Spectral theory of non-commutative harmonic oscillators: an introduction

DOI10.1007/978-3-642-11922-4zbMath1200.35346OpenAlexW602411825MaRDI QIDQ974682

Alberto Parmeggiani

Publication date: 4 June 2010

Published in: Lecture Notes in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-642-11922-4

zbMATH Keywords

dynamicseigenvaluesspectral theoryfunctional calculusnon-commutative harmonic oscillator

Mathematics Subject Classification ID

Pseudodifferential operators as generalizations of partial differential operators (35S05) Estimates of eigenvalues in context of PDEs (35P15) Asymptotic distributions of eigenvalues in context of PDEs (35P20) Applications of operator theory to differential and integral equations (47N20) Determinants and determinant bundles, analytic torsion (58J52) Research exposition (monographs, survey articles) pertaining to partial differential equations (35-02)

Related Items (20)

An exact solution of the second-order differential equation with the fractional/generalised boundary conditions ⋮ Simplicity of the lowest eigenvalue of non-commutative harmonic oscillators and the Riemann scheme of a certain Heun's differential equation ⋮ Ultra-weak time operators of Schrödinger operators ⋮ Covering families of the asymmetric quantum Rabi model: \(\eta\)-shifted non-commutative harmonic oscillators ⋮ On the spectral zeta function of second order semiregular non-commutative harmonic oscillators ⋮ \(L^p\)-\(L^q\) boundedness of Fourier multipliers associated with the anharmonic oscillator ⋮ Spectral asymptotic properties of semiregular non-commutative harmonic oscillators ⋮ Non-commutative harmonic oscillators and related problems ⋮ On a class of anharmonic oscillators ⋮ Schatten-von Neumann classes of integral operators ⋮ On the essential spectrum of certain non-commutative oscillators ⋮ Long time dynamics for the one dimensional non linear Schrödinger equation ⋮ Number Theoretic Study in Quantum Interactions ⋮ Growth of Sobolev norms for linear Schrödinger operators ⋮ Non-commutative Harmonic Oscillators ⋮ On the Problem of Positivity of Pseudodifferential Systems ⋮ SPECTRAL ZETA FUNCTIONS FOR THE QUANTUM RABI MODELS ⋮ On a class of anharmonic oscillators. II: General case ⋮ Spectral analysis of non-commutative harmonic oscillators: the lowest eigenvalue and no crossing ⋮ Symmetry of asymmetric quantum Rabi models

This page was built for publication: Spectral theory of non-commutative harmonic oscillators: an introduction