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2012 | 10 | 2 | 390-397
Tytuł artykułu

Physical implications of Fisher-information’s scaling symmetry

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We study the scaling properties of Fisher’s information measure (FIM) and show that from these one can straightforwardly deduce significant quantum-mechanical results. Specifically, we investigate the scaling properties of Fisher’s measure I and encounter that, from the concomitant operating rules, several interesting, albeit known, results can be derived. This entails that such results can be regarded as pre-configured by the conjunction of scaling and information theory. The central notion to be arrived at is that scaling entails that I must obey a certain partial differential equation (PDE). These PDE-solutions have properties that enable the application of a Legendre-transform (LT). The conjunction PDE+LT leads one to obtain several quantum results without recourse to the Schrödinger’s equation.
Wydawca

Czasopismo
Rocznik
Tom
10
Numer
2
Strony
390-397
Opis fizyczny
Daty
wydano
2012-04-01
online
2012-03-31
Twórcy
  • Facultad de Ingeniería, Grupo de Investigación Teórica y Aplicada en Teoría de la Información (GTyATI), Universidad Nacional de La Plata, 1900, La Plata, Argentina
Bibliografia
  • [1] P. W. Anderson, Science 177, 303 (1972) http://dx.doi.org/10.1126/science.177.4047.393[Crossref]
  • [2] J. Zinn-Justin, Quantum Field Theory and Critical Phenomena (Oxford University Press, Oxford, 2002) http://dx.doi.org/10.1093/acprof:oso/9780198509233.001.0001[Crossref]
  • [3] R. N. Silver, In: Physics and Probability, W. T. Grandy Jr. and P. W. Milonni (Eds.) (Cambridge University Press, Cambridge, England, 1992)
  • [4] B. R. Frieden, Physics from Fisher information measure (Cambridge, University Press, Cambridge, 1998) http://dx.doi.org/10.1017/CBO9780511622670[Crossref]
  • [5] B. R. Frieden, Science from Fisher information (Cambridge University Press, Cambidge, 2004) http://dx.doi.org/10.1017/CBO9780511616907[Crossref]
  • [6] B. R. Frieden, A. Plastino, A. R. Plastino, B. H. Soffer, Phys. Rev. E 60, 48 (1999) http://dx.doi.org/10.1103/PhysRevE.60.48[Crossref]
  • [7] S. P. Flego, B. R. Frieden, A. Plastino, A. R. Plastino, B. H. Soffer, Phys. Rev. E 68, 016105 (2003) http://dx.doi.org/10.1103/PhysRevE.68.016105[Crossref]
  • [8] F. Olivares, F. Pennini, A. Plastino, Physica A 389, 2218 (2010) http://dx.doi.org/10.1016/j.physa.2010.01.043[Crossref]
  • [9] S. P. Flego, F. Olivares, A. Plastino, M. Casas, Entropy 13, 184 (2011) http://dx.doi.org/10.3390/e13010184[Crossref]
  • [10] S. P. Flego, A. Plastino, A. R. Plastino, Physica A 390, 2276 (2011) http://dx.doi.org/10.1016/j.physa.2011.02.019[Crossref]
  • [11] M. J. W Hall, Phys. Rev. A 62, 012107 (2000) http://dx.doi.org/10.1103/PhysRevA.62.012107[Crossref]
  • [12] F. Pennini, A. Plastino, B. H. Soffer, C. Vignat, Phys. Lett. A 373, 817 (2009) http://dx.doi.org/10.1016/j.physleta.2009.01.007[Crossref]
  • [13] R. Gonzalez-Ferez, J. S. Dehesa, Phys. Rev. Lett. 91, 113001 (2003) http://dx.doi.org/10.1103/PhysRevLett.91.113001[Crossref]
  • [14] J. S. Dehesa, R. Gonzalez-Ferez, P. Sanchez-Moreno, J. Phys. A 40, 1845 (2007) http://dx.doi.org/10.1088/1751-8113/40/8/011[Crossref]
  • [15] A. Katz, Principles of Statistical Mechanics: The Information Theory Approach (Freeman and Co., San Francisco, 1967)
  • [16] E. T. Jaynes, Phys. Rev. 106, 620 (1957) http://dx.doi.org/10.1103/PhysRev.106.620[Crossref]
  • [17] H. Cramer, Mathematical methods of statistics (Princeton University Press, Princeton, NJ, 1946)
  • [18] C. R. Rao, Bull. Calcutta. Math. Soc 37, 81 (1945)
  • [19] W. Greiner and B. Mueller, Quantum mechanics. An introduction (Springer, Berlin, 1988).
  • [20] S. P. Flego, A. Plastino, A. R. Plastino, Physica A 390, 4702 (2011) http://dx.doi.org/10.1016/j.physa.2011.06.050[Crossref]
  • [21] The Schrödinger (SE) enters in [20] because, if one minimizes Fisher’s I subject to constraints, one is straightforwardly led to a SE as the result of the variational process (see, for instance, [6])
  • [22] E. A. Deslogue, Thermal Physics (Holt, Rinehart and Winston, New York, 1968)
  • [23] S. P. Flego, A. Plastino, A. R. Plastino, J. Math. Phys. 52, 082103 (2011) http://dx.doi.org/10.1063/1.3625265[Crossref]
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  • [26] R. Shankar, Principles of Quantum Mechanics (Plenum Press, New York, 1994)
Typ dokumentu
Bibliografia
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Identyfikator YADDA
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