The
Centre for Mathematical Physics
SEMINAR
Speaker: Prof. Tony Bracken, Mathematics, UQ
Title: What is semiquantum mechanics?
10am, Thursday 21st September,
2006
Priestley Blding,
room 140
Abstract:
Semiclassical approximations to quantum dynamics are
almost as old as quantum mechanics itself. In the approach pioneered by Wigner,
the evolution of his quasiprobability density
function on phase space is expressed as an asymptotic series in increasing powers
of Planck's constant, with the classical Liouvillean
evolution as leading term. Successive semiclassical approximations
to quantum dynamics are defined by successive terms in the series. We consider
a complementary approach, which explores the quantum-classical interface from
the other direction. Classical dynamics is formulated in Hilbert space, with
the Groenewold quasidensity
operator as the image of the Liouville density on phase
space. The evolution of the Groenewold operator is
then expressed as an asymptotic series in increasing powers of Planck's
constant. Successive semiquantum approximations to classical
dynamics are defined by successive terms in this series, with the familiar
quantum evolution as leading term.
All interested are invited to attend.
Enquiries to Katrina Hibberd
email: keh@maths.uq.edu.au