The Quantum of Action and Atomic Models

William Peddie

The atom, even in its simplest form, must possess a most complicated structure. The aim of physical science is to find a hypothetical structure, and mode of its functioning, which will give a good account of atomic phenomena. When the phenomena are complicated, and only very partially known, hypothetical investigations are most uncertain and provisional, and make little attempt to work otherwise than by analogy or illustration. In such cases help is often obtained through the discovery of a general law which unifies a wide range of phenomena, and which may be followed by many diverse structures in their activities. Well-known examples are found in the law of conservation of energy, the law of least action, and, recently, the law of quantum action.

Walter Dittrich

Eric Braaten, Dongqing Zhang

In a system of atoms with large positive scattering length, weakly bound diatomic molecules (dimers) are generated dynamically by the strong interactions between the atoms. If the atoms are modeled by a quantum field theory with an atom field only, condensates of dimers cannot be described by the mean-field approximation because there is no field associated with the dimers. We develop a method for describing dimer condensates in such a model based on the one-particle-irreducible (1PI) effective action. We construct an equivalent 1PI effective action that depends not only on the classical atom field but also on a classical dimer field. The method is illustrated by applying it to the many-body behavior of bosonic atoms with large scattering length at zero temperature using an approximation in which the two-atom amplitude is treated exactly, but irreducible $N$-atom amplitudes for $N\ensuremath{\geqslant}3$ are neglected. The two 1PI effective actions give identical results for the atom superfluid phase, but the one with a classical dimer field is much more convenient for describing the dimer superfluid phase. The results are also compared with previous work on the Bose gas near a Feshbach resonance.

Wei Guo

In this work, measurement in the near-field region of a sub-wavelength separation between two atoms is studied when the detector used to perform the measurement is modeled as another atom. Through an analysis of multiple scattering of an incident wave among the atoms, the back-action of the detector on the measurement is examined. It is found that, although the separation can never be measured exactly, the presence of the back-action makes the measurement more accurate. It is also found that the back-action enables the waves observed by the detector to avoid singularities that otherwise exist when the back-action is ignored.