Eigenvalue distributions of reduced density matrices (Q461414)

In this work the authors provide a method based on symplectic geometry to answer the question: What is the probability distribution of the eigenvalues of the one-body reduced density matrices of a pure many-particle quantum state drawn at random from the unitarily invariant distribution? As explained in the text, the eigenvalue distributions that are computed are Duistermaat-Heckman measures, which are defined using the push-forward of the Liouville measure on a symplectic manifold along the moment map. In the second part of the work, the authors study the representation theory connected to the one-body quantum marginal problem, and ''the relevant multiplicities include the Kronecker coefficients, which play a major role in the representation theory of the unitary and symmetric groups''.