38 research outputs found
Effective theories of scattering with an attractive inverse-square potential and the three-body problem
A distorted-wave version of the renormalisation group is applied to
scattering by an inverse-square potential and to three-body systems. In
attractive three-body systems, the short-distance wave function satisfies a
Schroedinger equation with an attractive inverse-square potential, as shown by
Efimov. The resulting oscillatory behaviour controls the renormalisation of the
three-body interactions, with the renormalisation-group flow tending to a limit
cycle as the cut-off is lowered. The approach used here leads to single-valued
potentials with discontinuities as the bound states are cut off. The
perturbations around the cycle start with a marginal term whose effect is
simply to change the phase of the short-distance oscillations, or the
self-adjoint extension of the singular Hamiltonian. The full power counting in
terms of the energy and two-body scattering length is constructed for
short-range three-body forces.Comment: 19 pages (RevTeX), 2 figure
Two-body correlations in N-body boson systems
We formulate a method to study two-body correlations in a system of N
identical bosons interacting via central two-body potentials. We use the
adiabatic hyperspherical approach and assume a Faddeev-like decomposition of
the wave function. For a fixed hyperradius we derive variationally an optimal
integro-differential equation for hyperangular eigenvalue and wave function.
This equation reduces substantially by assuming the interaction range much
smaller than the size of the N-body system. At most one-dimensional integrals
then remain. We view a Bose-Einstein condensate pictorially as a structure in
the landscape of the potential given as a function of the one-dimensional
hyperradial coordinate. The quantum states of the condensate can be located in
one of the two potential minima. We derive and discuss properties of the
solutions and illustrate with numerical results. The correlations lower the
interaction energy substantially. The new multi-body Efimov states are
solutions independent of details of the two-body potential. We compare with
mean-field results and available experimental data.Comment: 19 pages (RevTeX4), 13 figures (latex). Journal-link:
http://pra.aps.org
Classical Sphaleron Rate on Fine Lattices
We measure the sphaleron rate for hot, classical Yang-Mills theory on the
lattice, in order to study its dependence on lattice spacing. By using a
topological definition of Chern-Simons number and going to extremely fine
lattices (up to beta=32, or lattice spacing a = 1 / (8 g^2 T)) we demonstrate
nontrivial scaling. The topological susceptibility, converted to physical
units, falls with lattice spacing on fine lattices in a way which is consistent
with linear dependence on (the Arnold-Son-Yaffe scaling relation) and
strongly disfavors a nonzero continuum limit. We also explain some unusual
behavior of the rate in small volumes, reported by Ambjorn and Krasnitz.Comment: 14 pages, includes 5 figure
Universality in the Three-Body Problem for 4He Atoms
The two-body scattering length a for 4He atoms is much larger than their
effective range r_s. As a consequence, low-energy few-body observables have
universal characteristics that are independent of the interaction potential.
Universality implies that, up to corrections suppressed by r_s/a, all
low-energy three-body observables are determined by a and a three-body
parameter \Lambda_*. We give simple expressions in terms of a and \Lambda_* for
the trimer binding energy equation, the atom-dimer scattering phase shifts, and
the rate for three-body recombination at threshold. We determine \Lambda_* for
several 4He potentials from the calculated binding energy of the excited state
of the trimer and use it to obtain the universality predictions for the other
low-energy observables. We also use the calculated values for one potential to
estimate the effective range corrections for the other potentials.Comment: 23 pages, revtex4, 6 ps figures, references added, universal
expressions update
The Three-Boson System at Next-To-Next-To-Leading Order
We discuss effective field theory treatments of the problem of three
particles interacting via short-range forces (range R >> a_2, with a_2 the
two-body scattering length). We show that forming a once-subtracted scattering
equation yields a scattering amplitude whose low-momentum part is
renormalization-group invariant up to corrections of O(R^3/a_2^3). Since
corrections of O(R/a_2) and O(R^2/a_2^2) can be straightforwardly included in
the integral equation's kernel, a unique solution for 1+2 scattering phase
shifts and three-body bound-state energies can be obtained up to this accuracy.
We use our equation to calculate the correlation between the binding energies
of Helium-4 trimers and the atom-dimer scattering length. Our results are in
excellent agreement with the recent three-dimensional Faddeev calculations of
Roudnev and collaborators that used phenomenological inter-atomic potentials.Comment: 20 pages, 3 eps figure
Causality bounds for neutron-proton scattering
We consider the constraints of causality and unitarity for the low-energy
interactions of protons and neutrons. We derive a general theorem that
non-vanishing partial-wave mixing cannot be reproduced with zero-range
interactions without violating causality or unitarity. We define and calculate
interaction length scales which we call the causal range and the Cauchy-Schwarz
range for all spin channels up to J = 3. For some channels we find that these
length scales are as large as 5 fm. We investigate the origin of these large
lengths and discuss their significance for the choice of momentum cutoff scales
in effective field theory and universality in many-body Fermi systems.Comment: 36 pages, 10 figures, 7 tables, version to appear in Eur. Phys. J.
The Sphaleron Rate in SU(N) Gauge Theory
The sphaleron rate is defined as the diffusion constant for topological
number NCS = int g^2 F Fdual/32 pi^2. It establishes the rate of equilibration
of axial light quark number in QCD and is of interest both in electroweak
baryogenesis and possibly in heavy ion collisions. We calculate the
weak-coupling behavior of the SU(3) sphaleron rate, as well as making the most
sensible extrapolation towards intermediate coupling which we can. We also
study the behavior of the sphaleron rate at weak coupling at large Nc.Comment: 18 pages with 3 figure
The ^4He trimer as an Efimov system
We review the results obtained in the last four decades which demonstrate the
Efimov nature of the He three-atomic system.Comment: Review article for a special issue of the Few-Body Systems journal
devoted to Efimov physic
The Effect of Bound Dineutrons upon BBN
We have examined the effects of a bound dineutron, n2, upon big bang
nucleosynthesis (BBN) as a function of its binding energy B_n2. We find a
weakly bound dineutron has little impact but as B_n2 increases its presence
begins to alter the flow of free nucleons to helium-4. Due to this disruption,
and in the absence of changes to other binding energies or fundamental
constants, BBN sets a reliable upper limit of B_n2 <~ 2.5 MeV in order to
maintain the agreement with the observations of the primordial helium-4 mass
fraction and D/H abundance
Theory of Bose-Einstein condensation in trapped gases
The phenomenon of Bose-Einstein condensation of dilute gases in traps is
reviewed from a theoretical perspective. Mean-field theory provides a framework
to understand the main features of the condensation and the role of
interactions between particles. Various properties of these systems are
discussed, including the density profiles and the energy of the ground state
configurations, the collective oscillations and the dynamics of the expansion,
the condensate fraction and the thermodynamic functions. The thermodynamic
limit exhibits a scaling behavior in the relevant length and energy scales.
Despite the dilute nature of the gases, interactions profoundly modify the
static as well as the dynamic properties of the system; the predictions of
mean-field theory are in excellent agreement with available experimental
results. Effects of superfluidity including the existence of quantized vortices
and the reduction of the moment of inertia are discussed, as well as the
consequences of coherence such as the Josephson effect and interference
phenomena. The review also assesses the accuracy and limitations of the
mean-field approach.Comment: revtex, 69 pages, 38 eps figures, new version with more references,
new figures, various changes and corrections, for publ. in Rev. Mod. Phys.,
available also at http://www-phys.science.unitn.it/bec/BEC.htm