Rudolf A. Römer

On Large-Scale Diagonalization Techniques for the Anderson Model of Localization

We propose efficient preconditioning algorithms for an eigenvalue problem arising in quantum physics, namely, the computation of a few interior eigenvalues and their associated eigenvectors for large-scale sparse real and symmetric indefinite matrices of the Anderson model of localization. We compare the Lanczos algorithm in the 1987 implementation by Cullum and Willoughby with the shift-and-invert techniques in the implicitly restarted Lanczos method and in the Jacobi-Davidson method. Our preconditioning approaches for the shift-and-invert symmetric indefinite linear system are based on maximum weighted matchings and algebraic multilevel incomplete

Electronic Transport in DNA

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Quantum Hall transition in real space: from localized to extended states.

factorizations. These techniques can be seen as a complement to the alternative idea of using more complete pivoting techniques for the highly ill-conditioned symmetric indefinite Anderson matrices. We demonstrate the effectiveness and the numerical accuracy of these algorithms. Our numerical examples reveal that recent algebraic multilevel preconditioning solvers can accelerate the computation of a large-scale eigenvalue problem corresponding to the Anderson model of localization by several orders of magnitude.

Aharonov-Bohm effect for an exciton

We study the electronic properties of DNA by way of a tight-binding model applied to four particular DNA sequences. The charge transfer properties are presented in terms of localization lengths (crudely speaking, the length over which electrons travel). Various types of disorder, including random potentials, are employed to account for different real environments. We have performed calculations on poly(dG)-poly(dC), telomeric-DNA, random-ATGC DNA, and lambda-DNA. We find that random and lambda-DNA have localization lengths allowing for electron motion among a few dozen basepairs only. A novel enhancement of localization lengths is observed at particular energies for an increasing binary backbone disorder. We comment on the possible biological relevance of sequence-dependent charge transfer in DNA.

Direct comparison between potential landscape and local density of states in a disordered two-dimensional electron system.

Using scanning tunneling spectroscopy in an ultrahigh vacuum at low temperature (T=0.3 K) and high magnetic fields (B<or=12 T), we directly probe electronic wave functions across an integer quantum Hall transition. In accordance with theoretical predictions, we observe the evolution from localized drift states in the insulating phases to branched extended drift states at the quantum critical point. The observed microscopic behavior close to the extended state indicates points of localized quantum tunneling, which are considered to be decisive for a quantitative description of the transition.

Protein flexibility is key to cisplatin crosslinking in calmodulin.

We study theoretically the exciton absorption on a ring shreded by a magnetic flux. For the case when the attraction between electron and hole is short-ranged we get an exact solution of the problem. We demonstrate that, despite the electrical neutrality of the exciton, both the spectral position of the exciton peak in the absorption, and the corresponding oscillator strength oscillate with magnetic flux with a period

Point-mutation effects on charge-transport properties of the tumor-suppressor gene p53

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On the structure and topography of free-standing chemically modified graphene

---the universal flux quantum. The origin of the effect is the finite probability for electron and hole, created by a photon at the same point, to tunnel in the opposite directions and meet each other on the opposite side of the ring.

Weak disorder expansion for localization lengths of quasi-1D systems

The local density of states (LDOS) of the adsorbate-induced two-dimensional electron system (2DES) on n-InAs(110) is studied by scanning tunneling spectroscopy. In contrast to a similar 3DES, the 2DES LDOS exhibits 20 times stronger corrugations and rather irregular structures. Both results are interpreted as consequences of weak localization. Fourier transforms of the LDOS reveal that the k values of the unperturbed 2DES still dominate the 2DES, but additional lower k values contribute. To clarify the origin of the LDOS patterns, we measure the potential landscape of the 2DES area. We use it to calculate the expected LDOS and find reasonable agreement between calculation and experiment.

El Niño and the delayed action oscillator

Chemical crosslinking in combination with Fourier transform ion cyclotron resonance mass spectrometry (FTICR MS) has significant potential for studying protein structures and protein–protein interactions. Previously, cisplatin has been shown to be a crosslinker and crosslinks multiple methionine (Met) residues in apo‐calmodulin (apo‐CaM). However, the inter‐residue distances obtained from nuclear magnetic resonance structures are inconsistent with the measured distance constraints by crosslinking. Met residues lie too far apart to be crosslinked by cisplatin. Here, by combining FTICR MS with a novel computational flexibility analysis, the flexible nature of the CaM structure is found to be key to cisplatin crosslinking in CaM. It is found that the side chains of Met residues can be brought together by flexible motions in both apo‐CaM and calcium‐bound CaM (Ca4‐CaM). The possibility of cisplatin crosslinking Ca4‐CaM is then confirmed by MS data. Therefore, flexibility analysis as a fast and low‐cost computational method can be a useful tool for predicting crosslinking pairs in protein crosslinking analysis and facilitating MS data analysis. Finally, flexibility analysis also indicates that the crosslinking of platinum to pairs of Met residues will effectively close the nonpolar groove and thus will likely interfere with the binding of CaM to its protein targets, as was proved by comparing assays for cisplatin‐modified/unmodified CaM binding to melittin. Collectively, these results suggest that cisplatin crosslinking of apo‐CaM or Ca4‐CaM can inhibit the ability of CaM to recognize its target proteins, which may have important implications for understanding the mechanism of tumor resistance to platinum anticancer drugs.