ATTIVITA' DI RICERCA
a) LARGE
AND INFINITE EXTRA DIMENSIONS
b) BOSE-EINSTEIN
CONDENSATION IN THE PRESENCE OF GRAVITY AND IMPURITIES
a) Large and infinite extra dimensions
(Alexander A. Andrianov, Paola Giacconi and Roberto
Soldati)
The
recent development in theories with more than
three spatial dimensions has shifted from very
small compact extra dimensions (Kaluza-Klein picture)
towards a brane world picture, where the observable
3+1 dimensional world is located inside a domain
wall - see the review paper by V. Rubakov, hep-ph/0104152.
Among many points of attraction of this approach,
we mention the possibility to lower considerably
the Planck scale of quantum gravity effects, to
find solutions of fermion mass hierarchy in the
Standard Model and to predict new physical phenomena
for the next generation of high-energy colliders
indicating the presence of extra dimensions.
In spite of the exploding number of publications
in this subject, some basic and difficult problems
remain nowadays unsolved.
As particular examples, we mention:
1) the natural implementation on the domain wall
of light but massive fermions together with light
massive scalar fields of Higgs type and light
gauge fields;
2) the self-consistent mechanisms to create a
thin domain wall;
3) the way to provide several domain walls on
a controllable distance as it is needed in the
scenarios supporting the fermion mass hierarchies.
The above problems must be solved not only in
the flat space-time with extra dimensions but
also in the Anti-de
Sitter space and its relatives. We propose to
investigate the above problems and to develop
a self-consistent description of domain wall formation
based on local 4-fermion interaction and other
types of interaction of proto-particles living
in the extra dimensions. The preliminary calculation
has shown that this approach is visible, viable
and predictive for the mass spectrum and the Yukawa
coupling constants of fermions and bosons trapped
by a domain wall. We also plan to analyze the
similar mechanisms in 3+1 and lower dimensions
in a search for new physical
phenomena in the condensed matter physics.
b) Bose-Einstein
condensation in the presence of gravity and impurities.
(Paola Giacconi and Roberto Soldati)
The influence of the gravitational field on remarkable
phenomena in condensed matter physics appears
to be a new and stimulating research field, both
from the experimental and theoretical points of
view. In particular, the occurrence and the eventual
response of a Bose-Einstein condensates to the
presence of a gravitational field is worthwhile
to be investigated, as it can give rise to interesting
and observable effects. It is also quite relevant
to understand the role of the presence of localized
impurities, which are always present in any realistic
system, in the quantum dynamical mechanism which
eventually allows the formation of a condensate.
As a matter of fact, it has been recently shown
that an ideal boson gas in the absence of impurities
does notcondense if a uniform gravitational field
is present. We propose to investigate the existence
and the main features of a Stark-like effect,
which arises if an ideal boson gas is under the
influence of a uniform gravitational field and
of a point-like impurity in the non-relativistic
one-, two- and three-dimensional cases. We shall
also attempt to consider the cases of the presence
of more than one point-like impurity as well as
the possibility of a two-bodies interaction among
the molecules of the boson gas.
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