Rindler空间中的Bose-Einstein凝聚
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Physics Letters B 750 (2015) 209–217
Contents lists available at ScienceDirect
Physics Letters B
www.elsevier.com/locate/physletb
Bose–Einstein condensation in the Rindler space
Shingo Takeuchi
The Institute for Fundamental Study “The Tah Poe Academia Institute”, Naresuan University, Phitsanulok 65000, Thailand
a r t i c l e i n f o a b s t r a c t
Article history:
Received
2 July 2015
Received
in revised form 13 August 2015
Accepted
7 September 2015
Available
online 10 September 2015
Editor:
J. Hisano
Based on the Unruh effect, we calculate the critical acceleration of the Bose–Einstein condensation in a
free complex scalar field at finite density in the Rindler space. Our model corresponds to an ideal gas
performing constantly accelerating motion in a Minkowski space–time at zero-temperature, where the
gas is composed of the complex scalar particles and it can be thought to be in a thermal-bath with the
Unruh temperature. In the accelerating frame, the model will be in the Bose–Einstein condensation state
at low acceleration; on the other hand, there will be no condensation at high acceleration by the thermal
excitation brought into by the Unruh effect. Our critical acceleration is the one at which the Bose–Einstein
condensation begins to appear in the accelerating frame when we decrease the acceleration gradually. To
carry out the calculation, we assume that the critical acceleration is much larger than the mass of the
particle.
© 2015 The Author. Published by Elsevier B.V. This is an open access article under the CC BY license
(http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP
3
.
1. Introduction
The Bose–Einstein condensation is getting a lot of attention re-
cently
as a quantum fluid for the test of the analogy between
sound waves in quantum fluids and scalar field fluctuation in
curved space–times [1]. Thanks to this analogy, we can expect new
progress and insight which are difficult only in the gravitational
analysis in the quantum gravity and cosmology. Further, the ex-
periments
of the quantum gravity and cosmology are difficult due
to the required energy level and the scale of phenomena. How-
ever,
the experiments of the condensed matters will be free from
such problems to some extent. It is thought for these reasons that
pseudo experiments of the gravity are possible in the quantum flu-
ids
through the analogy.
In
order to understand the quantum phenomena in the gravity
and cosmology such as the Hawking radiation [2] and particle cre-
ation [3,4],
the Unruh effect [5–8] is important in terms of the role
that the event-horizons play.
The
Unruh effect is a prediction that one moving in the
Minkowski space–time with a linear constant acceleration expe-
riences
the space–time as a thermal-bath with the Unruh temper-
ature,
T
U
=
¯
ha/(2πck
B
) ≈ 4 × 10
−23
a/(cm/s
2
) [K], where a is the
acceleration.
Now,
various experimental attempts in the condensed matters
to observe the gravitational phenomena are being invented (see
E-mail address: shingo@nu.ac.th.
Ref. [9] for example). Particularly as for the experiments to de-
tect
the Unruh effect, there are attempts in Bose–Einstein con-
densates [11],
graphenes [12] and Berry phases [13]. For other
attempts see Ref. [14], for example, and related references.
We
also address the issue of the Unruh effect in the Bose–
Einstein
condensation. Whether the Bose–Einstein condensation
occurs or not is determined by temperature. We assume in this pa-
per
that the Unruh temperature exists in the constantly accelerat-
ing
system according to the Unruh effect mentioned above. At this
time we can think that the Unruh effect affects the Bose–Einstein
condensation. Although an enormous number of studies have been
done on the Unruh effect and the Bose–Einstein condensation so
far, these are performed separately and little is known about the
Unruh effect in the Bose–Einstein condensation at this moment.
Since both the Unruh effect and the Bose–Einstein condensation
are very important in the fundamental physics, new understand-
ings
could be expected by combining the Unruh effect and the
Bose–Einstein condensation. In this paper, from such a background,
we calculate the critical acceleration for the Bose–Einstein conden-
sation
based on the thermal excitation brought into by the Unruh
effect.
Let
us here explain the Bose–Einstein condensation briefly (for
more details, see Ref. [10] for example). The Bose–Einstein con-
densation
state is the situation that all the particle stay in the
least energy state uniformly owing to the Bose–Einstein statistics,
and it appears as a phase transition that all the particles uniformly
drop to the least energy state as the entropically-favored state due
to the Bose–Einstein statistics at some time. (In the Bose–Einstein
http://dx.doi.org/10.1016/j.physletb.2015.09.013
0370-2693/
© 2015 The Author. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by
SCOAP
3
.
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