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Time-Reversal, Irreversibility and Arrow of Time in Quantum Mechanics

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The aim of this paper is to analyze time-asymmetric quantum mechanics with respect of its validity as a non time-reversal invariant, time-asymmetric theory as well as of its ability to determine an arrow of time.

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References

  1. S. Brush, The Kind of Motion We Call Heat (North Holland, Amsterdam, 1976).

  2. Cohen-Tannoudji C., Diou B., Laloe F. (1977). Quantum Mechanics. Wiley, New York

    Google Scholar 

  3. Lee T.D. (1981). Particle Physics and Field Theory. Harwood, New York

    Google Scholar 

  4. A. Bohm and R. Scurek, “The phenomenological preparation–registration arrow of time and its semigroup representation in the RHS Quantum Theory” in Trends in Quantum Mechanics, H. D. Doebner, S. T. Ali, M. Keyl, and R. F. Werner eds., (World Scientific, Singapore-London, 2000); A. Bohm, M. Loewe, and B. Van de Ven, “Time asymmetric quantum theory—I. Modifying an axiom of quantum physics” Fortschr. Phys. 51, 551 (2003); A. Bohm, I. Antoniou, and P. Kielanowski, “A quantum mechanical arrow of time and the semigroup time evolution of Gamow vectors” \ J. Math. Phys. 36, 2593 (1994); A. Bohm, M. Gadella, and M. J. Mithaiwala, “Time asymmetric Quantum Theory: foundations and applications” in The Physics of Communication, Proceedings of the XXII Solvay Conference on Physics (World Scientific, Singapore, 2003), p. 117; R. C. Bishop, A. Bohm, and M. Gadella, “Irreversibility in Quantum Mechanics” Discrete Dynamics in Nature and Society 2004, 75–83 (2004).

    Google Scholar 

  5. I. Prigogine, From Being to Becoming. Time and Complexity in the Physical Sciences (Freeman, New York, 1980); T. Petroski and I. Prigogine, “Alternative formulation of classical and quantum dynamics for non-integrable systems” Physica A 175, 146 (1991); T. Petroski, I. Prigogine, and S. Tasaki, “Quantum theory of non-integrable systems” Physica A 173, 175 (1991).

    Google Scholar 

  6. Antoniou I., Prigogine I. (1993). “Intrinsic irreversibility and integrability of dynamics”. Physica A 192, 443

    Article  ADS  MathSciNet  Google Scholar 

  7. Petrosky T., Prigogine I. (1997). “The extension of classical dynamics for unstable Hamiltonian systems”. Comp. Math. Appl. 34, 1

    Article  MATH  MathSciNet  Google Scholar 

  8. Albert D. (2000). Time and Chance. Harvard, Cambridge (USA)

    MATH  Google Scholar 

  9. Arntzenius F. (2004). “Time reversal operations, representations of the Lorentz group, and the direction of time”. Stud. Hist. Phil. Mod. Phys 35, 31

    Article  MathSciNet  Google Scholar 

  10. Castagnino M., Lara L., Lombardi O. (2003). “The cosmological origin of time asymmetry”. Class. Quant. Grav. 20, 369

    Article  MATH  ADS  MathSciNet  Google Scholar 

  11. Tabor M. (1989). Chaos and Integrability in Nonlinear Dynamics. Wiley, New York

    MATH  Google Scholar 

  12. Castagnino M., Lombardi O. (2004). “Self-induced decoherence: a new approach”. Stud. Hist. Phil. Mod. Phys. 35, 73

    Article  MathSciNet  Google Scholar 

  13. R. Penrose, “Singularities and time asymmetry” in General Relativity, an Einstein Centenary Survey, S. Hawking and W. Israel, eds., (Cambridge, Cambridge, 1979).

  14. Sachs R.G. (1987). The Physics of Time-Reversal. University of Chicago, Chicago

    Google Scholar 

  15. Price H. (1996). Time’s Arrow and the Archimedes’ Point. Oxford, Oxford

    Google Scholar 

  16. Castagnino M., Lara L., Lombardi O. (2003). “The direction of time: from the global arrow to the local arrow”. Int. J. Theor. Phys. 42: 2487

    Article  MATH  MathSciNet  Google Scholar 

  17. Castagnino M., Lombardi O., Lara L. (2003). “The global arrow of time as a geometrical property of the Universe”. Found. Phys. 33, 877

    Article  MathSciNet  Google Scholar 

  18. M. Castagnino and O. Lombardi, “The generic nature of the global and non-entropic arrow of time and the dual role of the energy–momentum tensor” J. Phys. A: Math. and Gen. 37, 4445 (2004); M. Castagnino and O. Lombardi, “The global non-entropic arrow of time: from global geometrical asymmetry to local energy flow” Synthese forthcoming.

  19. J. P. Antoine, “Quantum mechanics beyond Hilbert space” in Irreversibility and Causality, A. Bohm, H-D Doebner and P. Kielanowski, eds., Springer Lecture Notes in Physics, Vol. 504 (Springer, Berlin and New York, 1998), pp 3–33.

  20. Bohm A. (1994). Quantum Mechanics: Fundations and Applications. Springer, Berlin and New York

    Google Scholar 

  21. A. Bohm and M. Gadella, Dirac Kets, Gamow Vectors and Gelfand Triplets, Springer Lecture Notes in Physics, Vol. 348 (Springer, New York, 1989); A. Bohm, M. Gadella, and S. Maxon, “Extending the stationary quantum mechanics of being to a nonstationary quantum theory of becoming and decaying”, Comp. Math. Appl. 34, 427–466 (1997).

    Google Scholar 

  22. M. Gadella and F. Gómez, “A unified mathematical formalism for the Dirac formulation of Quantum Mechanics” Found. Phys. 32, 815 (2002); M. Gadella and F. Gómez, “On the mathematical basis of the Dirac formulation of Quantum Mechanics” Int. J. Theor. Phys. 42, 2225–2254 (2003).

    Google Scholar 

  23. Paley R., Wiener N. (1934). Fourier Transforms in the Complex Domain. American Mathematical Society, New York

    MATH  Google Scholar 

  24. Antoniou I.E., Dmitrieva L., Kuperin Yu., Melnikov Yu. (1997).“Resonances and the extension of dynamics to rigged Hilbert space”. Comp. Math. Appl. 34, 339

    MathSciNet  Google Scholar 

  25. Gadella M., de la Madrid R. (1999). “Resonances and time reversal operator in Quantum mechanics”. Int. J. Theor. Phys. 38, 93

    Article  MATH  Google Scholar 

  26. Gadella M., Laura R. (2001). “Gamow dyads and expectation values” Int. J. Quant. Chem. 81, 307–320

    Article  Google Scholar 

  27. Castagnino M., Gadella M., Id Betan R., Laura R. (2001). “Gamow functionals on operator algebras”. J. Phys. A: Math. Gen. 34, 10067

    Article  MATH  ADS  MathSciNet  Google Scholar 

  28. Civitarese O., Gadella M., Id Betan R. (1999). “On the mean value of the energy for resonant states”. Nucl. Phys. A 660, 255

    Article  ADS  Google Scholar 

  29. Ludwig G. (1983–1985). Foundations of Quantum Mechanics, Vol. I and II, (Springer, Berlin

    MATH  Google Scholar 

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Castagnino, M., Gadella, M. & Lombardi, O. Time-Reversal, Irreversibility and Arrow of Time in Quantum Mechanics. Found Phys 36, 407–426 (2006). https://doi.org/10.1007/s10701-005-9021-0

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