dorsal/arxiv
View SchemaA path-integral approach to the collisionless Boltzmann gas
| Authors | C. Y. Chen |
|---|---|
| Categories | |
| ArXiv ID | physics/0006033 |
| URL | https://arxiv.org/abs/physics/0006033 |
Abstract
On contrary to the customary thought, the well-known ``lemma'' that the distribution function of a collisionless Boltzmann gas keeps invariant along a molecule's path represents not the strength but the weakness of the standard theory. One of its consequences states that the velocity distribution at any point is a condensed ``image'' of all, complex and even discontinuous, structures of the entire spatial space. Admitting the inability to describe the entire space with a microscopic quantity, this paper introduces a new type of distribution function, called the solid-angle-average distribution function. With help of the new distribution function, the dynamical behavior of collisionless Boltzmann gas is formulated in terms of a set of integrals defined by molecular paths. In the new formalism, not only that the difficulties associated with the standard theory are surmounted but also that some of practical gases become calculable in terms of today's computer.
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"abstract": "On contrary to the customary thought, the well-known ``lemma\u0027\u0027 that the\ndistribution function of a collisionless Boltzmann gas keeps invariant along a\nmolecule\u0027s path represents not the strength but the weakness of the standard\ntheory. One of its consequences states that the velocity distribution at any\npoint is a condensed ``image\u0027\u0027 of all, complex and even discontinuous,\nstructures of the entire spatial space. Admitting the inability to describe the\nentire space with a microscopic quantity, this paper introduces a new type of\ndistribution function, called the solid-angle-average distribution function.\nWith help of the new distribution function, the dynamical behavior of\ncollisionless Boltzmann gas is formulated in terms of a set of integrals\ndefined by molecular paths. In the new formalism, not only that the\ndifficulties associated with the standard theory are surmounted but also that\nsome of practical gases become calculable in terms of today\u0027s computer.",
"arxiv_id": "physics/0006033",
"authors": [
"C. Y. Chen"
],
"categories": [
"physics.data-an",
"physics.flu-dyn"
],
"title": "A path-integral approach to the collisionless Boltzmann gas",
"url": "https://arxiv.org/abs/physics/0006033"
},
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