132 research outputs found
Absence of a four-body Efimov effect in the 2 + 2 fermionic problem
In the free three-dimensional space, we consider a pair of identical
fermions of some species or in some internal state, and a pair of
identical fermions of another species or in another state. There
is a resonant -wave interaction (that is of zero range and infinite
scattering length) between fermions in different pairs, and no interaction
within the same pair. We study whether this fermionic system can exhibit
(as the fermionic system) a four-body Efimov effect in the absence of
three-body Efimov effect, that is the mass ratio between
and fermions and its inverse are both smaller than
13.6069{\ldots}. For this purpose, we investigate scale invariant zero-energy
solutions of the four-body Schr\"odinger equation, that is positively
homogeneous functions of the coordinates of degree {}, where is a
generalized Efimov exponent {that becomes purely imaginary in the presence of a
four-body Efimov effect.} Using rotational invariance in momentum space, it is
found that the allowed values of are such that has a zero
eigenvalue; here the operator , that depends on the total angular
momentum , acts on functions of two real variables (the cosine of the
angle between two wave vectors and the logarithm of the ratio of their moduli),
and we write it explicitly in terms of an integral matrix kernel. We have
performed a spectral analysis of , analytical and for an arbitrary
imaginary for the continuous spectrum, numerical and limited to and
for the discrete spectrum. We conclude that no eigenvalue of
crosses zero over the mass ratio interval , even if, in the parity sector , the continuous
spectrum of has everywhere a zero lower border. As a consequence, there
is no possibility of a four-body Efimov effect for the 2+2 fermions. We also
enunciated a conjecture for the fourth virial coefficient of the unitary
spin- Fermi gas,inspired from the known analytical form of the third
cluster coefficient and involving the integral over the imaginary -axis of
times the logarithmic derivative of the determinant of summed over
all angular momenta.The conjectured value is in contradiction with the
experimental results.Comment: 30 pages, 8 figures, final version published in Phys. Rev.
The unitary gas in an isotropic harmonic trap: symmetry properties and applications
We consider N atoms trapped in an isotropic harmonic potential, with s-wave
interactions of infinite scattering length. In the zero-range limit, we obtain
several exact analytical results: mapping between the trapped problem and the
free-space zero-energy problem, separability in hyperspherical coordinates,
SO(2,1) hidden symmetry, and relations between the moments of the trapping
potential energy and the moments of the total energy
Phase Dynamics of Bose-Einstein Condensates: Losses versus Revivals
In the absence of losses the phase of a Bose-Einstein condensate undergoes
collapses and revivals in time due to elastic atomic interactions. As
experiments necessarily involve inelastic collisions, we develop a model to
describe the phase dynamics of the condensates in presence of collisional
losses. We find that a few inelastic processes are sufficient to damp the
revivals of the phase. For this reason the observability of phase revivals for
present experimental conditions is limited to condensates with a few hundreds
of atoms.Comment: 24 pages, 9 figures. submitted to European Journal of Physics
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