Number Theoretic Study in Quantum Interactions

DOI10.1007/978-981-15-5191-8_10zbMath1459.81041OpenAlexW3094022745MaRDI QIDQ4964357

Masato Wakayama

Publication date: 25 February 2021

Published in: International Symposium on Mathematics, Quantum Theory, and Cryptography (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-981-15-5191-8_10

Mathematics Subject Classification ID

Quadratic forms over general fields (11E04) Estimates of eigenvalues in context of PDEs (35P15) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Asymptotic distributions of eigenvalues in context of PDEs (35P20) Plane and space curves (14H50) Elliptic curves (14H52) Selberg zeta functions and regularized determinants; applications to spectral theory, Dirichlet series, Eisenstein series, etc. (explicit formulas) (11M36)

Cites Work

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• Spectral theory of non-commutative harmonic oscillators: an introduction
• Some congruences for the Apéry numbers
• Rational period functions of the modular group. (Appendix by Georges Grinstein)
• A generalized supercongruence of Kimoto and Wakayama
• A supercongruence conjecture of Rodriguez-Villegas for a certain truncated hypergeometric function.
• Spectral analysis of non-commutative harmonic oscillators: the lowest eigenvalue and no crossing
• A special value of the spectral zeta function of the non-commutative harmonic oscillators
• Zeta functions for the spectrum of the non-commutative harmonic oscillators
• Oscillator representations and systems of ordinary differential equations
• Equivalence Between the Eigenvalue Problem of Non-Commutative Harmonic Oscillators and Existence of Holomorphic Solutions of Heun Differential Equations, Eigenstates Degeneration, and the Rabi Model
• On a conjecture of Kimoto and Wakayama
• SPECIAL VALUES OF THE SPECTRAL ZETA FUNCTION OF THE NON-COMMUTATIVE HARMONIC OSCILLATOR AND CONFLUENT HEUN EQUATIONS
• SPECTRAL ZETA FUNCTIONS FOR THE QUANTUM RABI MODELS
• APÉRY-LIKE NUMBERS ARISING FROM SPECIAL VALUES OF SPECTRAL ZETA FUNCTIONS FOR NON-COMMUTATIVE HARMONIC OSCILLATORS
• Exploring the Quantum
• Mahler measure under variations of the base group
• Symmetry of asymmetric quantum Rabi models

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