dorsal/arxiv
View SchemaStrong Coupling Perturbation Theory in Quantum Mechanics
| Authors | Marco Frasca |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0307237 |
| URL | https://arxiv.org/abs/quant-ph/0307237 |
| Journal | Mathematical Physics Research on the Leading Edge, Charles V. Benton (Ed.), pp. 1-19, (Nova Science Publisher, Hauppage NY, 2004), ISBN 1-59033-905-3 |
Abstract
We present a full introduction to the recent devised perturbation theory for strong coupling in quantum mechanics. In order to put the theory in a proper historical perspective, the approach devised in quantum field theory is rapidly presented, showing how it implies a kind of duality in perturbation theory, from the start. The approach of renormalization group in perturbation theory is then presented. This method permits to resum secularities in perturbation theory and makes fully algorithmical the resummation, transforming the perturbation calculations in a step by step computational procedure. The general theorem on which is founded a proper application of the strong coupling expansion, based on a result in the quantum adiabatic theory, is then exposed. This theorem gives the leading order of a strong coupling expansion. Then, after the introduction of the principle of duality in perturbation theory that puts in a proper context the quantum field theory method, the resulting theory of the strong coupling expansion and the free picture are presented. An algorithm for the computation of the perturbation series is finally given. This approach has a lot of applications in fields as quantum optics, condensed matter and so on, extending the original expectations of the quantum field theory method. So, we give some examples of application for a class of two-level systems that, in recent years, proved to be extremely important. One of the most interesting concepts that can be obtained in this way is that of a Quantum Amplifier (QAMP) that permits to obtain an amplification to the classical level of the quantum fluctuations of the ground state of a single radiation mode.
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"abstract": "We present a full introduction to the recent devised perturbation theory for\nstrong coupling in quantum mechanics. In order to put the theory in a proper\nhistorical perspective, the approach devised in quantum field theory is rapidly\npresented, showing how it implies a kind of duality in perturbation theory,\nfrom the start. The approach of renormalization group in perturbation theory is\nthen presented. This method permits to resum secularities in perturbation\ntheory and makes fully algorithmical the resummation, transforming the\nperturbation calculations in a step by step computational procedure. The\ngeneral theorem on which is founded a proper application of the strong coupling\nexpansion, based on a result in the quantum adiabatic theory, is then exposed.\nThis theorem gives the leading order of a strong coupling expansion. Then,\nafter the introduction of the principle of duality in perturbation theory that\nputs in a proper context the quantum field theory method, the resulting theory\nof the strong coupling expansion and the free picture are presented. An\nalgorithm for the computation of the perturbation series is finally given. This\napproach has a lot of applications in fields as quantum optics, condensed\nmatter and so on, extending the original expectations of the quantum field\ntheory method. So, we give some examples of application for a class of\ntwo-level systems that, in recent years, proved to be extremely important. One\nof the most interesting concepts that can be obtained in this way is that of a\nQuantum Amplifier (QAMP) that permits to obtain an amplification to the\nclassical level of the quantum fluctuations of the ground state of a single\nradiation mode.",
"arxiv_id": "quant-ph/0307237",
"authors": [
"Marco Frasca"
],
"categories": [
"quant-ph",
"cond-mat",
"hep-th"
],
"journal_ref": "Mathematical Physics Research on the Leading Edge, Charles V.\n Benton (Ed.), pp. 1-19, (Nova Science Publisher, Hauppage NY, 2004), ISBN\n 1-59033-905-3",
"title": "Strong Coupling Perturbation Theory in Quantum Mechanics",
"url": "https://arxiv.org/abs/quant-ph/0307237"
},
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