Transport Phenomena in Many-Particle Systems and the Quantum Statistical Approach to Nonequilibrium Thermodynamics

  • G. Röpke
Conference paper
Part of the Springer Series in Synergetics book series (SSSYN, volume 33)

Abstract

A many-particle system described by the Hamiltonian
$$ {\text{H}}_{\text{s}}\; = \;\sum\limits_{\text{k}} {\text{E}} \left( {\text{k}} \right){\text{a}}_{\text{k}}^ + {\text{a}}_{\text{k}} \; + \;1/2\sum\limits_{kpq} {{\text{V}}\left( {{\text{k,p,q}}} \right)} {\text{a}}_{{\text{k + q}}}^ + {\text{a}}_{{\text{p - q}}}^ + {\text{a}}_{\text{p}} {\text{a}}_{\text{k}} $$
(1)

is considered; k denotes the momentum and further internal quantumnumbers as spin ,isospin etc. of a single particle state, \( {\text{E}}\left( {\text{k}} \right) = \hbar ^2 \; * \; * \;{\text{k}}^2 /2{\text{m}}_{{\text{k}}\;} ;\;{\text{a}}_{\text{k}}^ + ,{\text{a}}_{\text{k}} \)are the Fermionic creation and annihilation operators, respectively. To be specific, let us consider a Coulomb system consisting of electrons and protons so that \({\text{V}}\left( {\text{k,p,q}} \right)\; = \;{\text{e}}_{\text{k}} {\text{e}}_{\text{p}} /\varepsilon _o {\text{q}}^2 \).As a consequence of this interaction, bound states such as Hydrogen atoms and molecules may be formed, and in the density-temperature plane different states occur, like the fully ionized plasma, the partially ionized plasma, atomic and molecular Hydrogen gas, solid, liquid, and metallic Hydrogen, cf. Fig. 1.

Keywords

Entropy Lism 

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Copyright information

© Springer-Verlag Berlin Heidelberg 1986

Authors and Affiliations

  • G. Röpke
    • 1
  1. 1.Sektion PhysikWilhelm-Pieck-Universität RostockRostockGermany

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