Continuous Time Monte Carlo and Driven Vortices in a Periodic Potential

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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.
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2D Lattice Coulomb gas
integer charges on a compensating uniform
background
charge neutrality fixes Nc particles
logarithmic interactions
periodic boundary conditions
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Continuous time Monte Carlo dynamics
Uniform applied force F
For a single particle move of displacement Dr 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 a,
Rates satisfy local detailed balance.
Probability to make the above move is,
Sample the distribution Pia to decide which move
to make, and then update the simulation clock by
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Periodic grid of lattice gas represents the
minima of a periodic potential with energy
barriers Eb. Algorithm describes thermal
activation over energy barriers when DU lt Eb.
Use particle density f 1/25
F 0 ground state charge configuration is a 5x5
square lattice
real space
k-space
Compute structure function
Real space correlation function
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F 0.10 in x direction
Large drive
T 0.004 L 50

• S(k) after 6000 passes
• S(k) after 107 passes
• S(k) after 6x107 passes
• C(r) corresponding to (c)

Long time steady state is smectic with flow of
particles in periodically spaced channels
channels are out of phase with each other.
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Low drive
F 0.04 in x direction
T 0.004 L 75
Coexisting liquid and solid phases, as in a 1st
order transition.
F
liquid
solid
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C(r) liquid
C(r) solid
F
Solid consists of particles moving in channels
parallel to F. Channels are separated by 3 grid
spacings. Particles within each channel are
separated by 81/3 grid spacings on average. This
is different than both the ground state or the
high drive smectic!
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.
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moving solid is transversely pinned