With the pair Hamiltonian model as the starting point, perturbation theory calculations are performed for the average energy and the momentum distribution through second order in the two-body interaction potential. A phenomenological theory of helium II is proposed. The chief underlying feature of this phenomenological theory, which is shown to have a firm basis in the microscopic theory, is the presence of a double quasiparticle spectrum. Phenomenological expressions for the average energy and other quantities of interest are also proposed. Simple prescriptions are obtained for calculating the quasiparticle energies and the chemical potential from the average energy. Via these prescriptions, the quasiparticle energies and the chemical potential are calculated through second order in the interaction potential at T ≠ 0 °K, and the results are compared with earlier work in the literature.With the pair Hamiltonian model as the starting point, perturbation theory calculations are performed for the average energy and the momentum distribution through second order in the two-body interaction potential. A phenomenological theory of helium II is proposed. The chief underlying feature of this phenomenological theory, which is shown to have a firm basis in the microscopic theory, is the presence of a double quasiparticle spectrum. Phenomenological expressions for the average energy and other quantities of interest are also proposed. Simple prescriptions are obtained for calculating the quasiparticle energies and the chemical potential from the average energy. Via these prescriptions, the quasiparticle energies and the chemical potential are calculated through second order in the interaction potential at T ≠ 0 °K, and the results are compared with earlier work in the literature.

Journal of Mathematical PhysicsAug 1, 19713 citations

Ultra-low energy elastic scattering in a system of three He atoms

Vladimir Roudnev

arXiv:physics/0206058Chemical Physics LettersJan 1, 200342 citations

Multichannel scattering and Feshbach resonances: Effective theory, phenomenology, and many-body effects

Georg M. Bruun, Andrew David Jackson, Evgeni E. Kolomeitsev

A low-energy effective theory based on a microscopic multichannel description of the atom-atom interaction is derived for the scattering of alkali-metal atoms in different hyperfine states. This theory describes all scattering properties, including medium effects, in terms of the singlet and triplet scattering lengths and the range of the atom-atom potential and provides a link between a microscopic description of Feshbach scattering and more phenomenological approaches. It permits the calculation of medium effects on the resonance coming from the occupation of closed channel states. The examination of such effects is demonstrated to be of particular relevance to an experimentally important Feshbach resonance for $^{40}\mathrm{K}$ atoms. We analyze a recent rethermalization rate experiment on $^{40}\mathrm{K}$ and demonstrate that a measurement of the temperature dependence of this rate can determine the magnetic moment of the Feshbach molecule. Finally, the energy dependence of the Feshbach interaction is shown to introduce a negative effective range inversely proportional to the width of the resonance. Since our theory is based on a microscopic multichannel picture, it allows the explicit calculation of corrections to commonly used approximations such as the neglect of the effective range and the treatment of the Feshbach molecule as a point boson.A low-energy effective theory based on a microscopic multichannel description of the atom-atom interaction is derived for the scattering of alkali-metal atoms in different hyperfine states. This theory describes all scattering properties, including medium effects, in terms of the singlet and triplet scattering lengths and the range of the atom-atom potential and provides a link between a microscopic description of Feshbach scattering and more phenomenological approaches. It permits the calculation of medium effects on the resonance coming from the occupation of closed channel states. The examination of such effects is demonstrated to be of particular relevance to an experimentally important Feshbach resonance for $^{40}\mathrm{K}$ atoms. We analyze a recent rethermalization rate experiment on $^{40}\mathrm{K}$ and demonstrate that a measurement of the temperature dependence of this rate can determine the magnetic moment of the Feshbach molecule. Finally, the energy dependence of the Feshbach interaction is shown to introduce a negative effective range inversely proportional to the width of the resonance. Since our theory is based on a microscopic multichannel picture, it allows the explicit calculation of corrections to commonly used approximations such as the neglect of the effective range and the treatment of the Feshbach molecule as a point boson.

arXiv:cond-mat/0501407Physical Review AMay 26, 200544 citations

Low-momentum interactions for few-body systems

S. K. Bogner

Few-Body SystemsDec 1, 20081 citation

Effective field theory of interactions and renormalization

Manuel Valiente, Nikolaj Thomas Zinner

Here, we introduce the notion of low-energy interactions in non-relativistic quantum mechanics. The goal is to reproduce low-energy phenomenology only, which generally generates infinities, just as in relativistic quantum field theories. The resulting low-energy theory is called effective field theory of interactions, in analogy with the non-relativistic ‘pionless’ effective field theory widely used in nuclear physics. The predictive power of the effective theory depends upon the renormalizability of the theory, which removes the infinities while obtaining sound low-energy physics. Most of the chapter deals with perturbative and non-perturbative renormalization, which will be subsequently needed throughout the rest of the book.Here, we introduce the notion of low-energy interactions in non-relativistic quantum mechanics. The goal is to reproduce low-energy phenomenology only, which generally generates infinities, just as in relativistic quantum field theories. The resulting low-energy theory is called effective field theory of interactions, in analogy with the non-relativistic ‘pionless’ effective field theory widely used in nuclear physics. The predictive power of the effective theory depends upon the renormalizability of the theory, which removes the infinities while obtaining sound low-energy physics. Most of the chapter deals with perturbative and non-perturbative renormalization, which will be subsequently needed throughout the rest of the book.

Institute of Physics eBooksSep 1, 20230 citations

^{40}\mathrm{K}

atoms. We analyze a recent rethermalization rate experiment on

^{40}\mathrm{K}

and demonstrate that a measurement of the temperature dependence of this rate can determine the magnetic moment of the Feshbach molecule. Finally, the energy dependence of the Feshbach interaction is shown to introduce a negative effective range inversely proportional to the width of the resonance. Since our theory is based on a microscopic multichannel picture, it allows the explicit calculation of corrections to commonly used approximations such as the neglect of the effective range and the treatment of the Feshbach molecule as a point boson.