1,813 research outputs found
Lattice two-body problem with arbitrary finite range interactions
We study the exact solution of the two-body problem on a tight-binding
one-dimensional lattice, with pairwise interaction potentials which have an
arbitrary but finite range. We show how to obtain the full spectrum, the bound
and scattering states and the "low-energy" solutions by very efficient and
easy-to-implement numerical means. All bound states are proven to be
characterized by roots of a polynomial whose degree depends linearly on the
range of the potential, and we discuss the connections between the number of
bound states and the scattering lengths. "Low-energy" resonances can be located
with great precission with the methods we introduce. Further generalizations to
include more exotic interactions are also discussed.Comment: 6 pages, 3 figure
Can one detect a non-smooth null infinity?
It is shown that the precession of a gyroscope can be used to elucidate the
nature of the smoothness of the null infinity of an asymptotically flat
spacetime (describing an isolated body). A model for which the effects of
precession in the non-smooth null infinity case are of order is
proposed. By contrast, in the smooth version the effects are of order .
This difference should provide an effective criterion to decide on the nature
of the smoothness of null infinity.Comment: 6 pages, to appear in Class. Quantum Gra
On the existence and convergence of polyhomogeneous expansions of zero-rest-mass fields
The convergence of polyhomogeneous expansions of zero-rest-mass fields in
asymptotically flat spacetimes is discussed. An existence proof for the
asymptotic characteristic initial value problem for a zero-rest-mass field with
polyhomogeneous initial data is given. It is shown how this non-regular problem
can be properly recast as a set of regular initial value problems for some
auxiliary fields. The standard techniques of symmetric hyperbolic systems can
be applied to these new auxiliary problems, thus yielding a positive answer to
the question of existence in the original problem.Comment: 10 pages, 1 eps figur
Strongly interacting confined quantum systems in one dimension
In one dimension, the study of magnetism dates back to the dawn of quantum
mechanics when Bethe solved the famous Heisenberg model that describes quantum
behaviour in magnetic systems. In the last decade, one-dimensional systems have
become a forefront area of research driven by the realization of the
Tonks-Girardeau gas using cold atomic gases. Here we prove that one-dimensional
fermionic and bosonic systems with strong short-range interactions are solvable
in arbitrary confining geometries by introducing a new energy-functional
technique and obtaining the full spectrum of energies and eigenstates. As a
first application, we calculate spatial correlations and show how both ferro-
and anti-ferromagnetic states are present already for small system sizes that
are prepared and studied in current experiments. Our work demonstrates the
enormous potential for quantum manipulation of magnetic correlations at the
microscopic scale.Comment: 11 pages, 2 figures, including methods, final versio
Multicomponent Strongly Interacting Few-Fermion Systems in One Dimension
The paper examines a trapped one-dimensional system of multicomponent
spinless fermions that interact with a zero-range two-body potential. We show
that when the repulsion between particles is very large the system can be
approached analytically. To illustrate this analytical approach we consider a
simple system of three distinguishable particles, which can be addressed
experimentally. For this system we show that for infinite repulsion the energy
spectrum is sixfold degenerate. We also show that this degeneracy is partially
lifted for finitely large repulsion for which we find and describe
corresponding wave functions.Comment: Paper in connection with the 22nd European Conference on Few-Body
Problems in Physics, Krakow, Poland, 9-13 September 201
Fractional energy states of strongly-interacting bosons in one dimension
We study two-component bosonic systems with strong inter-species and
vanishing intra-species interactions. A new class of exact eigenstates is found
with energies that are {\it not} sums of the single-particle energies with wave
functions that have the characteristic feature that they vanish over extended
regions of coordinate space. This is demonstrated in an analytically solvable
model for three equal mass particles, two of which are identical bosons, which
is exact in the strongly-interacting limit. We numerically verify our results
by presenting the first application of the stochastic variational method to
this kind of system. We also demonstrate that the limit where both inter- and
intra-component interactions become strong must be treated with extreme care as
these limits do not commute. Moreover, we argue that such states are generic
also for general multi-component systems with more than three particles. The
states can be probed using the same techniques that have recently been used for
fermionic few-body systems in quasi-1D.Comment: 6 pages, 4 figures, published versio
Engineering the Dynamics of Effective Spin-Chain Models for Strongly Interacting Atomic Gases
We consider a one-dimensional gas of cold atoms with strong contact
interactions and construct an effective spin-chain Hamiltonian for a
two-component system. The resulting Heisenberg spin model can be engineered by
manipulating the shape of the external confining potential of the atomic gas.
We find that bosonic atoms offer more flexibility for tuning independently the
parameters of the spin Hamiltonian through interatomic (intra-species)
interaction which is absent for fermions due to the Pauli exclusion principle.
Our formalism can have important implications for control and manipulation of
the dynamics of few- and many-body quantum systems; as an illustrative example
relevant to quantum computation and communication, we consider state transfer
in the simplest non-trivial system of four particles representing
exchange-coupled qubits.Comment: 10 pages including appendix, 3 figures, revised versio
Bound states of Dipolar Bosons in One-dimensional Systems
We consider one-dimensional tubes containing bosonic polar molecules. The
long-range dipole-dipole interactions act both within a single tube and between
different tubes. We consider arbitrary values of the externally aligned dipole
moments with respect to the symmetry axis of the tubes. The few-body structures
in this geometry are determined as function of polarization angles and dipole
strength by using both essentially exact stochastic variational methods and the
harmonic approximation. The main focus is on the three, four, and five-body
problems in two or more tubes. Our results indicate that in the weakly-coupled
limit the inter-tube interaction is similar to a zero-range term with a
suitable rescaled strength. This allows us to address the corresponding
many-body physics of the system by constructing a model where bound chains with
one molecule in each tube are the effective degrees of freedom. This model can
be mapped onto one-dimensional Hamiltonians for which exact solutions are
known.Comment: 22 pages, 7 figures, revised versio
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