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Special Seminar
The two sides of a semiclassical spin
Date: Thursday, March 7th
Time: 10:00 am
Place: 5310 Chamberlin
Speaker: Feifei Li, Northwestern University
Abstract: A spinning electron and a spinning gyroscope represent the two ultra limits that spin can behave. One is purely quantum, while the other is purely classical. In this talk, I would like to discuss what happens for a semiclassical spin with intermediate magnitude of angular momentum. My talk consists two parts. In the first half, I would like to tell a story about the single-molecular-magnet Fe8. Fe8 is a molecule made of about a hundred atoms, yet it behaves like a single giant spin of J = 10 at low temperatures. Quantum interference causes the tunneling gap of this molecule to oscillate with applied magnetic field and to vanish at certain magnitude and direction of the magnetic fields, known as diabolical points. My story is about how these diabolical points were discovered, missed and rediscovered. The second half of my talk will focus on the quantum-classical correspondence for spin. The quantum-classical correspondence for a particle has been formulated by Moyal, who in a seminal paper, showed that quantum mechanics can be expressed as a quasi-statistical theory in the phase space of coordinate and momentum. Moyal's formalism unified Weyl ordering and Wigner quasi-distribution function, providing an invertible map between dynamical variables on the classical phase space and operators on the quantum mechanical Hilbert space. Moyal has also shown that the commutator of two operators is the Poisson bracket to leading order of $hbar$. All this was done for position and momentum. Here I present a Moyal treatment for spin, and show that, in the classical limit, the Weyl symbol for a spin commutator is i times the Poisson bracket of the corresponding Weyl symbols.


[1] Feifei Li and Anupam Garg, Numerical search for diabolical points in the energy spectrum of the single-molecule magnet Fe8, Phys. Rev. B 83, 132401 (2011).

[2] José E. Moyal, Quantum Mechanics as a Statistical Theory, Proc. Cambridge Philos. Soc. 45, 99 (1949).

[3] Feifei Li, Carol Braun, and Anupam Garg, The Weyl-Wigner-Moyal Formalism for Spin, arXiv:1210.4075v2 (2012).

Host: Friesen & Coppersmith
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