  The transport of high-energy particles in the presence of small-scale,
turbulent magnetic fields is a long-standing issue in astrophysics. Analytical
theories disagree with numerical simulations at rigidities where the particles'
gyroradii are slightly smaller than the correlation length of turbulence. At
the same time, extending the numerical simulations to lower rigidities has
proven computationally prohibitive. In this letter, we provide a solution to
the problem of perpendicular transport in isotropic turbulence at both, high
and low rigidities. We also clarify the relation between the perpendicular
diffusion of particles and the transport of magnetic field lines. To this end,
we have run a large suite of test particle simulations at unprecedentedly low
rigidites, making extensive use of graphical processing units (GPUs). We have
also developed an analytical model, based on (1) initial particle transport
along field lines, (2) the transport of field lines and (3) the eventual
decorrelation of particles from field lines. Our numerical results exhibit a
non-standard rigidity-dependence for the perpendicular diffusion coefficient at
intermediate rigidites. At the lowest rigidities, the standard
rigidity-dependence is recovered. The simulated diffusion coefficients are
nicely reproduced by our analytical model. We have traced the non-standard
rigidity-dependence to a subdiffusive phase in the field line transport. Our
study has important implications for the transport of Galactic cosmic rays,
acceleration at perpendicular shocks and for high-energy particles in the
heliosphere.
