BEGIN:VCALENDAR VERSION:2.0 CALSCALE:GREGORIAN PRODID:UW-Madison-Physics-Events BEGIN:VEVENT SEQUENCE:0 UID:UW-Physics-Event-2959 DTSTART:20130307T160000Z DURATION:PT1H0M0S DTSTAMP:20260314T234504Z LAST-MODIFIED:20130228T162535Z LOCATION:5310 Chamberlin SUMMARY:The two sides of a semiclassical spin\, Special Seminar\, Feif ei Li\, Northwestern University DESCRIPTION: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 a ngular momentum. My talk consists two parts. In the first half\, I wou ld like to tell a story about the single-molecular-magnet Fe8. Fe8 is a molecule made of about a hundred atoms\, yet i t behaves like a single giant spin of J = 10 at low temperature s. Quantum interference causes the tunneling gap of this molecule to o scillate with applied magnetic field and to vanish at certain magnitud e and direction of the magnetic fields\, known as diabolical points. M y 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 corresponden ce for a particle has been formulated by Moyal\, who in a seminal pape r\, showed that quantum mechanics can be expressed as a quasi-statisti cal theory in the phase space of coordinate and momentum. Moyal's form alism unified Weyl ordering and Wigner quasi-distribution function\, p roviding an invertible map between dynamical variables on the classica l phase space and operators on the quantum mechanical Hilbert space. M oyal has also shown that the commutator of two operators is the Poisso n bracket to leading order of $hbar$. All this was done for position a nd 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>i times the Poisson bracket of the corresponding Weyl symbols. \n
\nReferences
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\n[1] Feifei Li and Anupam Garg\, Nu merical search for diabolical points in the energy spectrum of the sin gle-molecule magnet Fe8\, Phys. Rev. B 83\, 132401 (2011).< br> \n
\n[2] José E. Moyal\, Quantum Mechanics as a Statistical T heory\, Proc. Cambridge Philos. Soc. 45\, 99 (1949).
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\n[3] Feifei Li\, Carol Braun\, and Anupam Garg\, The Weyl-Wigner-Moyal Form alism for Spin\, arXiv:1210.4075v2 (2012).
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URL:https://www.physics.wisc.edu/events/?id=2959 END:VEVENT END:VCALENDAR