A note on classical ground state energies

Journal of Statistical Physics

Volumn 136, Issue 2, 2009, Pages 275-284

  Kiessling, Michael K H ^a  

^a RUTGERS UNIVERSITY   (United States)

Author keywords

Classical N body systems; Coulomb systems; Data analysis; Fekete points; Ground state energies; Riesz energies; Rigorous results; Thomson's problem

Indexed keywords

EID: 70349335436     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10955-009-9769-2     Document Type: Article

References (24)

1. Altschuler, E.L., Williams, T.J., Ratner, E.R., Tipton, R., Stong, R., Dowla, F., Wooten, F.: Possible global minimum lattice configurations for Thomson's problem of charges on the sphere. Phys. Rev. Lett. 78, 2681-2685 (1997)
2. Atiyah, M., Sutcliffe, P.: Polyhedra in physics, chemistry, and geometry. Milan J. Math. 71, 33-58 (2003)
3. Beck, J.: Sums of distances between points on a sphere-an application of the theory of irregularities of distribution to discrete geometry. Mathematica 31, 33-41 (1984)
4. Bendito, E., Carmona, A., Encinas, A.M., Gesto, J.M.: Estimation of Fekete points. J. Comput. Phys. 225, 2354-2376 (2007)
5. Bowick, M.J., Cacciuto, C., Nelson, D.R., Travesset, A.: Crystalline order on a sphere and the generalized Thomson problem. Phys. Rev. Lett. 89, 185502ff. (2002)
6. Bowick, M.J., Cacciuto, C., Nelson, D.R., Travesset, A.: Crystalline particle packings on a sphere with long range power law potentials. Phys. Rev. B 73, 024115ff (2006)
7. Bowick, M.J., Cecka, C., Middleton, A.: http://tristis.phy.syr.edu/thomson/thomson.php
8. Erber, T., Hockney, G.M.: Complex systems: equilibrium configurations of N equal charges on a sphere (2≤N≤112). In: Prigogine, I., Rice, S.A. (eds.) Adv. Chem. Phys., vol. XCVIII, pp. 495-594. Wiley, New York (1997)
9. Hardin, D.P., Saff, E.B.: Discretizing manifolds via minimum energy points. Not. Am. Math. Soc. 51, 1186-1194 (2004)
10. Hardin, D.P., Saff, E.B.: Minimal Riesz energy point configurations for rectifiable d-dimensional manifolds. Adv. Math. 193, 174-204 (2005)
11. Hardin, R.H., Sloan, N.J.A., Smith, W.D.: Minimal energy arrangements of points on a sphere, ©(1994) HSS. http://www.research.att.com/~njas/electrons
12. Kiessling, M.K.-H., Spohn, H.: A note on the eigenvalue density of random matrices. Commun. Math. Phys. 199, 683-695 (1999)
13. Kiessling, M.K.-H.: The Vlasov continuum limit for the classical microcanonical ensemble. Rev. Math. Phys. (2009, submitted)
14. Kleine Berkenbusch, M., Claus, I., Dunn, C., Kadanoff, L.P., Nicewicz, M., Venkataramani, S.C.: Discrete charges on a two dimensional conductor. J. Stat. Phys. 116, 1301-1358 (2004)
15. Kuijlaars, A.B.J., Saff, E.B.: Asymptotics for minimal discrete energy on the sphere. Trans. Am. Math. Soc. 350, 523-538 (1998)
16. Kuijlaars, A.B.J., Saff, E.B., Sun, X.: On separation of minimal Riesz energy points on spheres in Euclidean spaces. J. Comput. Appl. Math. 199, 172-180 (2007)
17. Pérez-Garrido, A., Dodgson, M.J.W., Moore, M.A., Ortuño, M., Díaz-Sánchez, A.: Comment on: 'Possible global minimum lattice configurations for Thomson's problem of charges on a sphere'. Phys. Rev. Lett. 79, 1417 (1997)
18. Rakhmanov, E.A., Saff, E.B., Zhou, Y.M.: Minimal discrete energy on the sphere. Math. Res. Lett. 1, 647-662 (1994)
19. Rakhmanov, E.A., Saff, E.B., Zhou, Y.M.: Electrons on the sphere. In: Ali, R.M., Ruscheweyh, S., Saff, E.B. (eds.) Computational Methods and Function Theory, pp. 111-127, World Scientific, Singapore, (1995)
20. Saff, E.B., Kuijlaars, A.B.J., Distributing many points on a sphere. Math. Intell. 19, 5-11 (1997)
21. Smale, S.: Mathematical problems for the next century. Math. Intell. 20, 7-15 (1998); see also version 2 on Steve Smale's home page: http://math.berkeley.edu/~smale/
22. Thomson, J.J.: On the structure of the atom: an investigation of the stability and periods of oscillation of a number of corpuscles arranged at equal intervals around the circumference of a circle; with application of the results to the theory of atomic structure. Philos. Mag. 7, 237-265 (1904)
23. Whyte, L.L.: Unique arrangements of points on a sphere. Am. Math. Mon. 59, 606-611 (1952)
24. Womersley, R.S.: Robert Womersley's home page. http://web.maths.unsw.edu.au/~rsw/