Undecidability of the Spectral Gap (short version) · HackerPapers discussions

Undecidability of the Spectral Gap (short version) — mentioned by woopsn

Thu, 05 Oct 2023 21:30:48 GMT

One response brings up the (un)decidability of determining if a physical system's ground state is separated from the rest of its spectrum: > And there are still cases going on today where undecidability results are of broad interest to those outside of logic. For example, the "spectral gap problem" in physics asked whether, given a description of a physical system, whether that system requires a minimum amount of energy to nudge it out of its ground state, or whether arbitrarily small amounts of energy can nudge it out of its ground state. This was proven to be undecidable in 2015, basically…

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Undecidability of the Spectral Gap (short version) — mentioned by vladTheInhaler

Mon, 12 Sep 2022 05:07:29 GMT

A while ago there was a result that relates to materials science: https://arxiv.org/abs/1502.04135

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Undecidability of the Spectral Gap (short version) — mentioned by dvt

Thu, 02 Sep 2021 01:40:36 GMT

Gave this a brief skim, and it's paradoxically both highfalutin and often times plain wrong at the same time. > Computers are universal machines. I use this term in a precise sense: anything that can be computed in the universe can in principle be computed by the kind of machine that we already have, given enough memory and time Yeah, this precise sense is precisely wrong. There are plenty of things computers can't do (and will never be able to do), including (probably) be conscious (see Searle), but maybe even more difficult to swallow, generally compute entropy[1], or compute the spectral…

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Undecidability of the Spectral Gap (short version) — mentioned by mathgenius

Thu, 10 Dec 2015 07:27:42 GMT

Long version: http://arxiv.org/abs/1502.04573 Short version: http://arxiv.org/abs/1502.04135

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