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      Configurational entropy of Wigner crystals



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          We present a theoretical study of classical Wigner crystals in two- and three-dimensional isotropic parabolic traps aiming at understanding and quantifying the configurational uncertainty due to the presence of multiple stable configurations. Strongly interacting systems of classical charged particles confined in traps are known to form regular structures. The number of distinct arrangements grows very rapidly with the number of particles, many of these arrangements have quite low occurrence probabilities and often the lowest-energy structure is not the most probable one. We perform numerical simulations on systems containing up to 100 particles interacting through Coulomb and Yukawa forces, and show that the total number of metastable configurations is not a well defined and representative quantity. Instead, we propose to rely on the configurational entropy as a robust and objective measure of uncertainty. The configurational entropy can be understood as the logarithm of the effective number of states; it is insensitive to the presence of overlooked low-probability states and can be reliably determined even within a limited time of a simulation or an experiment.

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          Power laws, Pareto distributions and Zipf's law

           MEJ Newman (2005)

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            26 April 2012
            1204.5998 10.1088/0953-8984/23/7/075302


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            A. Radzvilavi\v{c}ius and E. Anisimovas, J. Phys.: Condens. Matter 23, 075302 (2011)
            12 pages, 8 figures. This is an author-created, un-copyedited version of an article accepted for publication in J. Phys.: Condens. Matter. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The definitive publisher-authenticated version is available online at 10.1088/0953-8984/23/7/075302.'
            physics.plasm-ph cond-mat.str-el


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