arXiv subjects

H. -W. Hammer

Publications and source records attributed to H. -W. Hammer.

At least 145 records · Page 8Linked to original sources

arXiv2004

Effective Field Theory for Cold Atoms

Effective Field Theory (EFT) provides a powerful framework that exploits a separation of scales in physical systems to perform systematically improvable, model-independent calculations. Particularly interesting are few-body systems with short-range interactions and large two-body scattering length. Such systems display remarkable universal features. In systems with more than two particles, a three-body force with limit cycle behavior is required for consistent renormalization already at leading order. We will review this EFT and some of its applications in the physics of cold atoms. Recent extensions of this approach to the four-body system and N-boson droplets in two spatial dimensions will also be discussed.

cond-mat.other↗

arXiv2004

Universal Properties of the Four-Boson System in Two Dimensions

We consider the nonrelativistic four-boson system in two dimensions interacting via a short-range attractive potential. For a weakly attractive potential with one shallow two-body bound state with binding energy B_2, the binding energies B_N of shallow N-body bound states are universal and thus do not depend on the details of the interaction potential. We compute the four-body binding energies in an effective quantum mechanics approach. There are exactly two bound states: the ground state with B_4^(0)=197.3(1)B_2 and one excited state with B_4^(1)=25.5(1)B_2. We compare our results to recent predictions for N-body bound states with large N>>1.

cond-mat.other↗

arXiv2004

Enhanced Dimer Relaxation in an Atomic/Molecular BEC

We derive a universal formula for the rate constant βfor relaxation of a shallow dimer into deeply-bound diatomic molecules in the case of atoms with a large scattering length a. We show that βis determined by a and by two 3-body parameters that also determine the binding energies and widths of Efimov states. The rate constant βscales like \hbar a/m near the resonance, but the coefficient is a periodic function of ln(a) that may have resonant enhancement at values of a that differ by multiples of 22.7.

cond-mat.other↗

arXiv2004

Updated dispersion-theoretical analysis of the nucleon electromagnetic form factors

In the light of the new data on the various neutron and proton electromagnetic form factors taken in recent years, we update the dispersion-theoretical analysis of the nucleon electromagnetic form factors from the mid-nineties. The parametrization of the spectral functions includes constraints from unitarity, perturbative QCD, and recent measurements of the neutron charge radius. We obtain a good description of most modern form factor data, with the exception of the Jefferson Lab data on G_E^p/G_M^p in the four-momentum transfer range Q^2=3...6 GeV^2. For the magnetic radii of the proton and the neutron we find r_M^p = 0.857 fm and r_M^n = 0.879 fm, which is consistent with the recent determinations using continued fraction expansions.

hep-ph↗

arXiv2003

On the pion cloud of the nucleon

We evaluate the two--pion contribution to the nucleon electromagnetic form factors by use of dispersion analysis and chiral perturbation theory. After subtraction of the rho--meson component, we calculate the distributions of charge and magnetization in coordinate space, which can be interpreted as the effects of the pion cloud. We find that the charge distribution of this pion cloud effect peaks at distances of about 0.3 fm. Furthermore, we calculate the contribution of the pion cloud to the isovector charges and radii of the nucleon.

hep-ph↗

arXiv2003

Chiral Dynamics: Theory and Experiment (CD2003)

These are the proceedings of the fourth international workshop on "Chiral Dynamics: Theory and Experiment" which was held at the University of Bonn, September 8-13, 2003. The workshop concentrated on the various experimental andtheoretical aspects of chiral dynamics, including for the first time in this series detailed discussions of lattice gauge theory. It consisted of an introductory lecture, plenary talks, working group talks and working group summaries. Included is a short contribution per talk.

hep-ph↗

arXiv2003

An Infrared Renormalization Group Limit Cycle in QCD

We conjecture that QCD can be tuned to an infrared limit cycle in the three-nucleon system by adjusting the up and down quark masses to critical values at which the binding energies of the deuteron and its spin-singlet partner are tuned to zero. At the critical point, the triton would have infinitely many arbitrarily-shallow excited states with the ratio of the binding energies of successive states approaching a universal constant close to 515.

nucl-th↗

arXiv2003

Universality in the physics of cold atoms with large scattering length

Effective field theories exploit a separation of scales in physical systems in order to perform systematically improvable, model-independent calculations. They are ideally suited to describe universal aspects of a wide range of physical systems. I will discuss recent applications of effective field theory to cold atomic and molecular few-body systems with large scattering length.

cond-mat↗

arXiv2003

Efimov States in a Bose-Einstein Condensate near a Feshbach Resonance

Recent experiments with Bose-Einstein condensates of 85Rb atoms near a Feshbach resonance have produced evidence for a condensate of diatomic molecules coexisting with the atom condensate. It should also be possible to create condensates of the triatomic molecules predicted by Efimov coexisting with the atom and dimer condensates. The smoking gun for the trimer condensate would be oscillatory dependence of observables on the binding energy of the trimer. It may also be possible to deduce the existence of the trimer condensate from the spectra of the bursts of atoms and dimers created in the disappearance of the trimers.

cond-mat↗

arXiv2003

Narrow Resonances in Effective Field Theory

We discuss the power counting for effective field theories with narrow resonances near a two-body threshold. Close to threshold, the effective field theory is perturbative and only one combination of coupling constants is fine-tuned. In the vicinity of the resonance, a second, ``kinematic'' fine-tuning requires a nonperturbative resummation. We illustrate our results in the case of nucleon-alpha scattering.

nucl-th↗

arXiv2003

An Infrared Renormalization Group Limit Cycle in QCD

Small increases in the up and down quark masses of QCD would tune the theory to the critical renormalization group trajectory for an infrared limit cycle in the three-nucleon system. At critical values of the quark masses, the deuteron binding energy goes to zero and the triton has infinitely many excited states with an accumulation point at the 3-nucleon threshold. The ratio of the binding energies of successive states approaches a universal constant that is close to 515. The proximity of physical QCD to the critical trajectory for this limit cycle explains the success of an effective field theory of nucleons with contact interactions only in describing the low-energy 3-nucleon system.

nucl-th↗

arXiv2003

Universal Equation for Efimov States

Efimov states are a sequence of shallow 3-body bound states that arise when the 2-body scattering length is large. Efimov showed that the binding energies of these states can be calculated in terms of the scattering length and a 3-body parameter by solving a transcendental equation involving a universal function of one variable. We calculate this universal function using effective field theory and use it to describe the three-body system of 4He atoms. We also extend Efimov's theory to include the effects of deep 2-body bound states, which give widths to the Efimov states.

cond-mat↗

arXiv2003

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 Λ_*. We give simple expressions in terms of a and Λ_* for the trimer binding energy equation, the atom-dimer scattering phase shifts, and the rate for three-body recombination at threshold. We determine Λ_* 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.

cond-mat↗

arXiv2003

Comment on ``Ramsey Fringes in a Bose-Einstein Condensate between Atoms and Molecules''

In Phys. Rev. Lett. 89, 180401 (2002) [cond-mat/0204504], Kokkelmans and Holland interpret the results of a recent experiment at JILA that demonstrated atom-molecule coherence in a Bose-Einstein condensate. Using a mean-field approximation to a resonance field theory involving an atom condensate and a molecular condensate, they find that the molecular condensate is tiny compared to the atom condensate. We show that if the probability for the molecular field to create a diatomic molecule is correctly included, the numbers of atoms in the atom condensate and in the condensate of diatomic molecules are comparable.

cond-mat↗

arXiv2003

Nucleon Strangeness in Dispersion Theory

Dispersion relations provide a powerful tool to describe the low-energy structure of hadrons. We review the status of the strange vector form factors of the nucleon in dispersion theory. We also comment on open questions and the relation to chiral perturbation theory.

hep-ph↗

arXiv2002

Low Energy Expansion in the Three Body System to All Orders and the Triton Channel

We extend and systematise the power counting for the three-body system, in the context of the ``pion-less'' Effective Field Theory approach, to all orders in the low-energy expansion. We show that a sub-leading part of the three-body force appears at the third order and delineate how the expansion proceeds at higher orders. After discussing the renormalisation issues in a simple bosonic model, we compute the phase shifts for neutron-deuteron scattering in the doublet S wave (triton) channel and compare our results with phase shift analysis and potential model calculations.

nucl-th↗

arXiv2002

Effective Field Theory for Halo Nuclei: Shallow p-Wave States

Halo nuclei are a promising new arena for studies based on effective field theory (EFT). We develop an EFT for shallow p-wave states and discuss the application to elastic n-alpha scattering. In contrast to the s-wave case, both the scattering length and effective range enter at leading order. We also discuss the prospects of using EFT in the description of other halos, such as the three-body halo nucleus 6He.

nucl-th↗

arXiv2002

Effective Field Theory for Fermi Systems in a large N expansion

A system of fermions with short-range interactions at finite density is studied using the framework of effective field theory. The effective action formalism for fermions with auxiliary fields leads to a loop expansion in which particle-hole bubbles are resummed to all orders. For spin-independent interactions, the loop expansion is equivalent to a systematic expansion in 1/N, where "N" is the spin-isospin degeneracy g. Numerical results at next-to-leading order are presented and the connection to the Bose limit of this system is elucidated.

nucl-th↗