Speaker
Qiyun Yang, ENS Lyon
Abstract
Anyons with a statistical phase parameter \(\alpha \in (0,2)\) are a kind of quasi-particles that, for topological reasons, only exist in a 1D or 2D world. We consider the dimensional reduction for a 2D system of anyons in a tight waveguide. More specifically, we study the 2D magnetic-gauge picture model with an imposed anisotropic harmonic potential that traps particles much more strongly in the y-direction than in the x-direction. We prove that both the eigenenergies and the eigenfunctions are asymptotically decoupled into the loosely and tightly confined directions during this reduction. The limiting 1D system in the x-direction is given by the impenetrable Tonks-Girardeau Bose gas, which has no dependency on \alpha and leaves no trace of the long-range interactions present in the original 2D model.