publication . Article . Preprint . 2008

Information Geometry, Inference Methods and Chaotic Energy Levels Statistics

Cafaro, Carlo;
Open Access
  • Published: 10 Aug 2008 Journal: Modern Physics Letters B, volume 22, pages 1,879-1,892 (issn: 0217-9849, eissn: 1793-6640, Copyright policy)
  • Publisher: World Scientific Pub Co Pte Lt
Abstract
Comment: 9 pages, added correct journal reference
Subjects
free text keywords: Statistical and Nonlinear Physics, Condensed Matter Physics, Riemannian geometry, symbols.namesake, symbols, Physics, Integrable system, Energy level, Probability theory, Chaotic, Quantum mechanics, Magnetic field, Information geometry, Quantum, Statistics, Mathematical Physics
Related Organizations
29 references, page 1 of 2

[1] M. Gell-Mann, ”What is Complexity”, Complexity, vol. 1, no. 1 (1995).

[2] A. Caticha, ”Entropic Dynamics”, in Bayesian Inference and Maximum Entropy Methods in Science and Engineering, ed. by R.L. Fry, AIP Conf. Proc. 617, 302 (2002).

[3] A. Caticha and R. Preuss, ”Maximum entropy and Bayesian data analysis: Entropic prior distributions”, Phys. Rev. E70, 046127 (2004). [OpenAIRE]

[4] S. Amari and H. Nagaoka, Methods of Information Geometry, American Mathematical Society, Oxford University Press, 2000.

[5] A. Caticha, ”Insufficient Reason and Entropy in Quantum Theory” Found. Phys. 30, 227 (2000).

[6] T. Prosen and M. Znidaric, ”Is the efficiency of classical simulations of quantum dynamics related to integrability?”, Phys. Rev. E75, 015202 (2007); T. Prosen and I. Pizorn, ”Operator space entanglement entropy in transverse Ising chain”, Phys. Rev. A76, 032316 (2007). [OpenAIRE]

[7] C. Cafaro, S. A. Ali and A. Giffin, ”An Application of Reversible Entropic Dynamics on Curved Statistical Manifolds”, in Bayesian Inference and Maximum Entropy Methods in Science and Engineering, ed. by Ali Mohammad-Djafari, AIP Conf. Proc. 872, 243-251 (2006).

[8] C. Cafaro and S. A. Ali, ”Jacobi Fields on Statistical Manifolds of Negative Curvature”, Physica D234, 70-80 (2007).

[9] C. Cafaro, ”Information Geometry and Chaos on Negatively Curved Statistical Manifolds”, in Bayesian Inference and Maximum Entropy Methods in Science and Engineering, ed. by K. Knuth, et al., AIP Conf. Proc. 954, 175 (2007).

[10] A. Caticha and C. Cafaro, ”From Information Geometry to Newtonian Dynamics”, in Bayesian Inference and Maximum Entropy Methods in Science and Engineering, ed. by K. Knuth, et al., AIP Conf. Proc. 954, 165 (2007). [OpenAIRE]

[11] L. Casetti, C. Clementi, and M. Pettini, ”Riemannian theory of Hamiltonian chaos and Lyapunov exponents”, Phys. Rev. E54, 5969-5984 (1996). [OpenAIRE]

[12] M. Di Bari and P. Cipriani, ”Geometry and Chaos on Riemann and Finsler Manifolds”, Planet. Space Sci. 46, 1543 (1998).

[13] C. G. J. Jacobi, ”Vorlesungen uber Dynamik”, Reimer, Berlin (1866).

[14] T. Kawabe, ”Indicator of chaos based on the Riemannian geometric approach”, Phys. Rev. E71, 017201 (2005); T. Kawabe, ”Chaos based on Riemannian geometric approach to Abelian-Higgs dynamical system”, Phys. Rev. E67, 016201 (2003).

[15] T. Shibata and K. Kaneto, ”Collective Chaos”, Phys. Rev. Lett. 81, 4116 (1998).

29 references, page 1 of 2
Powered by OpenAIRE Research Graph
Any information missing or wrong?Report an Issue