Geometric Universality of Currents

We discuss a non-equilibrium statistical system on a graph or network. Identical particles are injected, interact with each other, traverse, and leave the graph in a stochastic manner described in terms of Poisson rates, possibly dependent on time and instantaneous occupation numbers at the nodes of the graph. We show that under the assumption of constancy of the relative rates, the system demonstrates a profound statistical symmetry, resulting in geometric universality of the statistics of the particle currents. This phenomenon applies broadly to many man-made and natural open stochastic systems, such as queuing of packages over the internet, transport of electrons and quasi-particles in mesoscopic systems, and chains of reactions in bio-chemical networks. We illustrate the utility of our general approach using two enabling examples from the two latter disciplines.Comment: 15 pages, 5 figure

Stub model for dephasing in a quantum dot

As an alternative to Buttiker's dephasing lead model, we examine a dephasing stub. Both models are phenomenological ways to introduce decoherence in chaotic scattering by a quantum dot. The difference is that the dephasing lead opens up the quantum dot by connecting it to an electron reservoir, while the dephasing stub is closed at one end. Voltage fluctuations in the stub take over the dephasing role from the reservoir. Because the quantum dot with dephasing lead is an open system, only expectation values of the current can be forced to vanish at low frequencies, while the outcome of an individual measurement is not so constrained. The quantum dot with dephasing stub, in contrast, remains a closed system with a vanishing low-frequency current at each and every measurement. This difference is a crucial one in the context of quantum algorithms, which are based on the outcome of individual measurements rather than on expectation values. We demonstrate that the dephasing stub model has a parameter range in which the voltage fluctuations are sufficiently strong to suppress quantum interference effects, while still being sufficiently weak that classical current fluctuations can be neglected relative to the nonequilibrium shot noise.Comment: 8 pages with 1 figure; contribution for the special issue of J.Phys.A on "Trends in Quantum Chaotic Scattering

Interference through quantum dots

We discuss the effect of quantum interference on transport through a quantum dot system. We introduce an indirect coherent coupling parameter alpha, which provides constructive/destructive interference in the transport current depending on its phase and the magnetic flux. We estimate the current through the quantum dot system using the non-equilibrium Green's function method as well as the master equation method in the sequential tunneling regime. The visibility of the Aharonov-Bohm oscillation is evaluated. For a large inter-dot Coulomb interaction, the current is strongly suppressed by the quantum interference effect, while the current is restored by applying an oscillating resonance field with the frequency of twice the inter-dot tunneling energy.Comment: 10 pages, 3 figure

Field-aligned current associated with low-latitude plasma blobs as observed by the CHAMP satellite

Here we give two examples of low-latitude plasma blobs accompanied by linearly polarized perpendicular magnetic deflections which imply that associated field-aligned currents (FACs) have a 2-D sheet structure located at the blob walls. The estimated FAC density is of the order of 0.1 μA/m<sup>2</sup>. The direction of magnetic deflections points westward of the magnetic meridian and there is a linear correlation between perpendicular and parallel variations. All these properties are similar to those of equatorial plasma bubbles (EPBs). According to CHAMP observations from August 2000 to July 2004, blobs show except for these two good examples no clear signatures of 2-D FAC sheets at the walls. Generally, perpendicular magnetic deflections inside blobs are weaker than inside EPBs on average. Our results are consistent with existing theories: if a blob exists, (1) a significant part of EPB FAC will be closed through it, exhibiting similar perpendicular magnetic deflection inside EPBs and blobs, (2) the FAC closure through blobs leads to smaller perpendicular magnetic deflection at its poleward/downward side, and (3) superposition of different FAC elements might result in a complex magnetic signature around blobs

Computation of saddle type slow manifolds using iterative methods

This paper presents an alternative approach for the computation of trajectory segments on slow manifolds of saddle type. This approach is based on iterative methods rather than collocation-type methods. Compared to collocation methods, that require mesh refinements to ensure uniform convergence with respect to $\epsilon$, appropriate estimates are directly attainable using the method of this paper. The method is applied to several examples including: A model for a pair of neurons coupled by reciprocal inhibition with two slow and two fast variables and to the computation of homoclinic connections in the FitzHugh-Nagumo system.Comment: To appear in SIAM Journal of Applied Dynamical System

Hamiltonian type Lie bialgebras

We first prove that, for any generalized Hamiltonian type Lie algebra $L$, the first cohomology group $H^1(L,L \otimes L)$ is trivial. We then show that all Lie bialgebra structures on $L$ are triangular.Comment: LaTeX, 16 page

Interactions at the silica-peptide interface: influence of the extent of functionalization on the conformational ensemble

In this contribution, the effect of silica particle size (28 and 210 nm) and surface chemistry (i.e. hydroxyl, methyl or amino groups) on peptide binding response is studied with a specific emphasis on the effect of extent of functionalization on binding. Exhaustive characterization of the silica surfaces was crucial for knowledge of the chemistry and topography of the solid surface under study; and thus, to understand their impact on adsorption and the conformational ensemble of the peptides. The extent of surface functionalization was shown to be particle-size dependent, a higher level of 3-aminopropyl functionality being obtained for smaller particles, while a higher degree of methyl group functionality was found on the larger particles. We demonstrated that peptide interactions at the aqueous interface were not only influenced by the surface chemistry but by the extent of functionalization where a 'switch' of peptide adsorption behavior was observed, while changes in the conformational ensemble revealed by circular dichroism were independent of the extent of functionalization. In addition to electrostatic interactions and hydrogen bonding driving interaction at the silica-peptide interface the data obtained suggested that stronger interactions such as hydrophobic and/or covalent interactions may moderate interaction. The insights gained from this peptide-mineral study give a more comprehensive view of mechanisms concerning mineral-peptide interactions which may allow for the design and synthesis of novel (nano)materials with properties tailored for specific applications

Overview of (pro-)Lie group structures on Hopf algebra character groups

Character groups of Hopf algebras appear in a variety of mathematical and physical contexts. To name just a few, they arise in non-commutative geometry, renormalisation of quantum field theory, and numerical analysis. In the present article we review recent results on the structure of character groups of Hopf algebras as infinite-dimensional (pro-)Lie groups. It turns out that under mild assumptions on the Hopf algebra or the target algebra the character groups possess strong structural properties. Moreover, these properties are of interest in applications of these groups outside of Lie theory. We emphasise this point in the context of two main examples: The Butcher group from numerical analysis and character groups which arise from the Connes--Kreimer theory of renormalisation of quantum field theories.Comment: 31 pages, precursor and companion to arXiv:1704.01099, Workshop on "New Developments in Discrete Mechanics, Geometric Integration and Lie-Butcher Series", May 25-28, 2015, ICMAT, Madrid, Spai

Image potential states as quantum probe of graphene interfaces

Image potential states (IPSs) are electronic states localized in front of a surface in a potential well formed by the surface projected bulk band gap on one side and the image potential barrier on the other. In the limit of a two-dimensional solid a double Rydberg series of IPSs has been predicted which is in contrast to a single series present in three-dimensional solids. Here, we confirm this prediction experimentally for mono- and bilayer graphene. The IPSs of epitaxial graphene on SiC are measured by scanning tunnelling spectroscopy and the results are compared to ab-initio band structure calculations. Despite the presence of the substrate, both calculations and experimental measurements show that the first pair of the double series of IPSs survives, and eventually evolves into a single series for graphite. Thus, IPSs provide an elegant quantum probe of the interfacial coupling in graphene systems.Comment: Accepted for publication in New Journal of Physic