Application of Dispersion Relations to the Many-Body Problem

Walter Greiner

P. E. Kornilovitch

A formula is derived that relates the ground-state dispersion of a many-body system with the end-to-end distribution of paths with open boundary conditions in imaginary time. The formula does not involve the energy estimator. It allows direct measurement of the ground-state dispersion by quantum Monte Carlo methods without analytical continuation or auxiliary fitting. The formula is applied to the lattice polaron problem. The exact polaron spectrum and density of states are calculated for several models in one, two, and three dimensions. In the adiabatic regime of the Holstein model, the polaron density of states deviates spectacularly from the free-particle shape.

Marcin Kalinowski, Yidan Wang, Przemysław Bienias +7 more

Rydberg polaritons provide an example of a rare type of system where three-body interactions can be as strong as or even stronger than two-body interactions.The three-body interactions can be either dispersive or dissipative, with both types possibly giving rise to exotic, strongly interacting, and topological phases of matter.Despite past theoretical and experimental studies of the regime with dispersive interaction, the dissipative regime is still mostly unexplored.Using a renormalization group technique to solve the quantum three-body problem, we show how the shape and strength of dissipative three-body forces can be universally enhanced for Rydberg polaritons.We demonstrate how these interactions relate to the transmission through a single-mode cavity, which can be used as a probe of the three-body physics in current experiments.

Walter Greiner

A Roussou, J Smyrnakis, M Magiropoulos +5 more

We study the rotational properties of a two-component Bose–Einstein condensed gas of distinguishable atoms which are confined in a ring potential using both the mean-field approximation, as well as the method of diagonalization of the many-body Hamiltonian. We demonstrate that the angular momentum may be given to the system either via single-particle, or 'collective' excitation. Furthermore, despite the complexity of this problem, under rather typical conditions the dispersion relation takes a remarkably simple and regular form. Finally, we argue that under certain conditions the dispersion relation is determined via collective excitation. The corresponding many-body state, which, in addition to the interaction energy minimizes also the kinetic energy, is dictated by elementary number theory.

Walter Greiner