%0 Generic
%A Klingmüller, Klaus
%D 2007
%F heidok:7846
%K Casimir-Kraft , Weltlinienformalismus , Weltliniennumerikcasimir effect , casimir force , Gross-Neveu model , worldline formalism , worldline numerics
%R 10.11588/heidok.00007846
%T Worldline approach to Casimir effect and Gross-Neveu model
%U https://archiv.ub.uni-heidelberg.de/volltextserver/7846/
%X We employ worldline numerics to study Casimir effect and Gross-Neveu model. In this approach, the quantum fluctuations are mapped onto quantum mechanical path integrals, which are evaluated with Monte Carlo methods. For the Casimir effect, this allows the precise computation of the interaction energy for a Dirichlet scalar in Casimir geometries inaccessible to other methods. We study geometries involving curvature and edges, both are important for experiments and applications in nanotechnology, respectively. Significant reduction of numerical cost is gained by exploiting the symmetries of the worldline ensemble in combination with those of the configurations. Our results reveal the tight validity bounds of the commonly used proximity force approximation (PFA) and provide first insight into the effect of edges of finite plates on the Casimir force. In the Gross-Neveu model, we compute the trace over the fermion fluctuations using a worldline path integral, whose numerical evaluation is demonstrated for various configurations in the two dimensional model. We incorporate temperature and chemical potential in our formalism and perform first worldline numeric computations at finite values of these quantities. We thereby rediscover aspects of the established phase diagram. The methods employed can be extended to higher dimensions, to study the existence of a spatially inhomogeneous ground state beyond the two dimensional Gross-Neveu model.