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Critical resonance in the non-intersecting lattice path model. Richard W. Kenyon Université Paris-Sud. David B. Wilson Microsoft Research. Non-intersecting lattice paths. Partition Function Z. Weights a,b,c and the Phases. a. Solid `a’ type edges. Solid `b’ type edges.
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Richard W. Kenyon
Université Paris-Sud
David B. Wilson
Microsoft Research
Topology: If a loop windsptimes horizontally,qtimes vertically,
then all loops wind (p,q) times, where gcd(p,q)=1
Weight horizontal cut-edges by (-1)
vertical cut-edges by (-1)
Fermions are particles that repel one another.
In 1 dimension, log(Z)/ -Li3/2(-)
density / -Li1/2(-).
Same equations for lattice paths when (presumed) ratchet number is 0.
When (presumed) ratchet number is nonzero,
behavior differs from free fermions.
Many physical systems exhibit resonance when ratios of frequencies nearly rational.
Does resonance for lattice paths resemble resonance in other systems?
