  We utilize Polyakov loop correlations to study d=3+1 compact U (1) flux tubes
and the static electron-positron potential in lattice gauge theory. With the
plaquette field operator, in U(1) lattice gauge theory, we probe directly the
components of the electric and magnetic fields. In order to improve the
signal-to-noise ratio in the confinement phase, we apply the L\"uscher-Weiss
multilevel algorithm. Our code is written in CUDA, and we run it in NVIDIA
FERMI generation GPUs, in order to achieve the necessary efficiency for our
computations. We measure in detail the quantum widening of the flux tube, as a
function of the intercharge distance and at different finite temperatures T <
Tc . Our results are compatible with the Effective String Theory.
