dorsal/arxiv
View SchemaQuantization of the Coulomb Chain in an External Focusing Field
| Authors | Andreas Kabel |
|---|---|
| Categories | |
| ArXiv ID | physics/0101102 |
| URL | https://arxiv.org/abs/physics/0101102 |
| DOI | 10.1142/9789812777447_0010 |
Abstract
With the appropriate choice of parameters and sufficient cooling, charged particles in a circular accelerator are believed to undergo a transition to a highly-ordered crystalline state. The simplest possible crystalline configuration is a one-dimensional chain of particles. In this paper, we write down the quantized version of its dynamics. We show that in a low-density limit, the dynamics is that of a theory of interacting phonons. There is an infinite sequence of $n$-phonon interaction terms, of which we write down the first orders, which involve phonon scattering and decay processes. The quantum formulation developed here can serve as a first step towards a quantum-mechanical treatment of the system at finite temperatures.
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"abstract": "With the appropriate choice of parameters and sufficient cooling, charged\nparticles in a circular accelerator are believed to undergo a transition to a\nhighly-ordered crystalline state. The simplest possible crystalline\nconfiguration is a one-dimensional chain of particles. In this paper, we write\ndown the quantized version of its dynamics. We show that in a low-density\nlimit, the dynamics is that of a theory of interacting phonons. There is an\ninfinite sequence of $n$-phonon interaction terms, of which we write down the\nfirst orders, which involve phonon scattering and decay processes. The quantum\nformulation developed here can serve as a first step towards a\nquantum-mechanical treatment of the system at finite temperatures.",
"arxiv_id": "physics/0101102",
"authors": [
"Andreas Kabel"
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"physics.acc-ph"
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"doi": "10.1142/9789812777447_0010",
"title": "Quantization of the Coulomb Chain in an External Focusing Field",
"url": "https://arxiv.org/abs/physics/0101102"
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