25-30 August 2019
Henry Ford Building
Europe/Berlin timezone

Time evolution of coupled spin systems in a generalized Wigner representation

28 Aug 2019, 13:55
Max Kade Auditorium (Henry Ford Building)

Max Kade Auditorium

Henry Ford Building

Prize lecture Spin physics Prize Lectures


Dr Bálint Koczor (Technische Universität München, now University of Oxford)


So-called phase-space representations such as Wigner functions, are a powerful tool for representing quantum states and characterizing their time evolution in the case of infinite-dimensional quantum systems and have been widely used in quantum optics and beyond. Continuous phase spaces have also been studied for the finite-dimensional quantum systems of individual spins. However, much less was known for coupled spin systems, and we present a complete theory of Wigner functions for this case. In particular, we provide a self-contained Wigner formalism for describing and predicting the time evolution of coupled spins which lends itself to visualizing the high-dimensional state space in a structured and intuitive way. We completely treat the case of an arbitrary number of coupled spins 1/2, thereby establishing the equation of motion using Wigner functions. The explicit form of the time evolution is then calculated for up to three spins 1/2. The underlying physical principles of our Wigner representations for coupled spin systems are illustrated for several NMR examples. This talk is based on Annals of Physics DOI 10.1016/j.aop.2018.11.020 (in press).

Primary authors

Dr Bálint Koczor (Technische Universität München, now University of Oxford) Dr Robert Zeier (Technische Universität München, now Forschungszentrum Jülich GmbH) Prof. Steffen Glaser (Technische Universität München)

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