Symmetry results for finite-temperature, relativistic Thomas-Fermi equations

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

In the semi-classical limit the relativistic quantum mechanics of a stationary beam of counter-streaming (negatively charged) electrons and one species of positively charged ions is described by a nonlinear system of finite-temperature Thomas-Fermi equations. In the high temperature/low density limit these Thomas-Fermi equations reduce to the (semi-)conformal system of Bennett equations discussed earlier by Lebowitz and the author. With the help of a sharp isoperimetric inequality it is shown that any hypothetical particle density function which is not radially symmetric about and decreasing away from the beam's axis would violate the virial theorem. Hence, all beams have the symmetry of the circular cylinder.

Original languageEnglish (US)
Pages (from-to)607-626
Number of pages20
JournalCommunications In Mathematical Physics
Volume226
Issue number3
DOIs
StatePublished - Apr 1 2002

Fingerprint

Finite Temperature
Symmetry
symmetry
hypothetical particles
Virial Theorem
virial theorem
Sharp Inequality
Semiclassical Limit
Isoperimetric Inequality
circular cylinders
Circular Cylinder
Violate
nonlinear systems
Streaming
Density Function
Quantum Mechanics
System of equations
temperature
quantum mechanics
counters

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

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Symmetry results for finite-temperature, relativistic Thomas-Fermi equations. / Kiessling, Michael.

In: Communications In Mathematical Physics, Vol. 226, No. 3, 01.04.2002, p. 607-626.

Research output: Contribution to journalArticle

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