Reyes-Bustos, Cid; Wakayama, Masato Covering families of the asymmetric quantum Rabi model: \(\eta\)-shifted non-commutative harmonic oscillators. (English) Zbl 07751294 Commun. Math. Phys. 403, No. 3, 1429-1476 (2023). MSC: 81S05 39B42 42B37 22E70 11F11 11G05 11M36 78A60 PDFBibTeX XMLCite \textit{C. Reyes-Bustos} and \textit{M. Wakayama}, Commun. Math. Phys. 403, No. 3, 1429--1476 (2023; Zbl 07751294) Full Text: DOI arXiv
Malagutti, Marcello On the spectral zeta function of second order semiregular non-commutative harmonic oscillators. (English) Zbl 07731022 Bull. Sci. Math. 187, Article ID 103286, 29 p. (2023). MSC: 11M41 81Q10 11M35 46L60 46N50 PDFBibTeX XMLCite \textit{M. Malagutti}, Bull. Sci. Math. 187, Article ID 103286, 29 p. (2023; Zbl 07731022) Full Text: DOI arXiv
Shabani, A.; Khellat, F. Quantum tomographic Aubry-Mather theory. (English) Zbl 1512.81013 J. Math. Phys. 64, No. 4, Article ID 042706, 12 p. (2023). MSC: 81P18 44A12 PDFBibTeX XMLCite \textit{A. Shabani} and \textit{F. Khellat}, J. Math. Phys. 64, No. 4, Article ID 042706, 12 p. (2023; Zbl 1512.81013) Full Text: DOI
Kimoto, Kazufumi; Reyes-Bustos, Cid; Wakayama, Masato Determinant expressions of constraint polynomials and the spectrum of the asymmetric quantum Rabi model. (English) Zbl 1514.81115 Int. Math. Res. Not. 2021, No. 12, 9458-9544 (2021). MSC: 81Q05 81V80 35P10 81V73 70H45 33C15 PDFBibTeX XMLCite \textit{K. Kimoto} et al., Int. Math. Res. Not. 2021, No. 12, 9458--9544 (2021; Zbl 1514.81115) Full Text: DOI arXiv
Zanelli, Lorenzo Schrödinger dynamics and optimal transport of measures. (English) Zbl 1483.81071 Infin. Dimens. Anal. Quantum Probab. Relat. Top. 24, No. 3, Article ID 2150016, 17 p. (2021). MSC: 81Q20 81Q05 49Q20 58J40 PDFBibTeX XMLCite \textit{L. Zanelli}, Infin. Dimens. Anal. Quantum Probab. Relat. Top. 24, No. 3, Article ID 2150016, 17 p. (2021; Zbl 1483.81071) Full Text: DOI arXiv
Zanelli, L.; Mandreoli, F.; Cardin, F. A weak KAM approach to the periodic stationary Hartree equation. (English) Zbl 1476.35094 NoDEA, Nonlinear Differ. Equ. Appl. 28, No. 6, Paper No. 56, 18 p. (2021). MSC: 35F21 37K55 81V70 PDFBibTeX XMLCite \textit{L. Zanelli} et al., NoDEA, Nonlinear Differ. Equ. Appl. 28, No. 6, Paper No. 56, 18 p. (2021; Zbl 1476.35094) Full Text: DOI
Zanelli, Lorenzo Periodic coherent states decomposition and quantum dynamics on the flat torus. (English) Zbl 1472.81121 Bastos, M. Amélia (ed.) et al., Operator theory, functional analysis and applications. Proceedings of the 30th international workshop on operator theory and its applications, IWOTA 2019, Lisbon, Portugal, July 22–26, 2019. Cham: Birkhäuser. Oper. Theory: Adv. Appl. 282, 647-657 (2021). MSC: 81R30 58J40 58C40 81Q05 PDFBibTeX XMLCite \textit{L. Zanelli}, Oper. Theory: Adv. Appl. 282, 647--657 (2021; Zbl 1472.81121) Full Text: DOI arXiv
Wakayama, Masato Number theoretic study in quantum interactions. (English) Zbl 1459.81041 Takagi, Tsuyoshi (ed.) et al., International symposium on mathematics, quantum theory, and cryptography. Proceedings of MQC 2019, Fukuoka, Japan, September 25–27, 2019. Singapore: Springer. Math. Ind. (Tokyo) 33, 95-101 (2021). MSC: 81Q05 35P20 35P15 14H50 14H52 11M36 11E04 PDFBibTeX XMLCite \textit{M. Wakayama}, Math. Ind. (Tokyo) 33, 95--101 (2021; Zbl 1459.81041) Full Text: DOI
Parmeggiani, Alberto; Zanelli, Lorenzo An exact version of the Egorov theorem for Schrödinger operators in \(L^2(\mathbb {T})\). (English) Zbl 1469.34116 J. Fourier Anal. Appl. 25, No. 4, 1759-1781 (2019). MSC: 34L40 34A55 35B27 35F21 35Q40 58J53 81Q20 PDFBibTeX XMLCite \textit{A. Parmeggiani} and \textit{L. Zanelli}, J. Fourier Anal. Appl. 25, No. 4, 1759--1781 (2019; Zbl 1469.34116) Full Text: DOI
Sugiyama, Shingo Spectral zeta functions for the quantum Rabi models. (English) Zbl 1426.11085 Nagoya Math. J. 229, 52-98 (2018). Reviewer: Roma Kačinskaitė (Kaunas) MSC: 11M41 81Q10 46N50 PDFBibTeX XMLCite \textit{S. Sugiyama}, Nagoya Math. J. 229, 52--98 (2018; Zbl 1426.11085) Full Text: DOI
Arai, Asao; Hiroshima, Fumio Ultra-weak time operators of Schrödinger operators. (English) Zbl 1404.81088 Ann. Henri Poincaré 18, No. 9, 2995-3033 (2017). Reviewer: Christian Seifert (Hamburg) MSC: 81Q05 81Q12 35J10 81Q10 PDFBibTeX XMLCite \textit{A. Arai} and \textit{F. Hiroshima}, Ann. Henri Poincaré 18, No. 9, 2995--3033 (2017; Zbl 1404.81088) Full Text: DOI arXiv
Wakayama, Masato Symmetry of asymmetric quantum Rabi models. (English) Zbl 1366.81328 J. Phys. A, Math. Theor. 50, No. 17, Article ID 174001, 22 p. (2017). MSC: 81V80 81Q10 17B81 20C35 17B35 81Q15 PDFBibTeX XMLCite \textit{M. Wakayama}, J. Phys. A, Math. Theor. 50, No. 17, Article ID 174001, 22 p. (2017; Zbl 1366.81328) Full Text: DOI arXiv
Zanelli, Lorenzo On the optimal transport of semiclassical measures. (English) Zbl 1361.81053 Appl. Math. Optim. 74, No. 2, 325-342 (2016); erratum ibid. 74, No. 2, 343 (2016). MSC: 81Q20 49Q20 35F21 81Q05 PDFBibTeX XMLCite \textit{L. Zanelli}, Appl. Math. Optim. 74, No. 2, 325--342 (2016; Zbl 1361.81053) Full Text: DOI
Hiroshima, Fumio; Sasaki, Itaru Spectral analysis of non-commutative harmonic oscillators: the lowest eigenvalue and no crossing. (English) Zbl 1315.34090 J. Math. Anal. Appl. 415, No. 2, 595-609 (2014). MSC: 34L15 47E05 81Q10 34L40 PDFBibTeX XMLCite \textit{F. Hiroshima} and \textit{I. Sasaki}, J. Math. Anal. Appl. 415, No. 2, 595--609 (2014; Zbl 1315.34090) Full Text: DOI arXiv
Paul, Thierry; Zanelli, Lorenzo On the dynamics of WKB wave functions whose phase are weak KAM solutions of H-J equation. (English) Zbl 1310.58019 J. Fourier Anal. Appl. 20, No. 6, 1291-1327 (2014). Reviewer: Sönke Hansen (Paderborn) MSC: 58J40 81S30 35F21 35D40 PDFBibTeX XMLCite \textit{T. Paul} and \textit{L. Zanelli}, J. Fourier Anal. Appl. 20, No. 6, 1291--1327 (2014; Zbl 1310.58019) Full Text: DOI arXiv
Parmeggiani, Alberto; Zanelli, Lorenzo Wigner measures supported on weak KAM tori. (English) Zbl 1339.37045 J. Anal. Math. 123, 107-137 (2014). Reviewer: Vladislav Nikolaevich Dumachev (Voronezh) MSC: 37J40 70H08 81S30 PDFBibTeX XMLCite \textit{A. Parmeggiani} and \textit{L. Zanelli}, J. Anal. Math. 123, 107--137 (2014; Zbl 1339.37045) Full Text: DOI
Parmeggiani, Alberto; Venni, Alberto On the essential spectrum of certain non-commutative oscillators. (English) Zbl 1285.81024 J. Math. Phys. 54, No. 12, 121507, 10 p. (2013). MSC: 81Q10 34L40 34L05 46L53 PDFBibTeX XMLCite \textit{A. Parmeggiani} and \textit{A. Venni}, J. Math. Phys. 54, No. 12, 121507, 10 p. (2013; Zbl 1285.81024) Full Text: DOI
Wakayama, Masato Simplicity of the lowest eigenvalue of non-commutative harmonic oscillators and the Riemann scheme of a certain Heun’s differential equation. (English) Zbl 1278.34099 Proc. Japan Acad., Ser. A 89, No. 6, 69-73 (2013). MSC: 34L15 34L40 81Q10 34M05 81S05 PDFBibTeX XMLCite \textit{M. Wakayama}, Proc. Japan Acad., Ser. A 89, No. 6, 69--73 (2013; Zbl 1278.34099) Full Text: DOI Euclid
Ochiai, Hiroyuki Non-commutative harmonic oscillators. (English) Zbl 1332.81101 Iohara, Kenji (ed.) et al., Symmetries, integrable systems and representations. Proceedings of the conference on infinite analysis: frontier of integrability, Tokyo, Japan, July 25–29, 2011 and the conference on symmetries, integrable systems and representations, Lyon, France, December 13–16, 2011. London: Springer (ISBN 978-1-4471-4862-3/hbk; 978-1-4471-4863-0/ebook). Springer Proceedings in Mathematics & Statistics 40, 483-490 (2013). MSC: 81S05 81R60 PDFBibTeX XMLCite \textit{H. Ochiai}, Springer Proc. Math. Stat. 40, 483--490 (2013; Zbl 1332.81101) Full Text: DOI
Parmeggiani, Alberto On the spectrum of certain non-commutative harmonic oscillators and semiclassical analysis. (English) Zbl 1168.47038 Commun. Math. Phys. 279, No. 2, 285-308 (2008). Reviewer: Anatoly N. Kochubei (Kyïv) MSC: 47E05 34L40 35S05 47G30 47N50 81Q20 PDFBibTeX XMLCite \textit{A. Parmeggiani}, Commun. Math. Phys. 279, No. 2, 285--308 (2008; Zbl 1168.47038) Full Text: DOI
Ichinose, Takashi; Wakayama, Masato On the spectral zeta function for the noncommutative harmonic oscillator. (English) Zbl 1190.11047 Rep. Math. Phys. 59, No. 3, 421-432 (2007). Reviewer: Olaf Ninnemann (Berlin) MSC: 11M36 81Q10 11Z05 PDFBibTeX XMLCite \textit{T. Ichinose} and \textit{M. Wakayama}, Rep. Math. Phys. 59, No. 3, 421--432 (2007; Zbl 1190.11047) Full Text: DOI
Ichinose, Takashi; Wakayama, Masato Zeta functions for the spectrum of the non-commutative harmonic oscillators. (English) Zbl 1145.81031 Commun. Math. Phys. 258, No. 3, 697-739 (2005). MSC: 81Q10 11M41 11Z05 47E05 PDFBibTeX XMLCite \textit{T. Ichinose} and \textit{M. Wakayama}, Commun. Math. Phys. 258, No. 3, 697--739 (2005; Zbl 1145.81031) Full Text: DOI
Boulton, L.; Marcantognini, S. A. M.; Morán, M. D. Finite lifetime eigenfunctions of coupled systems of harmonic oscillators. (English) Zbl 1065.34083 Lett. Math. Phys. 70, No. 2, 121-131 (2004). Reviewer: Mihai Pascu (Bucureşti) MSC: 34L10 34L40 81Q10 PDFBibTeX XMLCite \textit{L. Boulton} et al., Lett. Math. Phys. 70, No. 2, 121--131 (2004; Zbl 1065.34083) Full Text: DOI arXiv
Nagatou, K.; Nakao, M. T.; Wakayama, M. Verified numerical computations for eigenvalues of non-commutative harmonic oscillators. (English) Zbl 1016.65056 Numer. Funct. Anal. Optimization 23, No. 5-6, 633-650 (2002). Reviewer: Oscar Lopez-Pouso (Santiago de Compostela) MSC: 65L15 47N50 81Q05 65G20 65G40 34L16 34L40 47E05 PDFBibTeX XMLCite \textit{K. Nagatou} et al., Numer. Funct. Anal. Optim. 23, No. 5--6, 633--650 (2002; Zbl 1016.65056) Full Text: DOI
Karasev, M.; Novikova, E. Coherent transform of the spectral problem and algebras with nonlinear commutation relations. (English) Zbl 1040.81528 J. Math. Sci., New York 95, No. 6, 2703-2798 (1999). Reviewer: Martin Schlichenmaier (Luxembourg) (MR1712996) MSC: 81R30 37J15 37N20 53D50 81R12 81S10 PDFBibTeX XMLCite \textit{M. Karasev} and \textit{E. Novikova}, J. Math. Sci., New York 95, No. 6, 2703--2798 (1999; Zbl 1040.81528) Full Text: DOI
Borsari, I.; Graffi, S. Symbols of operators and quantum evolution. (English) Zbl 0822.47057 J. Math. Phys. 35, No. 9, 4439-4450 (1994). MSC: 47N50 81S05 PDFBibTeX XMLCite \textit{I. Borsari} and \textit{S. Graffi}, J. Math. Phys. 35, No. 9, 4439--4450 (1994; Zbl 0822.47057) Full Text: DOI