Speaker
Description
The configuration space, i.e. the Hilbert space, of compound quantum systems grows exponentially with the number of its subsystems: its dimensionality is given by the product of the dimensions of its constituents. Therefore a full quantum treatment, in general, is hardly possible analytically and can be carried out numerically for fairly small systems only. Yet, in order to obtain interesting physics, an approximation might very well suffice. One of these approximations is given by the cumulant expansion, where expectation values of products of operators are replaced by products of expectation values of said operators, neglecting higher-order correlations. The lowest order of these approximations is widely known as the mean field approximation and used routinely throughout quantum physics. Despite its ubiquitous presence, a general criterion for its applicability remains to be found. In this paper, we discuss two problems in quantum electrodynamics and quantum information, namely the collective radiative dissipation of a dipole-dipole interacting chain of atoms and the factorization of a bi-prime by annealing in an adiabatic quantum computer. On the one hand, we find smooth behaviour, where the approximation becomes increasingly better with higher orders, while, on the other hand, we are puzzled by completely uncontrolled solutions.
