dorsal/arxiv
View SchemaNewtonian Adiabatics Unified
| Authors | Alfred Scharff Goldhaber |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0502132 |
| URL | https://arxiv.org/abs/quant-ph/0502132 |
Abstract
Newtonian adiabatics is the consistent truncation of the adiabatic approximation to second order in small velocities. To be complete it must unify two hitherto disjoint intellectual streams in the study of adiabatic motion. The newer stream focuses on Berry's induced vector potential, or geometric magnetism, and Provost and Vallee's induced scalar potential, reflecting geometry in Hilbert space. The older stream focuses on Inglis' induced inertia, influencing the geometry of adiabatic-parameter space. Starting with the Hamiltonian of the newer stream, unification is simple: A naive or primitive inertia, whose inverse appears in two terms of that Hamiltonian, is replaced by the convention-independent sum of primitive and induced inertia tensors.
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"abstract": "Newtonian adiabatics is the consistent truncation of the adiabatic\napproximation to second order in small velocities. To be complete it must unify\ntwo hitherto disjoint intellectual streams in the study of adiabatic motion.\nThe newer stream focuses on Berry\u0027s induced vector potential, or geometric\nmagnetism, and Provost and Vallee\u0027s induced scalar potential, reflecting\ngeometry in Hilbert space. The older stream focuses on Inglis\u0027 induced inertia,\ninfluencing the geometry of adiabatic-parameter space. Starting with the\nHamiltonian of the newer stream, unification is simple: A naive or primitive\ninertia, whose inverse appears in two terms of that Hamiltonian, is replaced by\nthe convention-independent sum of primitive and induced inertia tensors.",
"arxiv_id": "quant-ph/0502132",
"authors": [
"Alfred Scharff Goldhaber"
],
"categories": [
"quant-ph",
"hep-th",
"math-ph",
"math.MP"
],
"title": "Newtonian Adiabatics Unified",
"url": "https://arxiv.org/abs/quant-ph/0502132"
},
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