Alex Barnett
Courant Institute.
| It is a long-standing question how quantum eigenfunctions behave in the semiclassical (short-wavelength) limit, when the corresponding classical dynamics is chaotic. For instance, do they become ergodic (equidistributed across space) or are remnants ('scars') of periodic orbits important? Recent analytic results in manifolds of uniform negative curvature have lead to a conjecture by Sarnak that every eigenfunction becomes ergodic. We study a point particle inside a 2D cavity ('billiard'), whose quantum equivalent is the familiar laplacian eigenproblem, namely the cavity's resonant modes. We numerically investigate the rate of equidistribution and compare to semiclassical estimates involving classical correlation functions. We have collected thousands of modes at energy ranges well beyond those in the literature; I will outline the numerical innovations which make this possible. These methods are orders of magnitude faster than standard boundary integral methods, and should find applications to resonance problems in acoustics and electromagnetism. |
Back to AML Seminar Schedule