THE INTERNATIONAL SERIES OF MONOGRAPHS ON PHYSICS ...

QUANTUM FRICTION IN ROTATING VACUUM 417
|vs | > c ⊥
ergoregion
|vs | = c ⊥
ergoplane
superfluid vacuum is
at rest
in inertial frame
vs = – Ωρ
inner
rotating cylinder
is at rest
in
corotating frame
Effective metric in corotating frame:
outer
cylinder
is at rest
in inertial frame
-2 -2 -2
ds 2 = – dt 2 + c ⊥ ρ 2 (dφ + Ωdt) 2 + c ⊥ dρ 2 + c|| dz 2
Fig. 31.3. Rotational quantum friction in superfluids as simulation of
Zel’dovich–Starobinsky effect. The inner cylinder rotates in superfluid vacuum
forming the preferred rotating reference frame. In this frame the effective
metric has an ergoregion, where the negative energy levels are empty. The
process of filling of these levels is similar to the radiation from the rotating
black hole.
It is instructive to consider the quantum friction in the frame rotating with
the inner cylinder.
31.4.2 Effective metric for quasiparticles under rotation
Let us first ignore the radiation from the rotating body and thus the slowing
down of the rotating cylinder. Then in the rotating frame, the cylinder and the
superfluid vacuum are stationary. If the velocity of rotation is not too high, so
that the superfluid velocity vs with respect to the surface of the cylinder does
not exceed the Landau criterion, all the perturbations of the superfluid caused
by the surface roughness of the cylinder are also stationary in the rotating frame.
Hence in the rotating frame the quasiparticle energy is a good quantum number.
Moreover, if the outer cylinder is far away, the inner cylinder represents the
proper environment for the quantum liquid, and the rotating frame becomes the
frame of the environment dictating the equilibrium conditions.
Far from the body the superfluid is at rest in the inertial frame. Thus in the
rotating frame the superfluid velocity is vs = −Ω × r. This is valid far enough
from the body, since close to the body there are space-dependent perturbations