SFB TRR 352 Mathematics of Many-Body Quantum Systems and Their Collective Phenomena

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B5 Numerics for Wigner–Weyl Methods in Many-Body Quantum Dynamics

Project Leaders

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Prof. Dr. Caroline Lasser, Prof. Dr. Christian Mendl


Leonardo Cancissu Araujo, Oliver Schwarze


The efficient numerical simulation of many-body quantum dynamics out of equilibrium is an outstanding problem due to the inherent curse of dimensionality. One class of simulation methods relies on the Wigner-Weyl formalism, usually defined in the phase space representation of quantum mechanics, to initiate an ensemble of classical trajectories for approximating the time-evolution of observables. Given a random phase space sampling of the initial quantum state, these truncated Wigner approximations are mesh-less by construction. They are well established for continuous variable quantum dynamics, where they have a rigorous mathematical underpinning by Egorov’s theorem. Recently, also discrete versions of this approximation type have been proposed. Despite remarkable successes for strongly correlated spin systems also for simulations over long times, rigorous analysis of this numerical approach for lattice models is largely lacking. In this project our goal is to fill this gap, and to further improve these methods by transferring ideas from continuous-variable semiclassical methods to the discrete (lattice) setting.