Harmonic oscillator chains as Wigner quantum systems: Periodic and fixed wall boundary conditions in gl(1|n) solutions

DOI10.1063/1.2948894zbMath1152.81531arXiv0709.0180OpenAlexW2093747186MaRDI QIDQ5504984

Stijn Lievens, Neli I. Stoilova, Joris Van der Jeugt

Publication date: 23 January 2009

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0709.0180

Mathematics Subject Classification ID

Dynamic lattice systems (kinetic Ising, etc.) and systems on graphs in time-dependent statistical mechanics (82C20) Quantum dynamics and nonequilibrium statistical mechanics (general) (82C10)

Related Items (7)

Interacting universes and the cosmological constant ⋮ A contour for the entanglement entropies in harmonic lattices ⋮ On entanglement Hamiltonians of an interval in massless harmonic chains ⋮ Entanglement negativity in extended systems: a field theoretical approach ⋮ Wigner oscillators, twisted Hopf algebras, and second quantization ⋮ Wigner quantization of some one-dimensional Hamiltonians ⋮ The interacting multiverse and its effect on the cosmic microwave background

Cites Work

• An algebraic formulation of quantum mechanics in fractional dimensions
• Wigner approach to noncanonical quantizations.
• Galilean covariant Lie algebra of quantum mechanical observables.
• On the eigenvalue problem for arbitrary odd elements of the Lie superalgebra and applications
• Harmonic oscillators coupled by springs: Discrete solutions as a Wigner quantum system
• Wigner quantum systems. Two particles interacting via a harmonic potential. I. Two-dimensional space
• Fock space representations of the Lie superalgebra A(0,n)
• Many-body Wigner quantum systems
• A non-commutativen-particle 3D Wigner quantum oscillator
• The non-commutative and discrete spatial structure of a 3D Wigner quantum oscillator
• INTRODUCTION TO THE BASICS OF ENTANGLEMENT THEORY IN CONTINUOUS-VARIABLE SYSTEMS
• Hall effect in noncommutative coordinates
• Wigner quantum oscillators. osp(3/2) oscillators
• Representations of the Lie superalgebra in a Gel'fand–Zetlin basis and Wigner quantum oscillators
• Do the Equations of Motion Determine the Quantum Mechanical Commutation Relations?
• A Generalized Method of Field Quantization
• Lie superalgebras
• Testing non-commutative QED, constructing non-commutative MHD
• Newton-equivalent Hamiltonians for the harmonic oscillator
• Aharonov-Bohm effect in noncommutative spaces

This page was built for publication: Harmonic oscillator chains as Wigner quantum systems: Periodic and fixed wall boundary conditions in gl(1|n) solutions