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)


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

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.


Transport Coefficient Perturbative Expansion Single Particle State Hamiltonian Dynamic Nonequilibrium Thermodynamic 
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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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