Unified dynamics for microscopic and macroscopic systems. (English) Zbl 1222.82047

Summary: An explicit model allowing a unified description of microscopic and macroscopic systems is exhibited. First, a modified quantum dynamics for the description of macroscopic objects is constructed and it is shown that it forbids the occurrence of linear superpositions of states localized in distant spatial regions and induces an evolution agreeing with classical mechanics. This dynamics also allows a description of the evolution in terms of trajectories. To set up a unified description of all physical phenomena, a modification of the dynamics, with respect to the standard Hamiltonian one, is then postulated for microscopic systems also. It is shown that one can consistently deduce from it the previously considered dynamics for the center of mass of macroscopic systems. Choosing in an appropriate way the parameters of the model so obtained, one can show that both the standard quantum theory for microscopic objects and the classical behavior for macroscopic objects can be derived in a consistent way. In the case of a macroscopic system one can obtain, by means of appropriate approximations, a description of the evolution in terms of a phase-space density distribution obeying a Fokker-Planck diffusion equation. The model also provides the basis for a conceptually appealing description of quantum measurement.


82B99 Equilibrium statistical mechanics
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[1] G. Ludwig, Commun. Math. Phys. 4 pp 331– (1967)
[2] G. Ludwig, Commun. Math. Phys. 9 pp 1– (1968) · Zbl 0159.59701
[3] A. J. Leggett, in: Essays in Theoretical Physics (1984)
[4] J. M. Jauch, Helv. Phys. Acta 37 pp 293– (1964)
[5] A. J. Leggett, Suppl. Progr. Theor. Phys. 69 pp 80– (1980)
[6] A. Barchielli, Nuovo Cimento pp 79– (1982)
[7] A. Barchielli, Found. Phys. 13 pp 779– (1983)
[8] V. Hakim, Phys. Rev. 32 pp 423– (1985)
[9] A. J. Leggett, Contemp. Phys. 25 pp 583– (1984)
[10] R. Haag, J. Math. Phys. 5 pp 848– (1964) · Zbl 0139.46003
[11] G. Ludwig, Commun. Math. Phys. 4 pp 331– (1967) · Zbl 0148.23702
[12] W. H. Zurek, in: Proceedings of the International Symposium on the Foundations of Quantum Mechanics
[13] S. W. Hawking, Commun. Math. Phys. 87 pp 395– (1983) · Zbl 0506.76138
[14] T. Banks, Nucl. Phys. B vec 244 pp 125– (1984)
[15] G. Lindblad, Commun. Math. Phys. 48 pp 119– (1976) · Zbl 0343.47031
[16] K. Kraus, in: States, Effects and Operations (1983) · Zbl 0545.46049
[17] E. Nelson, Phys. Rev. 150 pp 1070– (1966)
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