TY - JOUR

T1 - Geometric characterization of nodal domains

T2 - The area-to-perimeter ratio

AU - Elon, Yehonatan

AU - Gnutzmann, Sven

AU - Joas, Christian

AU - Smilansky, Uzy

PY - 2007/3/16

Y1 - 2007/3/16

N2 - In an attempt to characterize the distribution of forms and shapes of nodal domains inwavefunctions,we define a geometric parameter, the ratio p between the area of a domain and its perimeter, measured in units of the wavelength 1/√E. We show that the distribution function P(p) can distinguish between domains in which the classical dynamics is regular or chaotic. For separable surfaces, we compute the limiting distribution and show that it is supported on a compact interval, which is independent of the properties of the surface. In systems which are chaotic, or in random waves, the area-to-perimeter distribution has substantially different features which we study numerically. We compare the features of the distribution for chaotic wavefunctions with the predictions of the percolation model to find agreement, but only for nodal domains which are big with respect to the wavelength scale. This work is also closely related to and provides a newpoint of viewon isoperimetric inequalities.

AB - In an attempt to characterize the distribution of forms and shapes of nodal domains inwavefunctions,we define a geometric parameter, the ratio p between the area of a domain and its perimeter, measured in units of the wavelength 1/√E. We show that the distribution function P(p) can distinguish between domains in which the classical dynamics is regular or chaotic. For separable surfaces, we compute the limiting distribution and show that it is supported on a compact interval, which is independent of the properties of the surface. In systems which are chaotic, or in random waves, the area-to-perimeter distribution has substantially different features which we study numerically. We compare the features of the distribution for chaotic wavefunctions with the predictions of the percolation model to find agreement, but only for nodal domains which are big with respect to the wavelength scale. This work is also closely related to and provides a newpoint of viewon isoperimetric inequalities.

UR - http://www.scopus.com/inward/record.url?scp=50249159793&partnerID=8YFLogxK

U2 - 10.1088/1751-8113/40/11/007

DO - 10.1088/1751-8113/40/11/007

M3 - Journal article

AN - SCOPUS:50249159793

VL - 40

SP - 2689

EP - 2707

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 11

ER -