evanberkowitz / supervillain

MCMC for modified Villain constructions
https://supervillain.readthedocs.io/
Other
0 stars 0 forks source link

First pass at winding in the worldine formulation #30

Closed evanberkowitz closed 1 year ago

evanberkowitz commented 1 year ago

This is a PR that should ultimately implement the Winding_Winding and WindingSquared observables.

HOWEVER, it should not yet be merged. There is a big issue though:

If δ/δJ (dδJ) = 0 then the worldline WindingSquared is negative semidefinite and the Villain is positive semidefinite. If there is no mistake this would prove that WindingSquared = 0, which

evanberkowitz commented 1 year ago

With these edits the WindingSquared observable now matches between actions

Screenshot 2023-09-08 at 16 03 12

and so does the Winding_Winding observable

Screenshot 2023-09-08 at 17 41 36

(blue = Villain, orange = Worldline, x-axis: √(∆t^2 + ∆x^2), y-axis Winding_Winding)

The matching is sufficient to believe the observable is error-free.

evanberkowitz commented 1 year ago

Closed #29.