On the Existence of the Dynamics for Anharmonic Quantum Oscillator Systems
Bruno Nachtergaele, Benjamin Schlein, Robert Sims, Shannon Starr,, Valentin Zagrebnov
TL;DR
This paper constructs a mathematical framework for understanding the dynamics of anharmonic quantum oscillator lattice systems in the thermodynamic limit, utilizing Lieb-Robinson bounds to ensure rigorous results.
Contribution
It introduces a W^*-dynamical system model for anharmonic quantum oscillators, extending the analysis to infinite lattice systems.
Findings
Established a W^*-dynamical system for anharmonic oscillators
Applied Lieb-Robinson bounds to infinite lattice limits
Provided a rigorous mathematical description of quantum dynamics
Abstract
We construct a W^*-dynamical system describing the dynamics of a class of anharmonic quantum oscillator lattice systems in the thermodynamic limit. Our approach is based on recently proved Lieb-Robinson bounds for such systems on finite lattices.
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