ON THE EXISTENCE OF THE DYNAMICS FOR ANHARMONIC QUANTUM OSCILLATOR SYSTEMS

DOI10.1142/S0129055X1000393XzbMath1187.82071arXiv0909.2249OpenAlexW2031733889MaRDI QIDQ3552525

Shannon Starr, Bruno Nachtergaele, Robert Sims, Benjamin Schlein, Valentin A. Zagrebnov

Publication date: 22 April 2010

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

Full work available at URL: https://arxiv.org/abs/0909.2249

zbMATH Keywords

thermodynamic limitanharmonic latticeinfinite-system dynamics

Mathematics Subject Classification ID

Noncommutative dynamical systems (46L55) Dynamic lattice systems (kinetic Ising, etc.) and systems on graphs in time-dependent statistical mechanics (82C20) Perturbation theories for operators and differential equations in quantum theory (81Q15) Quantum dynamics and nonequilibrium statistical mechanics (general) (82C10) Lattice dynamics; integrable lattice equations (37K60)

Related Items (13)

The resolvent algebra for oscillating lattice systems: dynamics, ground and equilibrium states ⋮ A holographic model for black hole complementarity ⋮ Lieb-Robinson bounds for the Toda lattice ⋮ Dynamical localization in disordered quantum spin systems ⋮ Lieb-Robinson bounds and strongly continuous dynamics for a class of many-body fermion systems in \(\mathbb{R}^d\) ⋮ Automorphic equivalence within gapped phases of quantum lattice systems ⋮ Scaling limits of lattice quantum fields by wavelets ⋮ Improving the Lieb-Robinson bound for long-range interactions ⋮ Entanglement rates and the stability of the area law for the entanglement entropy ⋮ Tachyonic quench in a free bosonic field theory ⋮ Quasi-locality bounds for quantum lattice systems. I. Lieb-Robinson bounds, quasi-local maps, and spectral flow automorphisms ⋮ Dispersive estimates for harmonic oscillator systems ⋮ Hydrodynamic limit for a disordered quantum harmonic chain

Cites Work

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• Lieb-Robinson bounds for harmonic and anharmonic lattice systems
• Lieb-Robinson bounds and the exponential clustering theorem
• Spectral gap and exponential decay of correlations
• Estimating the Lieb-Robinson velocity for classical anharmonic lattice systems
• The smallest C\(^*\)-algebra for canonical commutation relations
• On the propagation of a perturbation in an anharmonic system
• Propagation of correlations in quantum lattice systems
• Quasi-free states of the C.C.R.-algebra and Bogoliubov transformations
• The Stability of Matter in Quantum Mechanics

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