Beyond Bogoliubov dynamics (Q2668153)

The starting point of the investigations of the authors is the model describing bosons in the mean-field or Hartree regime. This is characterized by weak, long-range interactions. The authors construct a norm approximation such that all corrections to correlation functions and expectation values of bounded operators are given in terms of the two-point correlation functions of a quasifree state. The advantage of their construction that it reduces the complexity of the \(N\)-body problem and makes it possible to numerical calculate these quantities to arbitrary precision. Hence the computation of the higher-order corrections reduces to solve first the well-studied Hartree equation and second the Bogoliubov equation. The second is equivalent to solving a \(2 \times 2\) matrix differential equation. Moreover, the \(N\)-independent corrections fulfill a generalized form of Wick's theorem.