Nirav Mehta

The hyperspherical four-fermion problem

The problem of a few interacting fermions in quantum physics has sparked intense interest, particularly in recent years owing to connections with the behaviour of superconductors, fermionic superfluids and finite nuclei. This review addresses recent developments in the theoretical description of four fermions having finite-range interactions, stressing insights that have emerged from a hyperspherical coordinate perspective. The subject is complicated, so we have included many detailed formulae that will hopefully make these methods accessible to others interested in using them. The universality regime, where the dominant length scale in the problem is the two-body scattering length, is particularly stressed, including its implications for the famous BCS–BEC crossover problem. Derivations and relevant formulae are also included for the calculation of challenging few-body processes such as recombination.

General Theoretical Description of N-Body Recombination

Formulas for the cross section and event rate constant describing recombination of N particles are derived in terms of general S-matrix elements. Our result immediately yields the generalized Wigner threshold scaling for the recombination of N bosons. A semianalytical formula encapsulates the overall scaling with energy and scattering length, as well as resonant modifications by the presence of N-body states near the threshold collision energy in the entrance channel. We then apply our model to the case of four-boson recombination into an Efimov trimer and a free atom.

Green's Functions and the Adiabatic Hyperspherical Method

We address the few-body problem using the adiabatic hyperspherical representation. A general form for the hyperangular Greens function in

Dimer-dimer collisions at finite energies in two-component Fermi gases

d

Efimov states embedded in the three-body continuum

dimensions is derived. The resulting Lippmann-Schwinger equation is solved for the case of three particles with

Three bosons in one dimension with short-range interactions: Zero-range potentials

s

Three-Body Recombination in One Dimension

-wave zero-range interactions. Identical particle symmetry is incorporated in a general and intuitive way. Complete semianalytic expressions for the nonadiabatic channel couplings are derived. Finally, a model to describe the atom loss due to three-body recombination for a three-component Fermi gas of

Microscopic Derivation of Multichannel Hubbard Models for Ultracold Nonreactive Molecules in an Optical Lattice

^{6}\mathrm{Li}

Low-energy operators in effective theories

atoms is presented.

Lattice-Model Parameters for Ultracold Nonreactive Molecules: Chaotic Scattering and Its Limitations

We introduce a major theoretical generalization of existing techniques for handling the three-body problem that accurately describes the interactions among four fermionic atoms. Application to a two-component Fermi gas accurately determines dimer-dimer scattering parameters at finite energies and can give deeper insight into the corresponding many-body phenomena. To account for finite temperature effects, we calculate the energy-dependent complex dimer-dimer scattering length, which includes contributions from elastic and inelastic collisions. Our results indicate that strong finite-energy effects and dimer dissociation are crucial for understanding the physics in the strongly interacting regime for typical experimental conditions. While our results for dimer-dimer relaxation are consistent with experiment, they confirm only partially a previously published theoretical result.