Bounds on integrals of the Wigner function: The hyperbolic case

Wigner functions play a central role in the phase space formulation of quantum mechanics. Although closely related to classical Liouville densities, Wigner functions are not positive definite and may take negative values on subregions of phase space. We investigate the accumulation of these negative values by studying bounds on the integral of an arbitrary Wigner function over noncompact subregions of the phase plane with hyperbolic boundaries. We show using symmetry techniques that this problem reduces to computing the bounds on the spectrum associated with an exactly solvable eigenvalue problem and that the bounds differ from those on classical Liouville distributions. In particular, we show that the total "quasiprobability" on such a region can be greater than 1 or less than zero. (C) 2005 American Institute of Physics.

Indefinite determiner introducing definite referent: a special use of 'yi 'one' + classifier' in Chinese

The indefinite determiner yi 'one'+ classifier' is the most approximate to an indefinite article, like the English a, in Chinese. It serves all the functions characteristic of representative stages of grammaticalization from a numeral to a generalized indefinite determiner as elaborated in the literature. It is established in this paper that the Chinese indefinite determiner has developed a special use with definite expressions, serving as a backgrounding device marking entities as of low thematic importance and unlikely to receive subsequent mentions in ensuing discourse. 'yi+ classifier' in the special use with definite expressions displays striking similarities in terms of semantic bleaching and phonological reduction with the same determiner at the advanced stage of grammaticalization characterized by uses with generics, nonspecifics and nonreferentials. An explanation is offered in terms of an implicational relation between nonreferentiality and low thematic importance which characterize the two uses of the indefinite determiner. While providing another piece of evidence in support of the claim that semantically nonreferentials and entities of low thematic importance tend to be encoded in terms of same linguistic devices in language, findings in this paper have shown how an indefinite determiner can undergo a higher degree of grammaticalization than has been reported in the literature-it expands its scope to mark not only indefinite but also definite expressions as semantically nonreferential and/or thematically unimportant. (C) 2003 Elsevier B.V. All rights reserved.

On the chaotic instability of a nonsliding liquid-filled top with a small spheroidal base via Melnikov-Holmes-Marsden integrals

Chaotic orientations of a top containing a fluid filled cavity are investigated analytically and numerically under small perturbations. The top spins and rolls in nonsliding contact with a rough horizontal plane and the fluid in the ellipsoidal shaped cavity is considered to be ideal and describable by finite degrees of freedom. A Hamiltonian structure is established to facilitate the application of Melnikov-Holmes-Marsden (MHM) integrals. In particular, chaotic motion of the liquid-filled top is identified to be arisen from the transversal intersections between the stable and unstable manifolds of an approximated, disturbed flow of the liquid-filled top via the MHM integrals. The developed analytical criteria are crosschecked with numerical simulations via the 4th Runge-Kutta algorithms with adaptive time steps.