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RESEARCH PRODUCT
Multifractal electronic wave functions in disordered systems
Heiko GrussbachMichael Schreibersubject
PhysicsCondensed matter physicsBiophysicsProbability density functionGeneral ChemistryMultifractal systemCondensed Matter PhysicsBiochemistryAtomic and Molecular Physics and OpticsLegendre transformationsymbols.namesakeLinear regressionsymbolsSingularity spectrumWave functionHamiltonian (quantum mechanics)Eigenvalues and eigenvectorsMathematical physicsdescription
Abstract To investigate the electronic states in disordered samples we diagonalize very large secular matrices corresponding to the Anderson Hamiltonian. The resulting probability density of single electronic eigenstates in 1-, 2-, and 3-dimensional samples is analysed by means of a box-counting procedure. By linear regression we obtain the Lipschitz-Holder exponents and the corresponding singularity spectrum, typical for a multifractal set in each case. By means of a Legendre transformation the mass exponents and the generalized dimensions are derived. Consequences for spectroscopic intensities and transport properties are discussed.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 1992-07-01 | Journal of Luminescence |