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.Scott

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So there is a new paper.

Presented here: http://arxiv.org/pdf/1502.04135.pdf

Published here: http://www.nature.com/nature/journal/v528/n7581/full/nature16059.html

And broadly described here: http://phys.org/news/2015-12-quantum-physics-problem-unsolvable-godel.html

Here is an excerpt from the abstract:

This suggests that there may be cases where you can experimentally determine whether there is a gap, but that, in theory, there is no way to determine this through analysis.

Is this true, and are there actual examples? For example, is there a specific superconductor that:

- relies on no spectral gap

- where there is enough known about its structure where a computation can be attempted

- but the computation is demonstrably undecidable.

??

Presented here: http://arxiv.org/pdf/1502.04135.pdf

Published here: http://www.nature.com/nature/journal/v528/n7581/full/nature16059.html

And broadly described here: http://phys.org/news/2015-12-quantum-physics-problem-unsolvable-godel.html

Here is an excerpt from the abstract:

These problems are all particular cases of the general spectral gap problem: Given a quantum many-body Hamiltonian, is the system it describes gapped or gapless? Here we show that this problem is undecidable, in the same sense as the Halting Problem was proven to be undecidable by Turing.6 A consequence of this is that the spectral gap of certain quantum many-body Hamiltonians is not determined by the axioms of mathematics, much as Godels incompleteness theorem implies ¨ that certain theorems are mathematically unprovable.

This suggests that there may be cases where you can experimentally determine whether there is a gap, but that, in theory, there is no way to determine this through analysis.

Is this true, and are there actual examples? For example, is there a specific superconductor that:

- relies on no spectral gap

- where there is enough known about its structure where a computation can be attempted

- but the computation is demonstrably undecidable.

??

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