Research PapersNo Access

INFORMATION GEOMETRY, INFERENCE METHODS AND CHAOTIC ENERGY LEVELS STATISTICS

CARLO CAFARO

Department of Physics, State University of New York at Albany-SUNY, 1400 Washington Avenue, Albany, NY 12222, USA

https://doi.org/10.1142/S0217984908016558Cited by:18 (Source: Crossref)

Abstract

In this letter, we propose a novel information-geometric characterization of chaotic (integrable) energy level statistics of a quantum antiferromagnetic Ising spin chain in a tilted (transverse) external magnetic field. Finally, we conjecture our results might find some potential physical applications in quantum energy level statistics.

Keywords:

PACS: 02.50.Tt, 02.40.Ky, 02.50.Cw, 05.45.-a

References

M. Gell-Mann, Complexity 1(1), 16 (1995). Crossref, Google Scholar
A. Caticha, AIP Conf. Proc. 617, 302 (2002), DOI: 10.1063/1.1477054. Crossref, ADS, Google Scholar
A. Caticha and R. Preuss, Phys. Rev. E 70, 046127 (2004), DOI: 10.1103/PhysRevE.70.046127. Crossref, Web of Science, Google Scholar
S. Amari and H. Nagaoka , Methods of Information Geometry ( American Mathematical Society , Oxford University Press , 2000 ) . Google Scholar
A. Caticha, Found. Phys. 30, 227 (2000), DOI: 10.1023/A:1003692916756. Crossref, Web of Science, Google Scholar
T. Prosen and M. Znidaric, Phys. Rev. E 75 (2007) 015202; T. Prosen and I. Pizorn, Phys. Rev. A 76 (2007) 032316 . Google Scholar
C. Cafaro, S. A. Ali and A. Giffin, AIP Conf. Proc. 872, 243 (2006), DOI: 10.1063/1.2423281. Crossref, ADS, Google Scholar
C. Cafaro and S. A. Ali, Physica D 234, 70 (2007), DOI: 10.1016/j.physd.2007.07.001. Crossref, Web of Science, ADS, Google Scholar
C. Cafaro, AIP Conf. Proc. 954, 175 (2007), DOI: 10.1063/1.2821260. Crossref, ADS, Google Scholar
A. Caticha and C. Cafaro, AIP Conf. Proc. 954, 165 (2007), DOI: 10.1063/1.2821259. Crossref, ADS, Google Scholar
L. Casetti, C. Clementi and M. Pettini, Phys. Rev. E 54, 5969 (1996), DOI: 10.1103/PhysRevE.54.5969. Crossref, Web of Science, Google Scholar
M. Di Bari and P. Cipriani, Planet. Space Sci. 46, 1543 (1998). Crossref, Web of Science, ADS, Google Scholar
C. G. J. Jacobi , Vorlesungen uber Dynamik ( Reimer , Berlin , 1866 ) . Google Scholar
T. Kawabe, Phys. Rev. E 71 (2005) 017201; T. Kawabe, ibid. 67 (2003) 016201 . Google Scholar
T. Shibata and K. Kaneto, Phys. Rev. Lett. 81, 4116 (1998), DOI: 10.1103/PhysRevLett.81.4116. Crossref, Web of Science, ADS, Google Scholar
E. N. Lorenz, J. Atmos. Sci. 20, 130 (1963). Crossref, Web of Science, ADS, Google Scholar
R. F. Fox and J. Keizer, Phys. Rev. A 43, 1709 (1991), DOI: 10.1103/PhysRevA.43.1709. Crossref, Web of Science, ADS, Google Scholar
W. H. Zurek and J. P. Paz, Phys. Rev. Lett. 72 (1994) 2508; Physica D 83 (1995) 300 . Google Scholar
C. M. Caves and R. Schack, Complexity 3 (1997) 46–57; A. J. Scott, T. A. Brun, C. M. Caves and R. Schack, J. Phys. A 39 (2006) 13405 . Google Scholar
W. H. Zurek, Prog. Theor. Phys. 89, 281 (1993), DOI: 10.1143/PTP.89.281. Crossref, ADS, Google Scholar
G. Casati and B. Chirikov, Quantum Chaos (Cambridge University Press, 1995); M. V. Berry, Chaotic Behavior in Dynamical Systems, ed. G. Casati (New York, Plenum, 1985); M. Robnik and T. Prosen, Comment on energy level statistics in the mixed regimes, arXiv: chao-dyn/9706023 (1997) . Google Scholar
F. Haake , Quantum Signatures of Chaos ( Springer-Verlag , Berlin , 1991 ) . Crossref, Google Scholar
A. Wolf et al., Physica D 16 (1985) 285–317; J. Wright, Phys. Rev. A 29 (1984) 2924–2927 . Google Scholar
P. Grassberger and I. Procaccia, Phys. Rev. A 28, 2591 (1983), DOI: 10.1103/PhysRevA.28.2591. Crossref, Web of Science, ADS, Google Scholar
O. Bohigaset al., Phys. Rev. Lett. 52, 1 (1984), DOI: 10.1103/PhysRevLett.52.1. Crossref, Web of Science, ADS, Google Scholar
M. C. Gutzwiller , Chaos in Classical and Quantum Mechanics ( Springer-Verlag , New York , 1990 ) . Crossref, Google Scholar
A. M. Garcia-Garcia and J. Wang, Universality in quantum chaos and the one parameter scaling theory, arXiv: 0707.3964 (2007); Acta Phys. Polonica A 112 (2007) 635–653 . Google Scholar
Y. Gu, Phys. Lett. A 149 (1990) 95–100; J. P. Keating, Nonlinearity 4 (1991) 277–307; J. P. Keating, ibid. 4 (1991) 309–341 . Google Scholar
F. M. Izrailev, Phys. Rep. 196, 299 (1990), DOI: 10.1016/0370-1573(90)90067-C. Crossref, Web of Science, ADS, Google Scholar