Lamb, Wilson and Murdoch, Ian and Stewart, John
(2001)
*On an operator identity central to projection operator methodology.*
Physica A: Statistical Mechanics and its Applications, 298 (1).
pp. 121-139.
ISSN 0378-4371

## Abstract

Derivations of master equations using projection operator methodology are based upon an identity whose validity has been established in only limited contexts. Its proof requires precise definitions of eLt and , where L is the Liouville operator and P the projection operator associated with the limited system information of interest. Here, for interacting particles confined to a box, the existence and uniqueness of system dynamics is demonstrated. A distributional extension of L defined in an L1 space is derived for which is the corresponding updating operator. Attempts to define within current semigroup theory are outlined, and a possible future approach indicated.

Item type: | Article |
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ID code: | 2019 |

Keywords: | liouville operator, projection operator, equations, semigroup theory, Mathematics, Statistics and Probability, Condensed Matter Physics |

Subjects: | Science > Mathematics |

Department: | Faculty of Science > Mathematics and Statistics Faculty of Engineering > Mechanical and Aerospace Engineering |

Depositing user: | Strathprints Administrator |

Date Deposited: | 16 Mar 2007 |

Last modified: | 10 Dec 2015 16:12 |

URI: | http://strathprints.strath.ac.uk/id/eprint/2019 |

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