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Unformatted text preview: (x) ; E )dx.
b) Find the bounce path describing quantum escape from a cubic parabola
U (x) = ax ; bx3
with particle initially con ned at the local minimum x = ; a=3b.
t E Bounce path x(t) U(x) x x -U(x) Figure 1: Classical bounce path for tunneling out of a metastable state. 2. Escape at nite temperature. Periodic bounce trajectories. In the setting of Problem 1 (Fig. 1), at a nite temperature, escape may take place
(i) via tunneling directly from the ground state,
(ii) by Arrhenius thermal activation over the barrier, and, sometimes,
(iii) in two stages, via a combination of tunneling and thermal activation.
In the latter case, the particle is thermally excited to a higher energy level En in the
metastable well, and then tunnels through the barrier at an elevated energy. The bene t
of the barrier at a higher energy being thinner and more transparent can be compensated
by low thermal excitation probabili...
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This note was uploaded on 02/12/2014 for the course PHYS 8.514 taught by Professor Leonidlevitov during the Fall '04 term at MIT.
- Fall '04