| 词条 | Spectral gap (physics) |
| 释义 |
In quantum mechanics, the spectral gap of a system is the energy difference between its ground state and its lowest excited state.[1][2] The mass gap is the spectral gap between the vacuum and the lightest particle. A Hamiltonian with a spectral gap is called a gapped Hamiltonian, and those that do not are called gapless. In solid-state physics, the most important spectral gap is for the many-body system of electrons in a solid material, in which case it is often known as an energy gap. In 2015 it was shown that the problem of determining the existence of a spectral gap is undecidable.[3][4] The authors used an aperiodic tiling of quantum Turing machines and showed that this hypothetical material becomes gapped if and only if it halts.[5] See also
References1. ^{{Cite journal |title=Undecidability of the spectral gap |journal = Nature|volume = 528|issue = 7581|last=Cubitt |first=Toby S. |last2=Perez-Garcia |first2=David |date=2015-12-10 |publisher=National Center for Biotechnology Information, U.S. National Library of Medicine |location=US |pages=207–211 |language=en-us |doi=10.1038/nature16059 |pmid=26659181 |last3=Wolf |first3=Michael M.|arxiv = 1502.04135}} 2. ^{{cite web |url= https://futurism.com/19474|title=Scientists Just Proved A Fundamental Quantum Physics Problem is Unsolvable|last=Lim|first=Jappy|date=11 December 2015|website=Futurism|publisher= |access-date=18 December 2018|quote=}} 3. ^{{Cite journal | doi=10.1038/nature16059|pmid = 26659181| title=Undecidability of the spectral gap| journal=Nature| volume=528| issue=7581| pages=207–211| year=2015| last1=Cubitt| first1=Toby S.| last2=Perez-Garcia| first2=David| last3=Wolf| first3=Michael M.|bibcode = 2015Natur.528..207C|arxiv = 1502.04135}} 4. ^{{cite journal |last1=Kreinovich|first1=Vladik|date= |title=Why Some Physicists Are Excited About the Undecidability of the Spectral Gap Problem and Why Should We|url=https://digitalcommons.utep.edu/cgi/viewcontent.cgi?article=2163&context=cs_techrep|journal=Bulletin of the European Association for Theoretical Computer Science|volume=122|issue=2017|pages= |doi= |access-date=18 December 2018}} 5. ^{{cite magazine |last1=Cubitt|first1=Toby S.|last2=Perez-Garcia|first2=David|last3=Wolf|first3=Michael M.|date=November 2018|title=The Unsolvable Problem|url=https://www.scientificamerican.com/article/the-unsolvable-problem/|magazine=Scientific American|location= |publisher= |subscription=yes}} 3 : Quantum mechanics|Concepts in physics|Undecidable problems |
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