2,083 research outputs found
On the angular and energy distribution of solar neutrons generated in P-P reactions
The problem of high energy neutron generation in P-P reactions in the solar atmosphere is reconsidered. It is shown that the angular distribution of emitted neutrons is anisotropic and the energy spectrum of neutrons depends on the angle of neutron emission
Single-Particle Momentum Distribution of an Efimov trimer
Experimental progress in the study of strongly interacting ultracold atoms
has recently allowed the observation of Efimov trimers. We study theoretically
a non-conventional observable for these trimer states, that may be accessed
experimentally, the momentum distribution n(k) of the constitutive bosonic
particles. The large momentum part of the distribution is particularly
intriguing: In addition to the expected 1/k^4 tail associated to contact
interactions, it exhibits a subleading tail 1/k^5 which is a hall-mark of
Efimov physics and leads to a breakdown of a previously proposed expression of
the energy as a functional of the momentum distribution.Comment: This is a subpart of the (too long to be published) work
arXiv:1001.0774. This subpart has 11 pages and 2 figures. Revised version
correcting minor error
Classification of zero-energy resonances by dissociation of Feshbach molecules
We study the dissociation of Feshbach molecules by a magnetic field sweep
across a zero-energy resonance. In the limit of an instantaneous magnetic field
change, the distribution of atomic kinetic energy can have a peak indicating
dominance of the molecular closed-channel spin configuration over the entrance
channel. The extent of this dominance influences physical properties such as
stability with respect to collisions, and so the readily measurable presence or
absence of the corresponding peak provides a practical method of classifying
zero-energy resonances. Currently achievable ramp speeds, e.g. those
demonstrated by Duerr et al. [Phys. Rev. A 70, 031601 (2005)], are fast enough
to provide magnetic field changes that may be interpreted as instantaneous. We
study the transition from sudden magnetic field changes to asymptotically wide,
linear ramps. In the latter limit, the predicted form of the atomic kinetic
energy distribution is independent of the specific implementation of the
two-body physics, provided that the near-resonant scattering properties are
properly accounted for.Comment: 10 pages, 5 eps figure
Stable Heteronuclear Few-Atom Bound States in Mixed Dimensions
We study few-body problems in mixed dimensions with heavy atoms
trapped individually in parallel one-dimensional tubes or two-dimensional
disks, and a single light atom travels freely in three dimensions. By using the
Born-Oppenheimer approximation, we find three- and four-body bound states for a
broad region of heavy-light atom scattering length combinations. Specifically,
the existence of trimer and tetramer states persist to negative scattering
lengths regime, where no two-body bound state is present. These few-body bound
states are analogous to the Efimov states in three dimensions, but are stable
against three-body recombination due to geometric separation. In addition, we
find that the binding energy of the ground trimer and tetramer state reaches
its maximum value when the scattering lengths are comparable to the separation
between the low-dimensional traps. This resonant behavior is a unique feature
for the few-body bound states in mixed dimensions.Comment: Extended version with 14 pages and 14 figure
BEC-BCS Crossover of a Trapped Two-Component Fermi Gas with Unequal Masses
We determine the energetically lowest lying states in the BEC-BCS crossover
regime of s-wave interacting two-component Fermi gases under harmonic
confinement by solving the many-body Schrodinger equation using two distinct
approaches. Essentially exact basis set expansion techniques are applied to
determine the energy spectrum of systems with N=4 fermions. Fixed-node
diffusion Monte Carlo methods are applied to systems with up to N=20 fermions,
and a discussion of different guiding functions used in the Monte Carlo
approach to impose the proper symmetry of the fermionic system is presented.
The energies are calculated as a function of the s-wave scattering length a_s
for N=2-20 fermions and different mass ratios \kappa of the two species. On the
BEC and BCS sides, our energies agree with analytically-determined first-order
correction terms. We extract the scattering length and the effective range of
the dimer-dimer system up to \kappa = 20. Our energies for the
strongly-interacting trapped system in the unitarity regime show no shell
structure, and are well described by a simple expression, whose functional form
can be derived using the local density approximation, with one or two
parameters. The universal parameter \xi for the trapped system for various
\kappa is determined, and comparisons with results for the homogeneous system
are presented.Comment: 11 pages, 6 figures, extended versio
Exact relations for quantum-mechanical few-body and many-body problems with short-range interactions in two and three dimensions
We derive relations between various observables for N particles with
zero-range or short-range interactions, in continuous space or on a lattice, in
two or three dimensions, in an arbitrary external potential. Some of our
results generalise known relations between large-momentum behavior of the
momentum distribution, short-distance behavior of the pair correlation function
and of the one-body density matrix, derivative of the energy with respect to
the scattering length or to time, and the norm of the regular part of the
wavefunction; in the case of finite-range interactions, the interaction energy
is also related to dE/da. The expression relating the energy to a functional of
the momentum distribution is also generalised, and is found to break down for
Efimov states with zero-range interactions, due to a subleading oscillating
tail in the momentum distribution. We also obtain new expressions for the
derivative of the energy of a universal state with respect to the effective
range, the derivative of the energy of an efimovian state with respect to the
three-body parameter, and the second order derivative of the energy with
respect to the inverse (or the logarithm in the two-dimensional case) of the
scattering length. The latter is negative at fixed entropy. We use exact
relations to compute corrections to exactly solvable three-body problems and
find agreement with available numerics. For the unitary gas, we compare exact
relations to existing fixed-node Monte-Carlo data, and we test, with existing
Quantum Monte Carlo results on different finite range models, our prediction
that the leading deviation of the critical temperature from its zero range
value is linear in the interaction effective range r_e with a model independent
numerical coefficient.Comment: 51 pages, 5 figures. Split into three articles: Phys. Rev. A 83,
063614 (2011) [arXiv:1103.5157]; Phys. Rev. A 86, 013626 (2012)
[arXiv:1204.3204]; Phys. Rev. A 86, 053633 (2012) [ arXiv:1210.1784
Three fermions in a box at the unitary limit: universality in a lattice model
We consider three fermions with two spin components interacting on a lattice
model with an infinite scattering length. Low lying eigenenergies in a cubic
box with periodic boundary conditions, and for a zero total momentum, are
calculated numerically for decreasing values of the lattice period. The results
are compared to the predictions of the zero range Bethe-Peierls model in
continuous space, where the interaction is replaced by contact conditions. The
numerical computation, combined with analytical arguments, shows the absence of
negative energy solution, and a rapid convergence of the lattice model towards
the Bethe-Peierls model for a vanishing lattice period. This establishes for
this system the universality of the zero interaction range limit.Comment: 6 page
Unitary Fermi gas, epsilon expansion, and nonrelativistic conformal field theories
We review theoretical aspects of unitary Fermi gas (UFG), which has been
realized in ultracold atom experiments. We first introduce the epsilon
expansion technique based on a systematic expansion in terms of the
dimensionality of space. We apply this technique to compute the thermodynamic
quantities, the quasiparticle spectrum, and the critical temperature of UFG. We
then discuss consequences of the scale and conformal invariance of UFG. We
prove a correspondence between primary operators in nonrelativistic conformal
field theories and energy eigenstates in a harmonic potential. We use this
correspondence to compute energies of fermions at unitarity in a harmonic
potential. The scale and conformal invariance together with the general
coordinate invariance constrains the properties of UFG. We show the vanishing
bulk viscosities of UFG and derive the low-energy effective Lagrangian for the
superfluid UFG. Finally we propose other systems exhibiting the nonrelativistic
scaling and conformal symmetries that can be in principle realized in ultracold
atom experiments.Comment: 44 pages, 15 figures, contribution to Lecture Notes in Physics
"BCS-BEC crossover and the Unitary Fermi Gas" edited by W. Zwerge
Illustration of universal relations for trapped four-fermion system with arbitrary s-wave scattering length
A two-component four-fermion system with equal masses, interspecies s-wave
scattering length a and vanishing intraspecies interactions under external
spherically symmetric harmonic confinement is considered. Using a correlated
Gaussian basis set expansion approach, we determine the energies and various
structural properties of the energetically lowest-lying gas-like state
throughout the crossover for various ranges of the underlying two-body
potential. Extrapolating to the zero-range limit, our numerical results show
explicitly that the total energy, the trap energy as well as certain aspects of
the pair distribution function and of the momentum distribution are related
through the so-called integrated contact intensity I(a). Furthermore, it is
shown explicitly that the total energy and the trap energy are related through
a generalized virial theorem that accounts for a non-zero range.Comment: 9 figures with several subfigure
Three body problem in a dilute Bose-Einstein condensate
We derive the explicit three body contact potential for a dilute condensed
Bose gas from microscopic theory. The three body coupling constant exhibits the
general form predicted by T.T. Wu [Phys. Rev. 113, 1390 (1959)] and is
determined in terms of the amplitudes of two and three body collisions in
vacuum. In the present form the coupling constant becomes accessible to
quantitative studies which should provide the crucial link between few body
collisions and the stability of condensates with attractive two body forces
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