Abstract.
Atomic avoided crossings in strong magnetic and electric fields are usually identified by the energy level repulsion and by the sharp extremal value of the Shannon’s entropy of the two involved states. In this work the proposal of a new information-theoretic parameter, the continuous Fisher information, for the prediction and characterization of these nonlinear phenomena is done. For just around the irregular region it is found that Fisher’s informations of the two states cross over and show that the states exchange their informational character. Moreover, the state Fisher information sum keeps constant through the avoided crossing. This is illustrated for some hydrogenic excited states in strong magnetic fields as well as in parallel magnetic and electric fields.
Similar content being viewed by others
References
J. von Neumann, E.P. Wigner, Z. Phys. 30, 467 (1929)
H. Ruder, G. Wunner, H. Herold, F. Geyer, Atoms in Strong Magnetic Fields (Springer, Berlin, 1994)
Atoms and Molecules in Strong External Fields, edited by P. Schmelcher, W. Schweizer (Plenum Press, New York, 1998)
R. González-Férez, J.S. Dehesa, Chem. Phys. Lett. 373, 615 (2003)
R. González-Férez, J.S. Dehesa, Phys. Rev. Lett. 91, 113001 (2003)
C.E. Shannon, Bell Syst. Tech. J. 27, 623 (1948)
R.A. Fisher, Proc. Cambridge Philos. Soc. 32, 700 (1925)
C.E. Shannon, W. Weaver, The Mathematical Theory of Communication (University of Illinois Press, Urbana, 1949)
B.R. Frieden, Phys. Rev. A 41, 4265 (1990)
B.R. Frieden, Physics from Fisher Information (Cambridge University Press, Cambridge, 1998)
B.R. Frieden, Science from Fisher Information (Cambridge University Press, Cambridge, 2004)
W. Schweizer, P. Fassbinder, R. González-Férez, M. Braun, S. Kulla, M. Stehle, J. Comp. App. Math. 109, 95 (1999)
A. Stam, Inf. Control. 2, 101 (1959)
E. Romera, J.S. Dehesa, Phys. Rev. A 50, 256 (1994)
E. Romera, J.C. Angulo, J.S. Dehesa, Phys. Rev. A 59, 4064 (1999)
B.R. Frieden, A. Plastino, A.R. Plastino, B.H. Soffer, Phys. Rev. E 66, 046128 (2002)
Z. Chen, S.P. Goldman, Phys. Rev. A 48, 1107 (1993)
R.H. Garstang, Rep. Prog. Phys. 40, 105 (1977)
H. Friedrich, D. Wintgen, Phys. Rep. 183, 37 (1989)
C. Brukner, A. Zeilinger, Phys. Rev. A 63, 022113 (2001)
S. Luo, Found. Phys. 32, 1757 (2002)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
González-Férez, R., Dehesa, J. Characterization of atomic avoided crossings by means of Fisher’s information. Eur. Phys. J. D 32, 39–43 (2005). https://doi.org/10.1140/epjd/e2004-00182-3
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1140/epjd/e2004-00182-3