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CALSCALE:GREGORIAN
PRODID:UW-Madison-Physics-Events
BEGIN:VEVENT
SEQUENCE:0
UID:UW-Physics-Event-2959
DTSTART:20130307T160000Z
DURATION:PT1H0M0S
DTSTAMP:20211021T061030Z
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 Fe_{8. 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
\n
\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] JosÃ© E. Moyal\, Quantum Mechanics as a Statistical T
heory\, Proc. Cambridge Philos. Soc. 45\, 99 (1949).
\n
\n[3]
Feifei Li\, Carol Braun\, and Anupam Garg\, The Weyl-Wigner-Moyal Form
alism for Spin\, arXiv:1210.4075v2 (2012).
\n
URL:https://www.physics.wisc.edu/events/?id=2959
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}