65 research outputs found
Coalescence of Two Impurities in a Trapped One-dimensional Bose Gas
We study the ground state of a one-dimensional (1D) trapped Bose gas with two
mobile impurity particles. To investigate this set-up, we develop a variational
procedure in which the coordinates of the impurity particles are slow-like
variables. We validate our method using the exact results obtained for small
systems. Then, we discuss energies and pair densities for systems that contain
of the order of one hundred atoms. We show that bosonic non-interacting
impurities cluster. To explain this clustering, we calculate and discuss
induced impurity-impurity potentials in a harmonic trap. Further, we compute
the force between static impurities in a ring ({\it {\`a} la} the Casimir
force), and contrast the two effective potentials: the one obtained from the
mean-field approximation, and the one due to the one-phonon exchange. Our
formalism and findings are important for understanding (beyond the polaron
model) the physics of modern 1D cold-atom systems with more than one impurity.Comment: 10 pages, 6 figures, published versio
An interpolatory ansatz captures the physics of one-dimensional confined Fermi systems
Interacting one-dimensional quantum systems play a pivotal role in physics.
Exact solutions can be obtained for the homogeneous case using the Bethe ansatz
and bosonisation techniques. However, these approaches are not applicable when
external confinement is present. Recent theoretical advances beyond the Bethe
ansatz and bosonisation allow us to predict the behaviour of one-dimensional
confined systems with strong short-range interactions, and new experiments with
cold atomic Fermi gases have already confirmed these theories. Here we
demonstrate that a simple linear combination of the strongly interacting
solution with the well-known solution in the limit of vanishing interactions
provides a simple and accurate description of the system for all values of the
interaction strength. This indicates that one can indeed capture the physics of
confined one-dimensional systems by knowledge of the limits using wave
functions that are much easier to handle than the output of typical numerical
approaches. We demonstrate our scheme for experimentally relevant systems with
up to six particles. Moreover, we show that our method works also in the case
of mixed systems of particles with different masses. This is an important
feature because these systems are known to be non-integrable and thus not
solvable by the Bethe ansatz technique.Comment: 22 pages including methods and supplementary materials, 11 figures,
title slightly change
Integrable families of hard-core particles with unequal masses in a one-dimensional harmonic trap
We show that the dynamics of particles in a one-dimensional harmonic trap
with hard-core interactions can be solvable for certain arrangements of unequal
masses. For any number of particles, there exist two families of unequal mass
particles that have integrable dynamics, and there are additional exceptional
cases for three, four and five particles. The integrable mass families are
classified by Coxeter reflection groups and the corresponding solutions are
Bethe ansatz-like superpositions of hyperspherical harmonics in the relative
hyperangular coordinates that are then restricted to sectors of fixed particle
order. We also provide evidence for superintegrability of these Coxeter mass
families and conjecture maximal superintegrability.Comment: 9.5+4.5 pages, 5 figures, 2 tables; v3: a few corrections and
addition
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