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On the Spatial Density Matrix for the Centre of Mass of a One-Dimensional Perfect Gas

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Foundations of Physics Letters

Abstract

We examine the reduced density matrix of the centre of mass on position basis considering a one-dimensional system of Nnoninteracting distinguishable particles in a infinitely deep square potential well. We find a class of pure states of the system for which the off-diagonal elements of the matrix above go to zero as Nincreases. This property holds also for the state vectors which are factorized in the single particle wave functions. In this last case, if the average energy of each particle is less than a common bound, the diagonal elements are distributed according to the normal law with a mean square deviation which becomes smaller and smaller as Nincreases towards infinity. Therefore when the state vectors are of the type considered we cannot experience spatial superpositions of the centre of mass and we may conclude that position is a preferred basis for the collective variable.

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REFERENCES

  1. G. C. Ghirardi, A. Rimini, and T. Weber Phys. Rev. D 34, 470 (1986). P. Pearle, Phys. Rev. A 39, 2277 (1989). G. C. Ghirardi, P. Pearle, and A. Rimini Phys. Rev. A 42, 78 (1990).

    Article  ADS  MathSciNet  Google Scholar 

  2. W. H. Zurek, Phys. Rev. D 26 1862 (1982). E. Joos and H. D. Zeh, Z. Phys. B 59, 223 (1985). A. O. Caldeira and A. J. Legget, Phys. Rev. A 31, 1059 (1985). W. H. Zurek, Phys. Today 44, 86 (1991); 46, 81 (1993); Prog. Theor. Phys. 89, 281 (1993). J. P. Paz and W. H. Zurek, Phys. Rev. D 48, 2728 (1993). R. Omnès, The Interpretation of Quantum Mechanics (University Press, Princeton, 1994), Chap. 7.

    Article  ADS  MathSciNet  Google Scholar 

  3. W. Feller, An Introduction to Probability Theory and Its Applications (Wiley, New York, 1966), p. 264.

    MATH  Google Scholar 

  4. M. Tegmark and H. S. Shapiro, Phys. Rev. E 50, 2538 (1994).

    Article  ADS  Google Scholar 

  5. A. Reny, Foundations of Probability (Holden-Day, San Francisco, 1970).

    Google Scholar 

  6. Don N. Page, Phys. Rev. Lett. 71, 1291 (1993).

    Article  ADS  MathSciNet  Google Scholar 

  7. B. Carazza, Found. Phys. Lett. 9 79 (1996).

    Article  MathSciNet  Google Scholar 

  8. B. d'Expagnat, Found. Phys. 20, 1147 (1990).

  9. M. Jammer, The Philosophy of Quantum Mechanics (Wiley, New York, 1974), p. 218.

    Google Scholar 

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  1. Dipartimento di Fisica dell' Università, viale delle Scienze, 143100, Parma, INFN Sezione di Cagliari, Italy

    B. Carazza

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  1. B. Carazza
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Carazza, B. On the Spatial Density Matrix for the Centre of Mass of a One-Dimensional Perfect Gas. Found Phys Lett 10, 581–590 (1997). https://doi.org/10.1023/A:1022449319701

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  • DOI: https://doi.org/10.1023/A:1022449319701

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