Journal article

Publication year: 1997

Pages: 91-100

Journal: Zeitschrift für Physik A, Hadrons and Nuclei

Volume number: 358

Issue number: 1

ISSN: 0939-7922

DOI Link: https://doi.org/10.1007/s002180050281

Publisher: Springer

Abstract: 
We investigate the convergence properties of the cluster expansion of equal-time Green functions in scalar theories with quartic self-coupling in (0 + 1), (1 + 1), and (2 + 1) space-time dimensions. The computations are carried out within the equal-time correlation dynamics approach, which consists in a closed set of coupled equations of motion for connected Green functions as obtained by a truncation of the BBGKY hierarchy. We find that the cluster expansion shows good convergence as long as the system is in a localized state (single phase configuration) and that it breaks down in a non-localized state (two phase configuration), as one would naively expect. Furthermore, in the case of dynamical calculations with a time dependent Hamiltonian for the evaluation of the effective potential we find two timescales determining the adiabaticity of the propagation; these are the time required for adiabaticity in the single phase region and the time required for tunneling into the non-localized lowest energy state in the two phase region. Our calculations show a good convergence for the effective potentials in (1 + 1) and (2 + 1) space-time dimensions since tunneling is suppressed in higher space-time dimensions.

Harvard Citation style: Peter, A., Cassing, W., Hauser, J. and Thoma, M. (1997) Convergence properties of the cluster expansion for equal-time Green functions in scalar theories, Zeitschrift für Physik A Hadrons and Nuclei, 358(1), pp. 91-100. https://doi.org/10.1007/s002180050281

APA Citation style: Peter, A., Cassing, W., Hauser, J., & Thoma, M. (1997). Convergence properties of the cluster expansion for equal-time Green functions in scalar theories. Zeitschrift für Physik A Hadrons and Nuclei. 358(1), 91-100. https://doi.org/10.1007/s002180050281