Boundary Integral Method for Stationary States of Two-Dimensional Quantum Systems

The boundary integral method for calculating the stationary states of a quantum particle in nano-devices and quantum billiards is presented in detail at an elementary level. According to the method, wave functions inside the domain of the device or billiard are expressed in terms of line integrals of the wave function and its normal derivative along the domain's boundary; the respective energy eigenvalues are obtained as the roots of Fredholm determinants. Numerical implementations of the method are described and applied to determine the energy level statistics of billiards with circular and stadium shapes and demonstrate the quantum mechanical characteristics of chaotic motion. The treatment of other examples as well as the advantages and limitations of the boundary integral method are discussed.Comment: RevTeX3.0, 24 pages, 9 EPS figures (included); To be published in Int. J. of Mod. Phys.

3-dimensional Gravity from the Turaev-Viro Invariant

We study the $q$-deformed su(2) spin network as a 3-dimensional quantum gravity model. We show that in the semiclassical continuum limit the Turaev-Viro invariant obtained recently defines naturally regularized path-integral $\grave{\rm a}$ la Ponzano-Regge, In which a contribution from the cosmological term is effectively included. The regularization dependent cosmological constant is found to be ${4\pi^2\over k^2} +O(k^{-4})$, where $q^{2k}=1$. We also discuss the relation to the Euclidean Chern-Simons-Witten gravity in 3-dimension.Comment: 11page

Quantum Zeno Effect Explains Magnetic-Sensitive Radical-Ion-Pair Reactions

Chemical reactions involving radical-ion pairs are ubiquitous in biology, since not only are they at the basis of the photosynthetic reaction chain, but are also assumed to underlie the biochemical magnetic compass used by avian species for navigation. Recent experiments with magnetic-sensitive radical-ion pair reactions provided strong evidence for the radical-ion-pair magnetoreception mechanism, verifying the expected magnetic sensitivities and chemical product yield changes. It is here shown that the theoretical description of radical-ion-pair reactions used since the 70's cannot explain the observed data, because it is based on phenomenological equations masking quantum coherence effects. The fundamental density matrix equation derived here from basic quantum measurement theory considerations naturally incorporates the quantum Zeno effect and readily explains recent experimental observations on low- and high-magnetic-field radical-ion-pair reactions.Comment: 10 pages, 5 figure

Fluctuation-Driven Molecular Transport in an Asymmetric Membrane Channel

Channel proteins, that selectively conduct molecules across cell membranes, often exhibit an asymmetric structure. By means of a stochastic model, we argue that channel asymmetry in the presence of non-equilibrium fluctuations, fueled by the cell's metabolism as observed recently, can dramatically influence the transport through such channels by a ratchet-like mechanism. For an aquaglyceroporin that conducts water and glycerol we show that a previously determined asymmetric glycerol potential leads to enhanced inward transport of glycerol, but for unfavorably high glycerol concentrations also to enhanced outward transport that protects a cell against poisoning.Comment: REVTeX4, 4 pages, 3 figures; Accepted for publication in Phys. Rev. Let

Binding pathway of retinal to bacterio-opsin: a prediction by molecular dynamics simulations

Formation of bacteriorhodopsin (bR) from apoprotein and retinal has been studied experimentally, but the actual pathway, including the point of entry, is little understood. Molecular dynamics simulations provide a surprisingly clear prediction. A window between bR helices E and F in the transmembrane part of the protein can be identified as an entry point for retinal. Steered molecular dynamics, performed by applying a series of external forces in the range of 200–1000 pN over a period of 0.2 ns to retinal, allows one to extract this chromophore from bR once the Schiff base bond to Lys216 is cleaved. Extraction proceeds until the retinal tail forms a hydrogen bond network with Ala144, Met145, and Ser183 side groups lining the exit/entry window. The manipulation induces a distortion with a fitted root mean square deviation of coordinates (ignoring retinal, water, and hydrogen atoms) of less than 1.9 A by the time the retinal carbonyl reaches the protein surface. The forces needed to extract retinal are due to friction and do not indicate significant potential barriers. The simulations therefore suggest a pathway for the binding of retinal. Water molecules are found to play a crucial role in the binding process

Structure and dynamics of the E. coli chemotaxis core signaling complex by cryo-electron tomography and molecular simulations

To enable the processing of chemical gradients, chemotactic bacteria possess large arrays of transmembrane chemoreceptors, the histidine kinase CheA, and the adaptor protein CheW, organized as coupled core-signaling units (CSU). Despite decades of study, important questions surrounding the molecular mechanisms of sensory signal transduction remain unresolved, owing especially to the lack of a high-resolution CSU structure. Here, we use cryo-electron tomography and sub-tomogram averaging to determine a structure of the Escherichia coli CSU at sub-nanometer resolution. Based on our experimental data, we use molecular simulations to construct an atomistic model of the CSU, enabling a detailed characterization of CheA conformational dynamics in its native structural context. We identify multiple, distinct conformations of the critical P4 domain as well as asymmetries in the localization of the P3 bundle, offering several novel insights into the CheA signaling mechanism

Hyperfine interaction and magnetoresistance in organic semiconductors

We explore the possibility that hyperfine interaction causes the recently discovered organic magnetoresistance (OMAR) effect. Our study employs both experiment and theoretical modelling. An excitonic pair mechanism model based on hyperfine interaction, previously suggested by others to explain magnetic field effects in organics, is examined. Whereas this model can explain a few key aspects of the experimental data, we, however, uncover several fundamental contradictions as well. By varying the injection efficiency for minority carriers in the devices, we show experimentally that OMAR is only weakly dependent on the ratio between excitons formed and carriers injected, likely excluding any excitonic effect as the origin of OMAR.Comment: 10 pages, 7 figures, 1 tabl

Dynamics and Efficiency of Brownian Rotors

Brownian rotors play an important role in biological systems and in future nano-technological applications. However the mechanisms determining their dynamics, efficiency and performance remain to be characterized. Here the F0 portion of the F-ATP synthase is considered as a paradigm of a Brownian rotor. In a generic analytical model we analyze the stochastic rotation of F0-like motors as a function of the driving free energy difference and of the free energy profile the rotor is subjected to. The latter is composed of the rotor interaction with its surroundings, of the free energy of chemical transitions, and of the workload. The dynamics and mechanical efficiency of the rotor depends on the magnitude of its stochastic motion driven by the free energy energy difference and its rectification on the reaction-diffusion path. We analyze which free energy profiles provide maximum flow and how their arrangement on the underlying reaction-diffusion path affects rectification and -- by this -- the efficiency.Comment: 22 pages, 11 figures, pdflatex, JCP in pres

The limit of N=(2,2) superconformal minimal models

The limit of families of two-dimensional conformal field theories has recently attracted attention in the context of AdS/CFT dualities. In our work we analyse the limit of N=(2,2) superconformal minimal models when the central charge approaches c=3. The limiting theory is a non-rational N=(2,2) superconformal theory, in which there is a continuum of chiral primary fields. We determine the spectrum of the theory, the three-point functions on the sphere, and the disc one-point functions.Comment: 37 pages, 3 figures; v2: minor corrections in section 5.3, version to be published in JHE