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The Nonlinear Diffusion of a Planckian Particle in Superspace–Time

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Russian Physics Journal Aims and scope

It is shown that there is a nonlinear differential equation of a diffusion type possessing time asymmetry. The equation can be used for description of irreversible evolution of a Planckian particle in superspace–time.

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References

  1. A. Einstein, Collection of Research Papers, V. I [Russian translation], Nauka, Moscow, 1965.

    Google Scholar 

  2. D. Hilbert, Selected Works, V. 2 [Russian translation], Factorial, Moscow, 1998.

    Google Scholar 

  3. B. S. De Witt, 160 D, 1113 (1967).

  4. B. S. De Witt, Phys. Rev., 162 D, 1195 (1967).

    Google Scholar 

  5. A. A. Logunov, Gravitation-Field Theory [in Russian], Nauka, Moscow, 2001.

    Google Scholar 

  6. A. A. Logunov and M. A. Mestvirishvili, Usp. Fiz. Nauk, 165, 187–203 (1995).

    Article  Google Scholar 

  7. S. S. Gerstein, A. A. Logunov, and M. A. Mestvirishvili, Usp. Fiz. Nauk, 176, 1207–1225 (2006).

    Article  Google Scholar 

  8. S. S. Gerstein, A. A. Logunov, M. A. Mestvirishvili, and N. P. Tkachenko, Elem.Part. Atom. Nucl., 36, Vyp. 5, 1003–1050 (2005).

    Google Scholar 

  9. A. A. Logunov and M. A. Mestvirishvili, Relativistic Gravitation Theory [in Russian], Nauka, Moscow, 1989.

    Google Scholar 

  10. A. A. Logunov, Yu. M. Loskutov, and M. A. Mestvirishvili, Usp. Fiz. Nauk, 155, 369– 395 (1988).

    Article  ADS  MathSciNet  Google Scholar 

  11. E. B. Gliner, Usp. Fiz. Nauk, 172, 221 (2002).

    Article  Google Scholar 

  12. E. B. Gliner, Zh. Eks. Teor. Fiz., 49, 342 (1965).

    Google Scholar 

  13. E. B. Gliner, Dokl. Akad. Nauk SSSR, 192, 771 (1970).

    ADS  Google Scholar 

  14. I. G. Dymnikova, Zh. Eks. Teor. Fiz., 90, 1900 (1986).

    ADS  Google Scholar 

  15. E. B. Gliner and I. G. Dymnikova, Pis’ma v Astron. Zh., 1, 7 (1975).

    ADS  Google Scholar 

  16. I. G. Dymnikova, Phys. Lett. B, 472, 33 (2000).

    Article  ADS  MATH  MathSciNet  Google Scholar 

  17. I. G. Dymnikova, Gen. Rel. Grav., 24, 235 (1992).

    Article  ADS  MathSciNet  Google Scholar 

  18. I. G. Dymnikova, Int. J. Mod. Phys., 5, 529 (1996).

    Article  ADS  MathSciNet  Google Scholar 

  19. B. L. Altshuler and A. O. Barvinskii, Usp. Fiz. Nauk, 166, 46 (1996).

    Google Scholar 

  20. V. V. Lasukov, Russ. Phys. J., 47, No. 1, 31 (2004).

    Article  MATH  Google Scholar 

  21. V. V. Lasukov, Russ. Phys. J., 52, No. 6, 568 (2009).

    Article  MATH  Google Scholar 

  22. V. V. Lasukov, Russ. Phys. J., 52, No. 9, 920 (2009).

    Article  MATH  Google Scholar 

  23. V. V. Lasukov, Russ. Phys. J., 55, No. 1, 1 (2012).

    Article  MATH  MathSciNet  Google Scholar 

  24. V. V. Lasukov, Russ. Phys. J., 45, No. 5, 528 (2002).

    Article  MATH  Google Scholar 

  25. V. V. Lasukov, Russ. Phys. J., 46, No. 4, 407 (2003).

    Article  MathSciNet  Google Scholar 

  26. V. V. Lasukov, Russ. Phys. J., 46, No. 9, 903 (2003).

    Article  Google Scholar 

  27. V. V. Lasukov, Russ. Phys. J., 47, No. 1, 31 (2004).

    Article  MATH  Google Scholar 

  28. V. V. Lasukov, Russ. Phys. J., 47, No. 4, 345 (2004).

    Article  MathSciNet  Google Scholar 

  29. V. V. Lasukov, Russ. Phys. J., 47, No. 6, 638 (2004).

    Article  MATH  Google Scholar 

  30. V. V. Lasukov, Russ. Phys. J., 48, No. 1, 15 (2005).

    Article  Google Scholar 

  31. V. V. Lasukov, Russ. Phys. J., 49, No. 4, 352 (2006).

    Article  MATH  MathSciNet  Google Scholar 

  32. V. V. Lasukov, Russ. Phys. J., 50, No. 4, 326 (2007).

    Article  MATH  MathSciNet  Google Scholar 

  33. V. V. Lasukov, Russ. Phys. J., 50, No. 8, 839 (2007).

    Article  MATH  Google Scholar 

  34. V. V. Lasukov, Russ. Phys. J., 50, No. 9, 898 (2007).

    Article  MATH  Google Scholar 

  35. V. V. Lasukov, Russ. Phys. J., 51, No. 3, 321 (2008).

    Article  MATH  MathSciNet  Google Scholar 

  36. V. V. Lasukov, Russ. Phys. J., 51, No. 8, 815 (2008).

    Article  MATH  MathSciNet  Google Scholar 

  37. V. V. Lasukov, Russ. Phys. J., 52, No. 2, 176 (2009).

    Article  Google Scholar 

  38. V. V. Lasukov, Russ. Phys. J., 52, No. 4, 337 (2009).

    Article  MATH  MathSciNet  Google Scholar 

  39. V. V. Lasukov, Russ. Phys. J., 52, No. 6, 568 (2009).

    Article  MATH  Google Scholar 

  40. V. V. Lasukov, Russ. Phys. J., 52, No. 9, 920 (2009).

    Article  MATH  Google Scholar 

  41. V. V. Lasukov, Russ. Phys. J., 52, No. 8, 816 (2009).

    Article  MATH  Google Scholar 

  42. V. V. Lasukov, Russ. Phys. J., 53, No. 3, 296 (2010).

    Article  MATH  MathSciNet  Google Scholar 

  43. V. V. Lasukov, Russ. Phys. J., 54, No. 1, 1 (2011).

    Article  Google Scholar 

  44. V. V. Lasukov, Russ. Phys. J., 54, No. 7, 801 (2011).

    Article  MathSciNet  Google Scholar 

  45. V. V. Lasukov, Russ. Phys. J., 54, No. 10, 1093 (2011).

    Article  MathSciNet  Google Scholar 

  46. V. V. Lasukov, Russ. Phys. J., 55, No. 2, 140 (2012).

    Article  Google Scholar 

  47. V. V. Lasukov, Russ. Phys. J., 55, No. 10, 1157 (2012).

    Article  MathSciNet  Google Scholar 

  48. C. W. Misner and J. A. Wheeler, Ann. Phys., 2, 525 (1957).

    Article  ADS  MATH  MathSciNet  Google Scholar 

  49. J. A. Wheeler, Ann. Phys., 2, 604–614 (1957).

    Article  ADS  MATH  Google Scholar 

  50. J. M. Burgers, The Nonlinear Diffusion Equation, D. Reidel, Dordrecht, 1974.

    Book  MATH  Google Scholar 

  51. J. D. Bekenstein, Nuovo Cim. Lett., 4, 737 (1972).

    Article  ADS  Google Scholar 

  52. J. D. Bekenstein, Phys. Rev. D, 7, 2333 (1973).

    Article  ADS  MathSciNet  Google Scholar 

  53. J. D. Bekenstein, Phys. Rev. D, 9, 3292 (1974).

    Article  ADS  Google Scholar 

  54. S. W. Hawking, Commun. Math. Phys., 43, 199 (1975).

    Article  ADS  MathSciNet  Google Scholar 

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Correspondence to V. V. Lasukov.

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Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 92–98, September, 2013.

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Lasukov, V.V. The Nonlinear Diffusion of a Planckian Particle in Superspace–Time. Russ Phys J 56, 1076–1082 (2014). https://doi.org/10.1007/s11182-014-0142-9

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