The waveoperator representation of quantum and classical dynamics
Gerard Mccaul (Loughborough)
What does it mean to take the classical limit of a quantum system? Surprisingly, this question underlies many of the deepest challenges in quantum theory, both in its foundations and applications. Topics from quantum computation to chaos rely on concepts which are only meaningfully defined classically. For this reason, a systematic understanding of how quantum dynamics transitions into its classical limit is crucial. In this talk, I will outline a new approach to this problem, via the wave operator representation: a reformulation of quantum dynamics based on the square root of the density matrix. This representation offers a unified bridge between Hilbert and phase space, with a transparent route to semiclassical limits. I’ll show how both quantum and classical dynamics can be simultaneously described within this formalism, and - time permitting - sketch how this can be applied both as a novel mechanism for the emergence of chaos, and as a benchmark for quantum computational advantage.
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