Geometric characterization of nodal domains: The area-to-perimeter ratio
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Geometric characterization of nodal domains : The area-to-perimeter ratio. / Elon, Yehonatan; Gnutzmann, Sven; Joas, Christian; Smilansky, Uzy.
In: Journal of Physics A: Mathematical and Theoretical, Vol. 40, No. 11, 16.03.2007, p. 2689-2707.Research output: Contribution to journal › Journal article › Research › peer-review
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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 -
ID: 226827552