Reference : Multifractal wave functions of simple quantum maps
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Physics
http://hdl.handle.net/2268/73789
Multifractal wave functions of simple quantum maps
English
Martin, John mailto [Université de Liège - ULg > Département de physique > Spectroscopie atomique et Physique des atomes froids >]
Garcia-Mata, Ignacio [> >]
Giraud, Olivier [> >]
Georgeot, Bertrand [> >]
2010
Physical Review. E : Statistical, Nonlinear, and Soft Matter Physics
American Physical Society
82
046206
Yes (verified by ORBi)
International
1539-3755
College Park
MD
[en] We study numerically multifractal properties of two models of one-dimensional quantum maps: a map with pseudointegrable dynamics and intermediate spectral statistics and a map with an Anderson-like transition recently implemented with cold atoms. Using extensive numerical simulations, we compute the multifractal exponents of quantum wave functions and study their properties, with the help of two different numerical methods used for classical multifractal systems (box-counting and wavelet methods). We compare the results of the two methods over a wide range of values. We show that the wave functions of the Anderson map display a multifractal behavior similar to eigenfunctions of the three-dimensional Anderson transition but of a weaker type. Wave functions of the intermediate map share some common properties with eigenfunctions at the Anderson transition (two sets of multifractal exponents, with similar asymptotic behavior), but other properties are markedly different (large linear regime for multifractal exponents even for strong multifractality, different distributions of moments of wave functions, and absence of symmetry of the exponents). Our results thus indicate that the intermediate map presents original properties, different from certain characteristics of the Anderson transition derived from the nonlinear sigma model. We also discuss the importance of finite-size effects.
http://hdl.handle.net/2268/73789
10.1103/PhysRevE.82.046206
http://link.aps.org/doi/10.1103/PhysRevE.82.046206

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