Many-body physics and resolvent algebras
Detlev Buchholz, Jakob Yngvason
November 07, 2024
Some advantages of the algebraic approach to many body physics, based on
resolvent algebras, are illustrated by the simple example of non-interacting
bosons which are confined in compact regions with soft boundaries. It is shown
that the dynamics of these systems converges to the spatially homogeneous
dynamics for increasing regions and particle numbers and a variety of boundary
forces. The corresponding correlation functions of thermal equilibrium states
also converge in this limit. Depending on the filling of the regions with
particles, the limits can either be spatially homogeneous, including the
Bose-Einstein condensates, or they become inhomogeneous with varying, but
finite local particle densities. In case of this spontaneous breakdown of the
spatial symmetry, the presence of condensates can be established by exhibiting
temporal correlations over large temporal distances (memory effects).
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