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The maximum entropy method and relaxation for multiple collisions involving highly charged ions
Author(s) -
Goscinski Osvaldo,
Hägg Lotten
Publication year - 1996
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/(sici)1097-461x(1996)58:6<689::aid-qua11>3.0.co;2-t
Subject(s) - hessian matrix , positive definiteness , principle of maximum entropy , gaussian , statistical physics , definiteness , computation , mathematics , relaxation (psychology) , hermite polynomials , charge (physics) , physics , quantum mechanics , positive definite matrix , eigenvalues and eigenvectors , algorithm , psychology , social psychology , linguistics , statistics , philosophy
Advantages and disadvantages of the maximum entropy method ( MEM ) in application to the theory of relaxation are studied. The time evolution of distributions and of associated moments must obey stringent conditions for both finite and infinite intervals. The theoretical considerations are illustrated with examples from charge‐state distributions arising in beam‐foil spectroscopy. The examples indicate that the possibility to include more than two moments (extension to non‐Gaussian case) is severely limited (though feasible) in the static case due to nonpositive definiteness as well as stiffness of the Hessian matrices appearing in the computations. This takes place already for the finite charge‐state distribution intervals. For infinite intervals, this is a severe problem as required by the Marcinkiewicz theorem, affecting characteristic functions and, hence, the description of the time evolution of distributions. © 1996 John Wiley & Sons, Inc.