64 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.
Efimov states in excited nuclear halos
Universality -- an essential concept in physics -- implies that different
systems show the same phenomenon and can be described by a unified theory. A
prime example of the universal quantum phenomena is the Efimov effect, which is
the appearance of multiples of low-energy three-body bound states with
progressively large sizes dictated by the discrete scale invariance. The Efimov
effect, originally proposed in the nuclear physics context, has been observed
in cold atoms and molecules. The search for the Efimov effect
in nuclear physics, however, has been a long-standing challenge owing to the
difficulty in identifying ideal nuclides with a large -wave scattering
length; such nuclides can be unambiguously considered as Efimov states. Here,
we propose a systematic method to identify nuclides that exhibit Efimov states
in their excited states in the vicinity of the neutron separation threshold.
These nuclei are characterised by their enormous low-energy neutron capture
cross-sections, hence giant -wave scattering length. Using our protocol, we
identified Zr and Gd as novel candidate nuclides that show the
Efimov states. They are well inside the valley of stability in the nuclear
chart, and are suited for experimental realisation of the Efimov states in
nuclear physics.Comment: 13 pages, 3 figures, 2 table
Crossover trimers connecting continuous and discrete scaling regimes
For a system of two identical fermions and one distinguishable particle
interacting via a short-range potential with a large s-wave scattering length,
the Efimov trimers and Kartavtsev-Malykh trimers exist in different regimes of
the mass ratio. The Efimov trimers are known to exhibit a discrete scaling
invariance, while the Kartavtsev-Malykh trimers feature a continuous scaling
invariance. We point out that a third type of trimers, "crossover trimers",
exist universally regardless of short-range details of the potential. These
crossover trimers have neither the discrete nor continuous scaling invariance.
We show that the crossover trimers continuously connect the discrete and
continuous scaling regimes as the mass ratio and the scattering length are
varied. We identify the regions for the Kartavtsev-Malykh trimers, Efimov
trimers, crossover trimers, and non-universal trimers as a function of the mass
ratio and the s-wave scattering length by investigating the scaling property
and model-independence of the trimers.Comment: 14 pages, 9 figure
Universality of an impurity in a Bose-Einstein condensate
Universality is a powerful concept in physics, allowing one to construct
physical descriptions of systems that are independent of the precise
microscopic details or energy scales. A prime example is the Fermi gas with
unitarity limited interactions, whose universal properties are relevant to
systems ranging from atomic gases at microkelvin temperatures to the inner
crust of neutron stars. Here we address the question of whether unitary Bose
systems can possess a similar universality. We consider the simplest strongly
interacting Bose system, where we have an impurity particle ("polaron")
resonantly interacting with a Bose-Einstein condensate (BEC). Focusing on the
ground state of the equal-mass system, we use a variational wave function for
the polaron that includes up to three Bogoliubov excitations of the BEC, thus
allowing us to capture both Efimov trimers and associated tetramers. Unlike the
Fermi case, we find that the length scale associated with Efimov trimers (i.e.,
the three-body parameter) can strongly affect the polaron's behaviour, even at
boson densities where there are no well-defined Efimov states. However, by
comparing our results with recent quantum Monte Carlo calculations, we argue
that the polaron energy is a \emph{universal} function of the Efimov three-body
parameter for sufficiently low boson densities. We further support this
conclusion by showing that the energies of the deepest bound Efimov trimers and
tetramers at unitarity are universally related to one another, regardless of
the microscopic model. On the other hand, we find that the quasiparticle
residue and effective mass sensitively depend on the coherence length of
the BEC, with the residue tending to zero as diverges, in a manner akin
to the orthogonality catastrophe.Comment: 11 pages and 7 figures + supplemental materia
Eigenvalues of two-state quantum walks induced by the Hadamard walk
Existence of the eigenvalues of the discrete-time quantum walks is deeply
related to localization of the walks. We revealed the distributions of the
eigenvalues given by the splitted generating function method (the SGF method)
of the quantum walks we had treated in our previous studies. In particular, we
focused on two kinds of the Hadamard walk with one defect models and the
two-phase QWs that have phases at the non-diagonal elements of the unitary
transition operators. As a result, we clarified the characteristic parameter
dependence for the distributions of the eigenvalues with the aid of numerical
simulation.Comment: 9 pages, 4 figure
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