Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Adiabatic and Non-Adiabatic Contributions to the Free Energy from the
  Electron-Phonon Interaction for Na, K, Al, and Pb   We calculate the adiabatic contributions to the free energy due to the
electron--phonon interaction at intermediate temperatures, $0 \leqslant k_{B} T
< \epsilon_{F}$ for the elemental metals Na, K, Al, and Pb. Using our
previously published results for the nonadiabatic contributions we show that
the adiabatic contribution, which is proportional to $T^{2}$ at low
temperatures and goes as $T^{3}$ at high temperatures, dominates the
nonadiabatic contribution for temperatures above a cross--over temperature,
$T_{c}$, which is between 0.5 and 0.8 $T_{m}$, where $T_{m}$ is the melting
temperature of the metal. The nonadiabatic contribution falls as $T^{-1}$ for
temperatures roughly above the average phonon frequency.

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The categories of this paper are: gr-qc
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The categories of this paper are: hep-lat
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The categories of this paper are: econ
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The categories of this paper are: q-fin
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The categories of this paper are: nucl-th
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The categories of this paper are: solv-int
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The categories of this paper are: mtrl-th
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The categories of this paper are: nlin
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The categories of this paper are: plasm-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: q-bio
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The categories of this paper are: hep-ex
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The categories of this paper are: patt-sol
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The categories of this paper are: atom-ph
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The categories of this paper are: physics
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The categories of this paper are: hep-th