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The quartic oscillator: a non-perturbative study by continuous unitary transformations
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The quantum quartic oscillator is investigated in order to test the many-body technique of the continuous unitary transformations. The quartic oscillator is sufficiently simple to allow a detailed study and comparison of various approximation schemes. Due to its simplicity, it can be used as pedagogical introduction in the unitary transformations. Both the spectrum and the spectral weights are discussed.
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Cross validation of a variety of different physical systems is an approach to assess the reliability of AQSs.
“One approach is by cross validation of a variety of different physical systems (e.g., atoms in optical lattices, ions in traps, and superconductors) [74].”
From Can one trust quantum simulators? (2012) · cites this paper as [74]
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Metadata
- Authors
- Dusuel, S., & Uhrig, G. S.
- Affiliations
- École Normale Supérieure de Lyon (FR)
- University of Cologne (DE)
- ORCID
- Uhrig, Götz S
- Venue
- Journal of Physics A: Mathematical and General
- Publisher
- IOP Publishing
- Published
- 2004-09-16
- Volume
- 37
- Issue
- 39
- Pages
- 9275-9294
- ISSN
- 0305-4470 (ISSN-L)
- 1361-6447
- OpenAlex
- W2001520181
- Cited by
- 38
- References
- 19
- Citations by year
- 2026: 1 · 2025: 1 · 2022: 5 · 2020: 2 · 2016: 1 · 2015: 1 · 2014: 2 · 2013: 2 · 2012: 2
- FWCI
- 1.84
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Journal of Physics A Mathematical and General (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
- Physical Sciences › Mathematics › Mathematical Physics › Spectral Theory in Mathematical Physics
- Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Theoretical and Computational Physics
- Keywords
- quartic oscillator, continuous unitary transformations, non-perturbative methods, energy spectrum, spectral weight, approximation methods
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