THE INTERNATIONAL SERIES OF MONOGRAPHS ON PHYSICS ...

ANALOG OF PAIR PRODUCTION IN STRONG FIELDS 327
E=M
E=0
E=–M
bound state is
occupied by e -
(full bucket)
conduction band
Dirac sea
(valence band)
(a)
e -
(c)
vacant bound state
(empty bucket)
e +
e + is released
e -
(d)
(b)
bound state is
occupied by e -
Fig. 26.2. Pumping of electron–positron pairs from the Dirac sea using
draw-well.
breaking of a Cooper pair into two quasiparticles. The experiments, in which the
mechanism of the pair production is similar to the Gershtein–Zel’dovich mechanism,
have been conducted by Castelijns et al. (1986) and Carney et al. (1989).
A cylindrical wire was vibrating in superfluid 3 He-B and the pair production was
observed when the amplitude of the velocity of the wire exceeded some critical
value. Since the Bogoliubov–Nambu fermions in 3 He-B are in many respects similar
to Dirac electrons, we can map the quasiparticle radiation by a periodically
driven wire in a supercritical regime to the particle production in an alternating
electric field.
Let us discuss the rough model of how pair creation occurs in 3 He-B when
the wire is oscillating with velocity v = v0 cos(ωt) (Lambert 1990; Calogeracos
and Volovik 1999b). There are two features of the energy spectrum which are
important: the continuous spectrum at |E| > ∆0 and bound states which appear
near the surface of the wire, where the gap is reduced providing the potential well
for quasiparticles in Fig. 26.3 and Fig. 26.4(a). Let ∆0−ɛ be the energies of bound
states in the range ∆0 > ∆0 − ɛ ≥ ∆0 − ɛ0 ≥ 0. When the wire is oscillating, in
the reference frame of the wire which can serve as an environmentthe the energy
spectrum exhibits the Doppler shift. The velocity field around the wire is nonuniform:
it equals the velocity of wire v at infinity and reaches the maximal value
αv near the surface of the wire (for a perfect cylindrical wire α = 2). That is why
in the frame of the wire the continuous spectrum in the bulk and bound state