Quasi-particle expansion for a boson system

Pedro Ribeiro, Masudul Haque, Achilleas Lazarides

We provide an account of the static and dynamic properties of hard-core bosons in a one-dimensional lattice subject to a multichromatic quasiperiodic potential for which the single-particle spectrum has mobility edges. We use the mapping from strongly interacting bosons to weakly interacting fermions and provide exact numerical results for hard-core bosons in and out of equilibrium. In equilibrium, we find that the system behaves like a quasi-condensate (insulator) depending on whether the Fermi surface of the corresponding fermionic system lies in a spectral region where the single-particle states are delocalized (localized). We also study nonequilibrium expansion dynamics of initially trapped bosons and demonstrate that the extent of partial localization is determined by the single-particle spectrum.

R. Bijker, Stuart Pittel, J. Dukelsky

Masahiko HIROOKA, Shuichiro Yamasaki

The infrared divergence of the interaction among Bogoliubov's quasi· particles in a degener­ ate boson system can be avoided by introducing improved quasi-particles. A formula is given which relates the single· particle operators ap directly to the improved quasi-particle operators bp ' which have been defined in terms of collective variables in a preceding paper. The operators ap are expressed in terms of bp as a series using N112 as a formal expansion parameter, where N is the number of particles in the system. Terms up to order N312 are given together with a tenn of order N2 which is necessary for the calculation of the ground· state energy to order N2 • The fonnula makes the reason clear why the operators b p enable us to eliminate the ultraviolet divergence haunting collective theories including the quantum hydrodynamics.

Richard David Etters

Ulf Bissbort, Michael Buchhold, Walter Hofstetter

We present a generalized quasi-particle theory for bosonic lattice systems, which naturally contains all relevant collective modes, including the Higgs amplitude in the strongly correlated superfluid. In contrast to Bogoliubov theory, this non-perturbative method does not rely on a small condensate depletion and is valid for any interaction strength in three spatial dimensions. It is based on an expansion around the bosonic Gutzwiller ground state in terms of appropriately chosen fluctuation operators and lays the foundation for the description of real-time dynamics in terms of the natural, weakly interacting quasi-particles. Furthermore, it provides a systematic framework for efficiently calculating observables beyond the Gutzwiller approximation and for including external perturbations, as well as higher order decay and interactions in terms of quasi-particle operators. It allows for the construction of an alternative path integral approach in terms of quasi-particle coherent states.

Richard David Etters