"Nanoscale Nonlinear Thermoelectricity - Cooling, Catastrophes and Carnot"
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I start by summarizing thermoelectric effects, and how we might be able
to use them for refrigeration, perhaps to cool nanoscale systems to previously
unreachable temperatures (as low as a few mK). However quantum effects
cannot be ignored in such low temperature nanoscale systems. Thus, I develop a
quantum theory of thermoelectric effects, which is capable of dealing with the
highly non-linear effects necessary for efficient refrigerators.
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I apply the theory to refrigeration by point-contacts including Hartree-type
interaction effects,
and predict a discontinuity in the cooling response (a ``fold-catastrophe'' in
mathematics).  I then turn to arbitrary such quantum systems, and show that
there are certain fundamental bounds on heat-flow.
Some of these bounds are thermodynamic in nature,
such as Carnot's thermodynamic bounds on heat engines and refrigeration,
while others are purely quantum.
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References:
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R.S. Whitney, Preprint arXiv:1208.6130
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R.S. Whitney, Preprint arXiv:1211.4737