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Biomedical subjects

B Mehlig

Publications and source records attributed to B Mehlig.

11 recordsLinked to original sources
PubMed2002

Optical response of two-dimensional electron fluids beyond the kohn regime: strong nonparabolic confinement and intense laser light.

We investigate the linear and nonlinear optical response of two-dimensional interacting electron fluids confined by a strong nonparabolic potential. We show that such fluids may exhibit higher-harmonic spectra under realistic experimental conditions. Higher harmonics arise as the electrons explore anharmonicities of the confinement potential (electron-electron interactions reduce this nonlinear effect). This opens the possibility of controlling the optical functionality by engineering the confinement potential. Our results were obtained within time-dependent density-functional theory. A classical hydrodynamical model is in good agreement with the quantum-mechanical results.

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PubMed2002

Statistics of selectively neutral genetic variation.

Random models of evolution are instrumental in extracting rates of microscopic evolutionary mechanisms from empirical observations on genetic variation in genome sequences. In this context it is necessary to know the statistical properties of empirical observables (such as the local homozygosity, for instance). Previous work relies on numerical results or assumes Gaussian approximations for the corresponding distributions. In this paper we give an analytical derivation of the statistical properties of the local homozygosity and other empirical observables assuming selective neutrality. We find that such distributions can be very non-Gaussian.

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PubMed2001

Spectral correlations: understanding oscillatory contributions.

We give a different derivation of a relation obtained using a supersymmetric nonlinear sigma model by Andreev and Altshuler [Phys. Rev. Lett. 72, 902 (1995)], which connects smooth and oscillatory components of spectral correlation functions. We show that their result is not specific to the random matrix theory. Also, we show that despite an apparent contradiction, the results obtained using their formula are consistent with earlier perspectives on random matrix models.

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PubMed2001

Universal eigenvector statistics in a quantum scattering ensemble.

We calculate eigenvector statistics in an ensemble of non-Hermitian matrices describing open quantum systems [F. Haake et al., Z. Phys. B 88, 359 (1992)] in the limit of large matrix size. We show that ensemble-averaged eigenvector correlations corresponding to eigenvalues in the center of the support of the density of states in the complex plane are described by an expression recently derived for Ginibre's ensemble of random non-Hermitian matrices.

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PubMed1999

Phase space localization and matrix element distributions in systems with mixed classical phase space.

We consider distributions of diagonal matrix elements for smooth observables in systems whose classical phase space has a mixture of chaotic and nearly integrable regions. The quantum distributions agree very well with distributions obtained from classical trajectory segments whose length is the Heisenberg time. Non-Gaussian wings in the distributions can be linked to classical trapping in certain parts of phase space, sometimes connected to islands, but also to regions separated by other barriers to transport. Thus classical deviations from ergodicity are quantitatively reflected in quantum matrix elements. The relation to scars is discussed.

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PubMed1999

Spectral correlations in systems undergoing a transition from periodicity to disorder.

We study the spectral statistics for extended yet finite quasi-one-dimensional systems, which undergo a transition from periodicity to disorder. In particular, we compute the spectral two-point form factor, and the resulting expression depends on the degree of disorder. It interpolates smoothly between the two extreme limits-the approach to Poissonian statistics in the (weakly) disordered case, and the universal expressions derived in T. Dittrich, B. Mehlig, H. Schanz, and U. Smilansky, Chaos Solitons Fractals 8, 1205 (1997); Phys. Rev. E 57, 359 (1998); B. D. Simons and B. L. Altshuler, Phys. Rev. Lett. 70, 4063 (1993); and N. Taniguchi and B. L. Altshuler, ibid. 71, 4031 (1993) for the periodic case. The theoretical results agree very well with the spectral statistics obtained numerically for chains of chaotic billiards and graphs.

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