Borcherds products and arithmetic intersection theory on Hilbert modular surfaces

We prove an arithmetic version of a theorem of Hirzebruch and Zagier saying that Hirzebruch-Zagier divisors on a Hilbert modular surface are the coefficients of an elliptic modular form of weight 2. Moreover, we determine the arithmetic selfintersection number of the line bundle of modular forms equipped with its Petersson metric on a regular model of a Hilbert modular surface, and we study Faltings heights of arithmetic Hirzebruch-Zagier divisors.

Nucleation and growth of GaN nanorods on Si (111) surfaces by plasma-assisted molecular beam epitaxy - The influence of Si- and Mg-doping

The self-assembled growth of GaN nanorods on Si (111) substrates by plasma-assisted molecular beam epitaxy under nitrogen-rich conditions is investigated. An amorphous silicon nitride layer is formed in the initial stage of growth that prevents the formation of a GaN wetting layer. The nucleation time was found to be strongly influenced by the substrate temperature and was more than 30 min for the applied growth conditions. The observed tapering and reduced length of silicon-doped nanorods is explained by enhanced nucleation on nonpolar facets and proves Ga-adatom diffusion on nanorod sidewalls as one contribution to the axial growth. The presence of Mg leads to an increased radial growth rate with a simultaneous decrease of the nanorod length and reduces the nucleation time for high Mg concentrations.

Model for the emission of Si+ ions during oxygen bombardment of Si(100) surfaces

The variation in the emission of Si+ ions from ion-beam-induced oxidized silicon surfaces has been studied. The stoichiometry and the electronic structure of the altered layer has been characterized using x-ray photoelectron spectroscopy (XPS). The XPS analysis of the Si 2p core level indicates the strong presence of suboxide chemical states when bombarding at angles of incidence larger than 30 °. Since the surface stoichiometry or degree of oxidation varies with the angle of incidence, the corresponding valence-band structures also differ among each other. A comparison between experimental measurements and theoretically calculated Si and SiO2 valence bands indicates that the valence bands for the altered layers are formed by a combination of those two. Since Si-Si bonds are present in the suboxide molecules, the top of the respective new valence bands are formed by the corresponding 3p-3p Si-like subbands, which extend up to the Si Fermi level. The changes in stoichiometry and electronic structure have been correlated with the emission of Si+ ions from these surfaces. From the results a general model for the Si+ ion emission is proposed combining the resonant tunneling and local-bond-breaking models.

Stationary states and phase diagram for a model of the Gunn effect under realistic boundary conditions

A general formulation of boundary conditions for semiconductor-metal contacts follows from a phenomenological procedure sketched here. The resulting boundary conditions, which incorporate only physically well-defined parameters, are used to study the classical unipolar drift-diffusion model for the Gunn effect. The analysis of its stationary solutions reveals the presence of bistability and hysteresis for a certain range of contact parameters. Several types of Gunn effect are predicted to occur in the model, when no stable stationary solution exists, depending on the value of the parameters of the injecting contact appearing in the boundary condition. In this way, the critical role played by contacts in the Gunn effect is clearly established.

Lagrangian and Hamiltonian BRST structures of the antysimmetric tensor gauge theory

We study the Becchi-Rouet-Stora-Tyutin (BRST) structure of a self-interacting antisymmetric tensor gauge field, which has an on-shell null-vector gauge transformation. The Batalin-Vilkovisky covariant general formalism is briefly reviewed, and the issue of on-shell nilpotency of the BRST transformation is elucidated. We establish the connection between the covariant and the canonical BRST formalisms for our particular theory. Finally, we point out the similarities and differences with Wittens string field theory.

Hamiltonian and Lagrangian constraints of the bosonic string

We study the Hamiltonian and Lagrangian constraints of the Polyakov string. The gauge fixing at the Hamiltonian and Lagrangian level is also studied.

Gauge-invariant actions from constraint Hamiltonian dynamics

Dirac's constraint Hamiltonian formalism is used to construct a gauge-invariant action for the massive spin-one and -two fields.

Sorting on periodic surfaces

Particles moving on crystalline surfaces and driven by external forces or flow fields can acquire velocities along directions that deviate from that of the external force. This effect depends upon the characteristics of the particles, most notably particle size or particle index of refraction, and can therefore be (and has been) used to sort different particles. We introduce a simple model for particles subject to thermal fluctuations and moving in appropriate potential landscapes. Numerical results are compared to recent experiments on landscapes produced with holographic optical tweezers and microfabricated technology. Our approach clarifies the relevance of different parameters, the direction and magnitude of the external force, particle size, and temperature.

From subdiffusion to superdiffusion of particles on solid surfaces

We present a numerical and partially analytical study of classical particles obeying a Langevin equation that describes diffusion on a surface modeled by a two-dimensional potential. The potential may be either periodic or random. Depending on the potential and the damping, we observe superdiffusion, large-step diffusion, diffusion, and subdiffusion. Superdiffusive behavior is associated with low damping and is in most cases transient, albeit often long. Subdiffusive behavior is associated with highly damped particles in random potentials. In some cases subdiffusive behavior persists over our entire simulation and may be characterized as metastable. In any case, we stress that this rich variety of behaviors emerges naturally from an ordinary Langevin equation for a system described by ordinary canonical Maxwell-Boltzmann statistics.

Equivalence Between the Lagrangian and Hamiltonian Formalisms for Constrained Systems

The equivalence between the Lagrangian and Hamiltonian formalism is studied for constraint systems. A procedure to construct the Lagrangian constraints from the Hamiltonian constraints is given. Those Hamiltonian constraints that are first class with respect to the Hamiltonian constraints produce Lagrangian constraints that are FL-projectable.