The Adiabatic Theorem and Linear Response Theory for Extended Quantum Systems
| ISSN: | 1432-0916 0010-3616 |
|---|---|
| DOI: | 10.1007/s00220-018-3117-9 |
| Přístupová URL adresa: | https://explore.openaire.eu/search/publication?articleId=doi_dedup___::f2fd4d79b753d06b27e6d2c5505abde3 https://doi.org/10.1007/s00220-018-3117-9 |
| Rights: | OPEN |
| Přírůstkové číslo: | edsair.doi.dedup.....f2fd4d79b753d06b27e6d2c5505abde3 |
| Autor: | Sven Bachmann, Wojciech De Roeck, Martin Fraas |
| Rok vydání: | 2018 |
| Předmět: |
PROOF
Complex system Degrees of freedom (physics and chemistry) FOS: Physical sciences Quantum Hall effect Fixed point KUBO FORMULA 01 natural sciences Adiabatic theorem 0103 physical sciences 0101 mathematics Quantum Mathematical Physics Mathematical physics Physics Science & Technology STABILITY 010102 general mathematics Spectrum (functional analysis) GAP Statistical and Nonlinear Physics Mathematical Physics (math-ph) GROUND-STATES Manifold ELECTRONS Physics Mathematical DIFFERENTIAL EQUATIONS Physical Sciences 010307 mathematical physics |
| Zdroj: | Communications in Mathematical Physics. 361:997-1027 |
| ISSN: | 1432-0916 0010-3616 |
| DOI: | 10.1007/s00220-018-3117-9 |
| Popis: | The adiabatic theorem refers to a setup where an evolution equation contains a time-dependent parameter whose change is very slow, measured by a vanishing parameter $\epsilon$. Under suitable assumptions the solution of the time-inhomogenous equation stays close to an instantaneous fixpoint. In the present paper, we prove an adiabatic theorem with an error bound that is independent of the number of degrees of freedom. Our setup is that of quantum spin systems where the manifold of ground states is separated from the rest of the spectrum by a spectral gap. One important application is the proof of the validity of linear response theory for such extended, genuinely interacting systems. In general, this is a long-standing mathematical problem, which can be solved in the present particular case of a gapped system, relevant e.g.~for the integer quantum Hall effect. Comment: 25 pages; v1-->v2 minor typos, change in abstract, references; v2-->v3 remark added after main theorem on p.6; v3-->v4 Lemma 4.8 added, minor changes, one additional reference |
| Databáze: | OpenAIRE |
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