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Friday, February 4, 2000
Physics Building, Room 204
Note special time.
[Host: Joseph Poon]
University of Virginia
"Breaking a one-dimensional chain: fracture in 1 + 1 dimensions"
The breaking rate of an atomic chain stretched at zero temperature by a
constant force can be calculated in a quasiclassical approximation by
finding the localized solutions ("bounces") of the equations of classical
dynamics in imaginary time. We show that this theory is related to the
critical cracks of stressed solids, because the world lines of the atoms in
the chain form a two-dimensional crystal, and the bounce is a crack
configuration in (unstable) mechanical equilibrium. Thus the tunneling
time, Action, and the breaking rate in the limit of small forces are
determined by the classical results of Griffith. For the limit of large
forces we give an exact bounce solution that describes the quantum fracture
and classical crack close to the limit of mechanical stability. This limit
can be viewed as a critical phenomenon for which we establish a
Levanyuk-Ginzburg criterion of weakness of fluctuations, and propose a
scaling argument for the critical regime. The post-tunneling dynamics is
understood by the analytic continuation of the bounce solutions to real time.
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