How Wigner functions transform under symplectic maps

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Description

It is shown that, while Wigner and Liouville functions transform in an identical way under linear symplectic maps, in general they do not transform identically for nonlinear symplectic maps. Instead there are quantum corrections whose {Dirac_h} {r_arrow} 0 limit may be very complicated. Examples of the behavior of Wigner functions in the {Dirac_h} {r_arrow} 0 limit are given in order to examine to what extent the corresponding Liouville densities are recovered.

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9 p.

Creation Information

Dragt, A.J. & Habib, S. May 16, 1998.

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This article is part of the collection entitled: Office of Scientific & Technical Information Technical Reports and was provided by UNT Libraries Government Documents Department to Digital Library, a digital repository hosted by the UNT Libraries. More information about this article can be viewed below.

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  • Dragt, A.J. Univ. of Maryland, College Park, MD (United States). Center for Theoretical Physics
  • Habib, S. Los Alamos National Lab., NM (United States). Theoretical Div.

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Description

It is shown that, while Wigner and Liouville functions transform in an identical way under linear symplectic maps, in general they do not transform identically for nonlinear symplectic maps. Instead there are quantum corrections whose {Dirac_h} {r_arrow} 0 limit may be very complicated. Examples of the behavior of Wigner functions in the {Dirac_h} {r_arrow} 0 limit are given in order to examine to what extent the corresponding Liouville densities are recovered.

Physical Description

9 p.

Notes

INIS; OSTI as DE99001140

Source

  • Advanced ICFA beam dynamics workshop on quantum aspects of beam physics, Monterey, CA (United States), 4-9 Jan 1998

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  • Other: DE99001140
  • Report No.: LA-UR--98-2347
  • Report No.: CONF-980134--
  • Grant Number: W-7405-ENG-36;FG02-96ER40949
  • Office of Scientific & Technical Information Report Number: 291168
  • Archival Resource Key: ark:/67531/metadc687445

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Creation Date

  • May 16, 1998

Added to The UNT Digital Library

  • July 25, 2015, 2:20 a.m.

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  • July 28, 2016, 7:16 p.m.

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Dragt, A.J. & Habib, S. How Wigner functions transform under symplectic maps, article, May 16, 1998; New Mexico. (digital.library.unt.edu/ark:/67531/metadc687445/: accessed September 24, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.