  The magnetorotational instability (MRI) is a crucial mechanism of angular
momentum transport in a variety of astrophysical accretion disks. In systems
accreting at well below the Eddington rate, such as the central black hole in
the Milky Way (Sgr A*), the rate of Coulomb collisions between particles is
very small, making the disk evolve essentially as a collisionless plasma. We
present a nonlinear study of the collisionless MRI using first-principles
particle-in-cell (PIC) plasma simulations. In this initial study we focus on
local two-dimensional (axisymmetric) simulations, deferring more realistic
three-dimensional simulations to future work. For simulations with net vertical
magnetic flux, the MRI continuously amplifies the magnetic field until the
Alfv\'en velocity, v_A, is comparable to the speed of light, c (independent of
the initial value of v_A/c). This is consistent with the lack of saturation of
MRI channel modes in analogous axisymmetric MHD simulations. The amplification
of the magnetic field by the MRI generates a significant pressure anisotropy in
the plasma (with the perpendicular pressure being larger than the parallel
pressure). We find that this pressure anisotropy in turn excites mirror modes
and that the volume averaged pressure anisotropy remains near the threshold for
mirror mode excitation. Particle energization is due to both reconnection and
viscous heating associated with the pressure anisotropy. Reconnection produces
a distinctive power-law component in the energy distribution function of the
particles, indicating the likelihood of non-thermal ion and electron
acceleration in collisionless accretion disks. This has important implications
for interpreting the observed emission -- from the radio to the gamma-rays --
of systems such as Sgr A*.
