Universality in few-body systems with large scattering length

Universality in few-body systems with large scattering length

24 Feb 2005 | H.-W. Hammer
The paper discusses the application of Effective Field Theory (EFT) to few-body systems with large scattering lengths, focusing on the universal properties and scaling behaviors. EFT is a powerful framework that exploits the separation of scales in physical systems to perform systematic and model-independent calculations. For systems with short-range interactions and large two-body scattering lengths, EFT reveals remarkable universality. In three-body systems, a three-body force with limit cycle behavior is required for consistent renormalization at leading order. The paper reviews the EFT for three-body systems and its applications in nuclear and atomic physics, including the possibility of an infrared limit cycle in QCD. Recent extensions of the EFT to four-body systems and $N$-boson droplets in two spatial dimensions are also addressed. The universal properties of few-body systems with large scattering lengths are discussed, including the Efimov effect and scaling functions relating various few-body observables. The paper concludes with a discussion on the universal properties of $N$-boson droplets in two dimensions and the potential for universality in the $N$-body problem for $N \geq 4$.The paper discusses the application of Effective Field Theory (EFT) to few-body systems with large scattering lengths, focusing on the universal properties and scaling behaviors. EFT is a powerful framework that exploits the separation of scales in physical systems to perform systematic and model-independent calculations. For systems with short-range interactions and large two-body scattering lengths, EFT reveals remarkable universality. In three-body systems, a three-body force with limit cycle behavior is required for consistent renormalization at leading order. The paper reviews the EFT for three-body systems and its applications in nuclear and atomic physics, including the possibility of an infrared limit cycle in QCD. Recent extensions of the EFT to four-body systems and $N$-boson droplets in two spatial dimensions are also addressed. The universal properties of few-body systems with large scattering lengths are discussed, including the Efimov effect and scaling functions relating various few-body observables. The paper concludes with a discussion on the universal properties of $N$-boson droplets in two dimensions and the potential for universality in the $N$-body problem for $N \geq 4$.
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