Monte-Carlo calculation of the lateral Casimir forces between rectangular gratings within the formalism of lattice quantum field theory

We propose a new Monte-Carlo method for calculation of the Casimir forces. Our method is based on the formalism of noncompact lattice quantum electrodynamics. This approach has been tested in the simplest case of two ideal conducting planes. After this the method has been applied to the calculation of the lateral Casimir forces between two ideal conducting rectangular gratings. We compare our calculations with the results of PFA and "Optimal" PFA methods.Comment: 12 pages, 6 figures, accepted in Int. J. Mod. Phys.

Numerical evidence of the axial magnetic effect

The axial magnetic field, which couples to left- and right-handed fermions with opposite signs, may generate an equilibrium dissipationless energy flow of fermions in the direction of the field even in the presence of interactions. We report on numerical observation of this axial magnetic effect in quenched SU(2) lattice gauge theory. We find that in the deconfinement (plasma) phase the energy flow grows linearly with the increase of the strength of the axial magnetic field. In the confinement (hadron) phase the axial magnetic effect is absent. Our study indirectly confirms the existence of the chiral vortical effect since both these effects have the same physical origin related to the presence of the gravitational anomaly