Download
Skip this Video
Download Presentation
Critical resonance in the non-intersecting lattice path model
Loading in 2 Seconds...
Download
Download Presentation
1 / 23
Critical resonance in the non-intersecting lattice path model - PowerPoint PPT Presentation
- By neal
- Follow User
- 143 Views
- Uploaded on
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.
Download Presentation 
An Image/Link below is provided (as is) to download presentation
Critical resonance in the non-intersecting lattice path model
An Image/Link below is provided (as is) to download presentation
Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.
While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.
- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
Critical resonance in the non-intersecting lattice path model
Richard W. Kenyon
Université Paris-Sud
David B. Wilson
Microsoft Research
If m, n even, each loop has even length, (-1)=(-1)#loopsKasteleyn Matrices
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)
Free fermions in 1 dimension
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.
Resonance
Many physical systems exhibit resonance when ratios of frequencies nearly rational.
Does resonance for lattice paths resemble resonance in other systems?
