Spatially Inhomogeneous States of Many-Body Systems

Abstract

To treat many‐body systems in the presence of a static potential or problems of highly collective spatially inhomogeneous motions such as vortex lines, wavefunctions of a type Ψ= ∏ i=1 N g( x i )Φ( x 1 ,…, x N ) have been proposed. Here Φ is the exact ground state of the homogeneous system and g(x) is a one‐particle state introduced to describe the effect of the spatial inhomogeneity. However, to determine g(x) by the variation principle, one needs to know the spatial correlation functions of all orders for the homogeneous many‐body system. It is shown that the method of point transformations allows one to work with qualitatively similar but different states. The description of the system in the presence of a static impurity or of a state representing a vortex line in liquid helium requires a knowledge of only the average kinetic energy and x‐ray scattering factor for homogeneous liquid helium. Both of these are available from experiments. The treatment of a recoiling impurity atom, strictly speaking, requires a knowledge of the current correlation tensor for the ground state of the homogeneous many‐body system. This term vanishes in the Hartree limit of the theory for bosons.