Continuous Time Monte Carlo and Driven Vortices in a Periodic Potential V. Gotcheva, Yanting Wang, Albert Wang and S. Teitel University of Rochester Lattice gas dynamics for driven steady states. Particles can hop over energy barriers in a single bound! Can greatly speed up simulation time as compared to continuum molecular dynamics.

2D Lattice Coulomb gas integer charge on site i of a periodic square L x L grid f uniform background charge charge neutrality fixes N c particles logarithmic interactions periodic boundary conditions integer charges on a compensating uniform background

Continuous time Monte Carlo dynamics Uniform applied force F For a single particle move of displacement  r the energy difference for the move, including work done by F, is Define the rate to move a particle at site i a unit spacing in direction , Rates satisfy local detailed balance. Probability to make the above move is, Sample the distribution P i   to decide which move to make, and then update the simulation clock by

Periodic grid of lattice gas represents the minima of a periodic potential with energy barriers E b. Algorithm describes thermal activation over energy barriers when  U < E b. Use particle density f = 1/25 Compute structure function Real space correlation function F = 0 ground state charge configuration is a 5x5 square lattice real space k-space

F = 0.10 in x direction a)S(k) after 6000 passes b)S(k) after 10 7 passes c)S(k) after 6x10 7 passes d)C(r) corresponding to (c) Large drive Long time steady state is smectic with flow of particles in periodically spaced channels; channels are out of phase with each other. T = L = 50

Low drive F = 0.04 in x direction T = L = 75 Coexisting liquid and solid phases, as in a 1st order transition. liquid solid F

C(r) liquid C(r) solid Solid consists of particles moving in channels parallel to F. Channels are separated by 3 grid spacings. Particles within each channel are separated by 8 1/3 grid spacings on average. This is different than both the ground state or the high drive smectic! F The liquid has long ranged 6-fold orientational order! Local 6-fold clusters prefer to lock into the grid direction transverse to the driving force.

moving solid is transversely pinned