comment on Dynamical Randomness in Quantum Systems, Progress of Theoretical Physics Supplement, 116, 369-401 (1994) · Zbl 1229.82103
[36] (Giannoni, M.-J.; Voros, A.; Zinn-Justin, J., Chaos and Quantum Physics (1991), North-Holland: North-Holland Amsterdam)
[37] (Heiss, W. D., Chaos and Quantum Chaos (1992), Springer: Springer Berlin) · Zbl 0864.47048
[38] Hilborn, R. C., Chaos and Nonlinear Dynamics (1994), Oxford University Press: Oxford University Press New York · Zbl 0804.58002
[39] Hogg, T.; Huberman, B. A., Quantum Dynamics and Nonintegrability, Physical Review A, 28, 22-31 (1983)
[40] (Ikeda, K., Quantum and Chaos: How Incompatible? Proceedings of the 5th Yukawa International Seminar. Quantum and Chaos: How Incompatible? Proceedings of the 5th Yukawa International Seminar, Progress of Theoretical Physics Supplement (1994)), No. 116 · Zbl 0845.58001
[41] Ingraham, R. L., A Survey of Nonlinear Dynamics (1992), World Scientific: World Scientific Singapore · Zbl 0754.58001
[42] Ingraham, R. L.; Luna Acosta, G., On Chaos in Quantum Mechanics: The Two Meanings of Sensitive Dependence, Physics Letters A, 181, 450-452 (1993)
[43] Jensen, F. V., Quantum Chaos, (Krasner, S., The Ubiquity of Chaos (1990), AAAS: AAAS Washington, DC)
[44] Koopman, B. O., Hamiltonian Systems and Transformations in Hilbert Space, (Proceedings of the National Academy of Sciences, 18 (1931)), 315-318 · JFM 57.1010.02
[45] Kronz, F. M., Nonseparability and Quantum Chaos (1996), preprint
[46] Lan, B. L.; Fox, R. F., Quantum-Classical Correspondence and Quantum Chaos in the Periodically Kicked Pendulum, Physical Review A, 43, 646-655 (1991)
[47] Lichtenberg, A. J.; Lieberman, M. A., Regular and Chaotic Dynamics (1992), Springer: Springer New York · Zbl 0748.70001
[48] Mañé, R., Ergodic Theory and Differentiable Dynamics (1987), Springer: Springer New York · Zbl 0616.28007
[49] Martin-Löf, P., The Definition of a Random Sequence, Information and Control, 9, 602-619 (1966) · Zbl 0244.62008
[50] Narnhofer, H.; Pflug, A.; Thirring, W., Mixing and Entropy Increase in Quantum Systems, (Symmetry in Nature, Vol. 2 (1989), Scuola Normal Superiore: Scuola Normal Superiore Pisa), 597-696 · Zbl 0732.70009
[51] Peres, A., Instability of Quantum Motion of a Chaotic System, (Cerdeira; etal. (1991)), 73-101, (1991)
[52] Pour-El, M.; Richards, J. I., Computability in Analysis and Physics (1987), Springer: Springer New York
[53] Rohrlich, F., Pluralistic Ontology and Theory Reduction in the Physical Sciences, British Journal for the Philosophy of Science, 39, 295-312 (1988)
[54] Rohrlich, F., The Logic of Reduction: The Case of Gravitation, Foundations of Physics, 19, 1151-1170 (1989)
[55] Rohrlich, F., There Is Good Physics in Theory Reduction, Foundations of Physics, 20, 1399-1412 (1990)
[56] Sakagami, M., Emergence of Classical Properties from Quantum Theory, Progress of Theoretical Physics Supplement, 116, 393-401 (1994) · Zbl 1229.81018
[57] (Seligman, T. H.; Nishioka, H., Quantum Chaos and Statistical Nuclear Physics. Quantum Chaos and Statistical Nuclear Physics, Lecture Notes on Physics, Vol. 263 (1986), Springer: Springer Berlin)
[58] Sklar, L., Physics and Chance: Philosophical Issues in the Foundations of Statistical Mechanics (1993), Cambridge University Press: Cambridge University Press Cambridge
[59] Weigert, St., Stretching and Folding in the Configurational Quantum Cat, (Cerdeira; etal. (1991)), 323-345, (1991)
[60] Winnie, J., Computable Chaos, Philosophy of Science, 59, 263-275 (1992)
[61] White, H., Algorithmic Complexity of Points in Dynamical Systems, Ergodic Theory and Dynamical Systems, 13, 807-830 (1993) · Zbl 0791.58064
[62] (Yuan, J. M.; Feng, D. H.; Zaslavsky, G. M., Quantum Dynamics of Chaotic Systems (1993), Gordon and Breach: Gordon and Breach Amsterdam)
[63] Zaslavsky, G. M., (Yuan; etal., Classical Chaos Creates a New Challenge to the Quantum Classical Correspondence (1993)), 49-58, (1993) · Zbl 0867.70017
[64] Zurek, W. H.; Paz, J. P., Decoherence, Chaos, and the Second Law, Physical Review Letters, 72, 2508-2511 (1994)
[65] Zurek, W. H.; Paz, J. P., Quantum Chaos, A Decoherent Definition (1995), preprint · Zbl 1194.81111
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.