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U Gerland

Publications and source records attributed to U Gerland.

3 recordsLinked to original sources

Singular statistics.

We consider the statistical distribution of zeros of random meromorphic functions whose poles are independent random variables. It is demonstrated that correlation functions of these zeros can be computed analytically, and explicit calculations are performed for the two-point correlation function. This problem naturally appears in, e.g., rank-1 perturbation of an integrable Hamiltonian and, in particular, when a delta-function potential is added to an integrable billiard.

Journal Article↗

Force-induced denaturation of RNA.

We quantitatively describe an RNA molecule under the influence of an external force exerted at its two ends as in a typical single-molecule experiment. Our calculation incorporates the interactions between nucleotides by using the experimentally determined free energy rules for RNA secondary structure and models the polymeric properties of the exterior single-stranded regions explicitly as elastic freely jointed chains. We find that despite complicated secondary structures, force-extension curves are typically smooth in quasi-equilibrium. We identify and characterize two sequence/structure-dependent mechanisms that, in addition to the sequence-independent entropic elasticity of the exterior single-stranded regions, are responsible for the smoothness. These involve compensation between different structural elements on which the external force acts simultaneously and contribution of suboptimal structures, respectively. We estimate how many features a force-extension curve recorded in nonequilibrium, where the pulling proceeds faster than rearrangements in the secondary structure of the molecule, could show in principle. Our software is available to the public through an "RNA-pulling server."

Biomechanical Phenomena↗

Transmission phase shift of a quantum dot with kondo correlations

We study the effects of Kondo correlations on the transmission phase shift of a quantum dot in an Aharonov-Bohm ring. We predict in detail how the development of a Kondo resonance should affect the dependence of the phase shift on transport voltage, gate voltage, and temperature. This system should allow the first direct observation of the well-known scattering phase shift of pi/2 expected (but not directly measurable in bulk systems) at zero temperature for an electron scattering off a spin- 1 / 2 impurity that is screened into a singlet.

Journal Article↗