On the dynamics of infinitely many charged particles with magnetic confinement

P. Buttà; S. Caprino; G. Cavallaro; C. Marchioro

Bollettino dell'Unione Matematica Italiana (2006)

  • Volume: 9-B, Issue: 2, page 371-395
  • ISSN: 0392-4033

Abstract

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We study the time evolution of a system of infinitely many charged particles confined by an external magnetic field in an unbounded cylindrical conductor and mutually interacting via the Coulomb force. We prove the existence, uniqueness and quasi-locality of the motion. Moreover, we give some nontrivial bounds on its long time behavior.

How to cite

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Buttà, P., et al. "On the dynamics of infinitely many charged particles with magnetic confinement." Bollettino dell'Unione Matematica Italiana 9-B.2 (2006): 371-395. <http://eudml.org/doc/289628>.

@article{Buttà2006,
abstract = {We study the time evolution of a system of infinitely many charged particles confined by an external magnetic field in an unbounded cylindrical conductor and mutually interacting via the Coulomb force. We prove the existence, uniqueness and quasi-locality of the motion. Moreover, we give some nontrivial bounds on its long time behavior.},
author = {Buttà, P., Caprino, S., Cavallaro, G., Marchioro, C.},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {6},
number = {2},
pages = {371-395},
publisher = {Unione Matematica Italiana},
title = {On the dynamics of infinitely many charged particles with magnetic confinement},
url = {http://eudml.org/doc/289628},
volume = {9-B},
year = {2006},
}

TY - JOUR
AU - Buttà, P.
AU - Caprino, S.
AU - Cavallaro, G.
AU - Marchioro, C.
TI - On the dynamics of infinitely many charged particles with magnetic confinement
JO - Bollettino dell'Unione Matematica Italiana
DA - 2006/6//
PB - Unione Matematica Italiana
VL - 9-B
IS - 2
SP - 371
EP - 395
AB - We study the time evolution of a system of infinitely many charged particles confined by an external magnetic field in an unbounded cylindrical conductor and mutually interacting via the Coulomb force. We prove the existence, uniqueness and quasi-locality of the motion. Moreover, we give some nontrivial bounds on its long time behavior.
LA - eng
UR - http://eudml.org/doc/289628
ER -

References

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  1. ALEXANDER, R., Time evolution for infinitely many hard spheres, Commun. Math. Phys., 49 (1976), 217-232. 
  2. BAHN, C. - PARK, Y.M. - YOO, H.J., Nonequilibrium dynamics of infinite particle systems with infinite range interactions, J. Math. Phys., 40 (1999), 4337-4358. Zbl0988.82034
  3. BUTTÀ, P. - CAGLIOTI, E. - MARCHIORO, C., On the long time behavior of infinitely extended systems of particles interacting via a Kac potential, J. Stat. Phys., 108 (2002), 317-339. Zbl1031.82050
  4. BUTTÀ, P. - CAGLIOTI, E. - MARCHIORO, C., On the motion of a charged particle interacting with an infinitely extended system, Commun. Math. Phys., 233 (2003), 545-569. Zbl1034.82040
  5. CAGLIOTI, E. - MARCHIORO, C. - PULVIRENTI, M., Non-equilibrium dynamics of threedimensional infinite particle systems, Commun. Math. Phys., 215 (2000), 25-43. Zbl1019.82010
  6. CAGLIOTI, E. - MARCHIORO, C., On the long time behavior of a particle in an infinitely extended system in one dimension, J. Stat. Phys., 106 (2002), 663-680. Zbl1138.82340
  7. CALDERONI, P. - CAPRINO, S., Time evolution of infinitely many particles: an existence theorem, J. Stat. Phys., 28 (1982), 815-833. Zbl0514.60100
  8. DOBRUSHIN, R.L. - FRITZ, J., Non-equilibrium dynamics of one-dimensional infinite particle systems with a hard-core interaction, Commun. Math. Phys., 55 (1977), 275-292. Zbl0987.82502
  9. FRIEDMAN, A., Stochastic differential equations and applications, vol. I, Academic PressNew York (1975). Zbl0323.60056
  10. FRITZ, J. - DOBRUSHIN, R.L., Non-equilibrium dynamics of two-dimensional infinite particle systems with a singular interaction, Commun. Math. Phys., 57 (1977), 67-81. 
  11. LANFORD, O.E., Classical Mechanics of one-dimensional systems with infinitely many particles. I An existence theorem, Commun. Math. Phys., 9 (1968), 176-191. Zbl0164.25401
  12. Lanford, O.E., Classical Mechanics of one-dimensional systems with infinitely many particles. II Kinetic Theory, Commun. Math. Phys.11 (1969), 257-292. Zbl0175.21401
  13. LANFORD, O.E., Time evolution of large classical systems, Moser Ed. Lect. Notes in Phys., Springer38 (1975). Zbl0329.70011
  14. MARCHIORO, C. - PELLEGRINOTTI, A. - PRESUTTI, E., Existence of time evolution in ν -dimensional Statistical Mechanics, Commun. Math. Phys., 40 (1975), 175-185. 
  15. MARCHIORO, C. - PELLEGRINOTTI, A. - PULVIRENTI, M., Remarks on the existence of non-equilibrium dynamics, Coll. Math. Soc. Janos Bolyai, Proceedings Esztergom Summer School, 27 (1978), 733-746. Zbl0496.60100
  16. MARCHIORO, C. - PULVIRENTI, M., Time evolution of infinite one-dimensional Coulomb Systems, J. Stat. Phys., 27 (1982), 809-822. 
  17. PRESUTTI, E. - PULVIRENTI, M. - TIROZZI, B., Time evolution of infinite classical systems with singular, long-range, two-body interaction, Commun. Math. Phys., 47 (1976), 81-95. 
  18. PULVIRENTI, M., On the time evolution of the states of infinitely extended particle systems, J. Stat. Phys., 27 (1982), 693-713. Zbl0511.60096
  19. RUELLE, D., Statistical Mechanics. Rigorous Results, W.A. Benjamin, Inc., New York-Amsterdam1969. 
  20. SIGMUND-SCHULTZE, R., On non-equilibrium dynamics of multidimensional infinite particle systems in the translation invariant case, Commun. Math. Phys., 100 (1985), 245-265. Zbl0607.60097
  21. SINAI, Y., Construction of the dynamics for one-dimensional systems of Statistical Mechanics, Sov. Theor. Math. Phys., 12 (1973), 487-501. 
  22. SINAI, Y., The construction of the cluster dynamics of dynamical systems in Statistical Mechanics, Vest. Moskow Univ. Sez. I Math. Mech., 29 (1974), 153-176. 

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