On Kinetic Equations for Particles with Internal Degress of Freedom

Waldmann, L.

doi:10.1007/978-3-7091-8336-6_12

Cited by 3 publications

(2 citation statements)

References 30 publications

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“…For our purposes here it is still most convenient when discussing the dilute quantum gas to form from the yon Neumann equation We will not have space to here discuss the most interesting interference effects due to degeneracy of the internal states of the molecules, which lead to such "exotic" effects as the Senftleben-Beenakker effect, alignment of non-spherical molecules by transport processes, etc. [65,66]. These are described by a generalization of the Boltzmann equation due to Waldmann [67] and Snider [57].…”

Section: (3z6)mentioning

confidence: 99%

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Aspects of non-equilibrium quantum statistical mechanics: An introduction

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Lectures in Statistical Physics

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Section: (3z6)mentioning

confidence: 99%

“…Thus, the theorem is valid for polyatomic molecules. The only generalization of Boltzmann's H-theorem in terms of reduced distribution functions is to include internal structure using the Waldman-Snider equation [57,65,75]. However, the , .…”

Section: 18)mentioning

confidence: 99%

Aspects of non-equilibrium quantum statistical mechanics: An introduction

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Lectures in Statistical Physics

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Fock‐Space Methods for Identical Classical Objects

1980

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Fock-Space (annihilation/creation operator) methods are introduced to describe systems of identical classical objects. Specific examples to which this formalism is applied are branching processes (including age dependent ones), chemical reactions, deterministic (Hamiltonian) systems, and generalized kinetic equations. Finally, a generalization to stochastic quantum systems is proposed which is applied to a gas of spinning molecules.

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Some fundamental questions concerning the kinetic theory of electrons in molecular gases and the e–H₂vibrational cross section controversy

Robson

White

Morrison

2003

J. Phys. B: At. Mol. Opt. Phys.

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We commence a fundamental re-examination of the kinetic theory of charged particle swarms in molecular gases, focusing on collisional excitation of molecular rotational and ro-vibrational states by electrons. Modern day analysis of electron swarms has been based upon the kinetic equation of Wang-Chang et al, which simply treats all processes as scalar energy excitations, and ignores angular momentum conservation and the vector dynamics associated with rotational excitation. It is pointed out that there is no alternative, more exact kinetic equation readily available for electrons which enables one to directly ascertain the degree of error introduced by this approximation. Thus in this preliminary study, we approach the problem indirectly, from the standpoint of the neutral molecules, using the Waldmann-Snider quantum kinetic equation, and insist that an electron-molecule collision must look the same from the perspective of both electron and molecule. We give a formula for quantitatively assessing the importance of scalar versus vectorial treatments of rotational excitation by looking at the post-collisional 'echo' produced by an electron swarm as it passes through the gas. It is then pointed out that in order to remedy any deficiency, it will be necessary to introduce a kinetic collisional operator non-local in space to properly account for angular momentum conservation, as has long been established in the literature. This is a major exercise and given the preliminary nature of this study, we consider the inclusion of such effects from a formal point of view only. In particular we show how non-local effects lead to a spatially dependent 'source' term in the equation of continuity, and hence to corrections for both drift velocity and diffusion coefficients. The magnitude of these corrections has yet to be established.

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On Kinetic Equations for Particles with Internal Degress of Freedom

Cited by 3 publications

References 30 publications

Aspects of non-equilibrium quantum statistical mechanics: An introduction

Aspects of non-equilibrium quantum statistical mechanics: An introduction

Fock‐Space Methods for Identical Classical Objects

Some fundamental questions concerning the kinetic theory of electrons in molecular gases and the e–H₂vibrational cross section controversy

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On Kinetic Equations for Particles with Internal Degress of Freedom

Cited by 3 publications

References 30 publications

Aspects of non-equilibrium quantum statistical mechanics: An introduction

Aspects of non-equilibrium quantum statistical mechanics: An introduction

Fock‐Space Methods for Identical Classical Objects

Some fundamental questions concerning the kinetic theory of electrons in molecular gases and the e–H2vibrational cross section controversy

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Product

Resources

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Some fundamental questions concerning the kinetic theory of electrons in molecular gases and the e–H₂vibrational cross section controversy