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Abstracts
P4.34
Influence of
4
He coverage on resonance properties of quartz tuning
fork immersed in liquid
3
He
Dmitriev V.V.(1), Soldatov A.A.(1,2), Yudin A.N.(1)
1) P.L. Kapitza Institute for Physical Problems of RAS, 119334 Moscow, Russia
2) Moscow Institute of Physics and Technology, 141700 Dolgoprudny, Russia
Nowadays quartz tuning forks are commonly used for temperature measurements
in experiments with liquid (normal or superfluid)
3
He. In most of the experiments
pure
3
He is used, but in some of them small amount of
4
He is added in order to
cover surfaces by a few monolayers of
4
He. We report measurements of influence
of different
4
He coverages on the fork resonance properties at different pressures.
We have found that presence of even small paramagnetic
3
He may essentially
change the temperature calibration especially at high pressures.
P4.35
Surface states and Bose-Einstein condensation
Mart´ınez, J.G.(1,2), Garc´ıa J.(1,2) and Sol´ıs M.A.(2)
1) UNAM, Posgrado en Ciencias F´ısicas,
2) UNAM, Instituto de F´ısica, Apdo. postal 20-360, 01000 CDMX, Mexico.
We show that an energy gap in the particle energy of an infinite 3D Bose gas not
only increases the BEC critical temperature and gives the exponential behavior of
the specific heat near to
T
= 0 but when we generalize to include any dimension
d
we find a finite BEC critical temperature even at
d
= 0. Although an energy
gap in the boson energy for a gas inside a infinite box has not been found even for
an interacting gas [1], when surface states are created inside the box introducing
an appropriated external potential, an energy gap appears between the ground
and the first excited states of the particle energy spectrum. Here we report the
critical temperature, the condensed fraction, the internal energy and the specific
heat for a
d
-dimensional Bose gas with a generalized dispersion relation plus
an energy gap, i.e.,
ε
=
ε
0
for
k
= 0 and
ε
=
ε
0
+ ∆ +
c
s
k
s
, for
k >
0, where
~
k
is the particle momentum,
ε
0
the lowest particle energy,
c
s
a constant with
dimension of energy multiplied by a length to the power
s >
0. Thermodynamic
properties are
ε
0
independent since this is just a reference energy. For ∆ = 0 we
recover the results reported in Ref. [2].
[1] N.M. Hugenholtz and D. Pines, Phys. Rev.
116
, 489 (1959).
[2] V. C. Aguilera-Navarro, M. de Llano y M. A. Sol´ıs, Eur. J. Phys.
20
, 177
(1999).
We acknowledge partial support from grants PAPIIT IN107616 and CONACyT
221030, Mexico.
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