RE the exact solution of the many-body problem--there's a wonderful quote on the first page of Mattuck's "A Guide to Feynman Diagrams in the Many-Body Problem":
"In eighteenth-century Newtonian mechanics, the three-body problem was insoluble. With the birth of general relativity around 1910 and quantum electrodynamics in 1930, the two- and one-body problems became insoluble. And within modern quantum field theory, the problem of zero bodies (vacuum) is insoluble. So if we are out after exact solutions, no bodies at al is already too many."
The claim of 90+ percent efficiency for PV cells is true, sort of, but also of limited relevance. What you've essentially said is that if you limit the light falling on a cell to only the wavelengths that can be efficiently absorbed, then the cell will be efficient. You'd have a worldbeater if the sun emitted line radiation. But it doesn't. It emits very close to an ideal black-body spectrum, which is far from monochromatic. You can improve on single-material cells somewhat by stacking different materials (having different bandgaps), but even so, the best efficiency I've seen is still less than 40 percent. And these were aimed at space applications, where the economics is very different (launch costs dwarf the cost of the cells, so using fewer expensive but higher-efficiency cells is still cost-effective).
But there *is* a technology where what you've said is relevant--thermophotovoltaics. The idea here is to shine something hot (other than the sun) on a PV cell. If the light falling on the cell is monochromatic at the bandgap energy (or has a small bandwidth), the PV efficiency goes up substantially. You can generate narrow-bandwidth light by filtering a black- or grey-body source, reflecting what you can't use back to the source, and hoping it rethermalizes, or you can use a "selective emitter," that inherently emits in a narrow band. A common selective emitter is the Coleman lantern mantle, but most research I know about focusses on things like rare-earth doped YAG films. The technology is fairly undeveloped, and the cost is still high, but like a lot of things, it may look more attractive when the price of petroleum rises substantially.
Slashdot Mirror
RE the exact solution of the many-body problem--there's a wonderful quote on the first page of Mattuck's "A Guide to Feynman Diagrams in the Many-Body Problem":
"In eighteenth-century Newtonian mechanics, the three-body problem was insoluble. With the birth of general relativity around 1910 and quantum electrodynamics in 1930, the two- and one-body problems became insoluble. And within modern quantum field theory, the problem of zero bodies (vacuum) is insoluble. So if we are out after exact solutions, no bodies at al is already too many."
The claim of 90+ percent efficiency for PV cells is true, sort of, but also of limited relevance. What you've essentially said is that if you limit the light falling on a cell to only the wavelengths that can be efficiently absorbed, then the cell will be efficient. You'd have a worldbeater if the sun emitted line radiation. But it doesn't. It emits very close to an ideal black-body spectrum, which is far from monochromatic. You can improve on single-material cells somewhat by stacking different materials (having different bandgaps), but even so, the best efficiency I've seen is still less than 40 percent. And these were aimed at space applications, where the economics is very different (launch costs dwarf the cost of the cells, so using fewer expensive but higher-efficiency cells is still cost-effective).
But there *is* a technology where what you've said is relevant--thermophotovoltaics. The idea here is to shine something hot (other than the sun) on a PV cell. If the light falling on the cell is monochromatic at the bandgap energy (or has a small bandwidth), the PV efficiency goes up substantially. You can generate narrow-bandwidth light by filtering a black- or grey-body source, reflecting what you can't use back to the source, and hoping it rethermalizes, or you can use a "selective emitter," that inherently emits in a narrow band. A common selective emitter is the Coleman lantern mantle, but most research I know about focusses on things like rare-earth doped YAG films. The technology is fairly undeveloped, and the cost is still high, but like a lot of things, it may look more attractive when the price of petroleum rises substantially.