Non-commutative harmonic oscillators and related problems

DOI10.1007/s00032-014-0220-zzbMath1304.35450OpenAlexW1966051593MaRDI QIDQ475727

Alberto Parmeggiani

Publication date: 27 November 2014

Published in: Milan Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00032-014-0220-z

zbMATH Keywords

spectral theoryFredholm operatorsspectral zeta functionnon-commutative harmonic oscillatorsclustering propertiesPoisson relationsWeyl-Hörmander calculus

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) General topics in linear spectral theory for PDEs (35P05) Spectrum, resolvent (47A10) (Semi-) Fredholm operators; index theories (47A53)

Related Items

Determinant Expressions of Constraint Polynomials and the Spectrum of the Asymmetric Quantum Rabi Model ⋮ Covering families of the asymmetric quantum Rabi model: \(\eta\)-shifted non-commutative harmonic oscillators ⋮ Apéry-like numbers for non-commutative harmonic oscillators and automorphic integrals ⋮ \(M\)-ellipticity of Fredholm pseudo-differential operators on \(L^p (\mathbb{R}^n)\) and Gårding's inequality ⋮ Spectral asymptotic properties of semiregular non-commutative harmonic oscillators ⋮ On a class of anharmonic oscillators ⋮ Schatten-von Neumann classes of integral operators ⋮ SPECTRAL ZETA FUNCTIONS FOR THE QUANTUM RABI MODELS ⋮ On a class of anharmonic oscillators. II: General case

Cites Work

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• Simplicity of the lowest eigenvalue of non-commutative harmonic oscillators and the Riemann scheme of a certain Heun's differential equation
• A remark on the Fefferman-Phong inequality for \(2\times 2\) systems
• Lower bounds for systems with double characteristics.
• Non-commutative harmonic oscillators and the connection problem for the Heun differential equation
• Spectral theory of non-commutative harmonic oscillators: an introduction
• On the spectral zeta function for the noncommutative harmonic oscillator
• Positivity of a system of differential operators
• On the asymptotic distribution of the eigenvalues of pseudodifferential operators in \(R^n\)
• Sur le spectre des opérateurs elliptiques à bicaracteristiques toutes périodiques
• Weighted distribution spaces and pseudodifferential operators
• The spectrum of positive elliptic operators and periodic bicharacteristics
• The Cauchy problem for differential equations with double characteristics
• Asymptotics of eigenvalue clusters for the Laplacian plus a potential
• Perturbation theory for linear operators.
• Formule de Poisson pour les variétés riemanniennes
• Symplectic classification of quadratic forms, and general Mehler formulas
• 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
• On the spectrum of certain noncommutative harmonic oscillators
• On the spectrum of certain non-commutative harmonic oscillators and semiclassical analysis
• Zeta functions for the spectrum of the non-commutative harmonic oscillators
• Oscillator representations and systems of ordinary differential equations
• ON MELIN'S INEQUALITY FOR SYSTEMS
• On the Problem of Positivity of Pseudodifferential Systems
• MULTIPLICITY OF THE LOWEST EIGENVALUE OF NON-COMMUTATIVE HARMONIC OSCILLATORS
• SPECIAL VALUES OF THE SPECTRAL ZETA FUNCTION OF THE NON-COMMUTATIVE HARMONIC OSCILLATOR AND CONFLUENT HEUN EQUATIONS
• The uncertainty principle
• A Class of Counterexamples to the Fefferman–Phong Inequality for Systems
• The Dicke-type crossings among eigenvalues of differential operators in a class of non-commutative oscillators
• APÉRY-LIKE NUMBERS ARISING FROM SPECIAL VALUES OF SPECTRAL ZETA FUNCTIONS FOR NON-COMMUTATIVE HARMONIC OSCILLATORS
• Regularity Properties, Representation of Solutions, and Spectral Asymptotics of Systems with Multiplicities
• THE HEAT SEMIGROUP AND KERNEL ASSOCIATED WITH CERTAIN NON-COMMUTATIVE HARMONIC OSCILLATORS
• Proprietes spectrales d'operators pseduo-differentiels
• Espaces fonctionnels associés au calcul de Weyl-Hörmander
• Non-commutative harmonic oscillators-I
• ON THE SPECTRUM AND THE LOWEST EIGENVALUE OF CERTAIN NON-COMMUTATIVE HARMONIC OSCILLATORS
• VERIFIED NUMERICAL COMPUTATIONS FOR EIGENVALUES OF NON-COMMUTATIVE HARMONIC OSCILLATORS
• On positivity of certain systems of partial differential equations
• On the essential spectrum of certain non-commutative oscillators
• Non-commutative harmonic oscillators and Fuchsian ordinary differential operators