Intersections of class fields

Using class field theory, we prove a restriction on the intersection of the maximal abelian extensions associated with different number fields. This restriction is then used to improve a result of Rosen and Silverman about the linear independence of Heegner points. In addition, it yields effective restrictions for the special points lying on an algebraic subvariety in a product of modular curves. The latter application is related to the Andr\'e-Oort conjecture

No singular modulus is a unit

A result of the second-named author states that there are only finitely many CM-elliptic curves over $\mathbb{C}$ whose $j$-invariant is an algebraic unit. His proof depends on Duke's Equidistribution Theorem and is hence non-effective. In this article, we give a completely effective proof of this result. To be precise, we show that every singular modulus that is an algebraic unit is associated with a CM-elliptic curve whose endomorphism ring has discriminant less than $10^{15}$. Through further refinements and computer-assisted computations, we eventually rule out all remaining cases, showing that no singular modulus is an algebraic unit. This allows us to exhibit classes of subvarieties in $\mathbb{C}^n$ not containing any special points.Comment: Dedicated to David Masser on the occasion of his 70th birthday. Version 2 has a new title, updated references, and contains minor corrections. 31 pages, to appear in IMRN. Link to scripts https://github.com/philipphabegger/Effective-Bounds-for-Singular-Unit

Measles viral load may reflect SSPE disease progression

Subacute sclerosing panencephalitis (SSPE) is a rare, slowly progressive neurological disorder caused by the persistent infection with measles virus (MV). Despite much research into SSPE, its pathology remains obscure. We examined autopsy tissues of eight SSPE patients by real time quantitative PCR, immunohistochemistry and immunoblotting to determine viral load. MV N, M and H gene RNA could be detected in the central nervous system (CNS) of all patients and in two non-CNS tissues of one patient. The viral burden between patients differed up to four-fold by quantitative PCR and corresponded with detection of MV protein. The level of both viral RNA and antigen in the brain may correlate with disease progression

Electronic excitations and electron-phonon coupling in bulk graphite through Raman scattering in high magnetic fields

We use polarized magneto-Raman scattering to study purely electronic excitations and the electron-phonon coupling in bulk graphite. At a temperature of 4.2 K and in magnetic fields up to 28 T we observe $K$-point electronic excitations involving Landau bands with $\Delta |n|=0$ and with $\Delta |n|=\pm2$ that can be selected by controlling the angular momentum of the excitation laser and of the scattered light. The magneto-phonon effect involving the $E_{2g}$ optical phonon and $K$-point inter Landau bands electronic excitations with $\Delta |n|=\pm1$ is revealed and analyzed within a model taking into account the full $k_z$ dispersion. These polarization resolved results are explained in the frame of the Slonczewski-Weiss-McClure (SWM) model which directly allows to quantify the electron-hole asymmetry.Comment: 13 pages, 10 figure

Quantum critical dynamics of a S = 1/2 antiferromagnetic Heisenberg chain studied by 13C-NMR spectroscopy

We present a 13C-NMR study of the magnetic field driven transition to complete polarization of the S=1/2 antiferromagnetic Heisenberg chain system copper pyrazine dinitrate Cu(C_4H_4N_2)(NO_3)_2 (CuPzN). The static local magnetization as well as the low-frequency spin dynamics, probed via the nuclear spin-lattice relaxation rate 1/T_1, were explored from the low to the high field limit and at temperatures from the quantum regime (k_B T << J) up to the classical regime (k_B T >> J). The experimental data show very good agreement with quantum Monte Carlo calculations over the complete range of parameters investigated. Close to the critical field, as derived from static experiments, a pronounced maximum in 1/T_1 is found which we interpret as the finite-temperature manifestation of a diverging density of zero-energy magnetic excitations at the field-driven quantum critical point.Comment: 5 pages, 4 figure

Dynamics of a Heisenberg spin chain in the quantum critical regime: NMR experiment versus effective field theory

A comprehensive comparison between the magnetic field- and temperature-dependent low frequency spin dynamics in the antiferromagnetic spin-1/2 Heisenberg chain (AFHC) system copper pyrazine dinitrate, probed via the 13C-nuclear magnetic resonance (NMR) relaxation rate 1/T1, and the field theoretical approach in the Luttinger liquid (LL) regime has been performed. We have found a very good agreement between the experiment and theory in the investigated temperature and field range. Our results demonstrate how strongly the quantum critical point affects the spin dynamics of Heisenberg spin chain compounds.Comment: 5 pages, 3 figure

Polarization selection rules for inter-Landau level transitions in epitaxial graphene revealed by infrared optical Hall effect

We report on polarization selection rules of inter-Landau level transitions using reflection-type optical Hall effect measurements from 600 to 4000 cm-1 on epitaxial graphene grown by thermal decomposition of silicon carbide. We observe symmetric and anti-symmetric signatures in our data due to polarization preserving and polarization mixing inter-Landau level transitions, respectively. From field-dependent measurements we identify that transitions in decoupled graphene mono-layers are governed by polarization mixing selection rules, whereas transitions in coupled graphene mono-layers are governed by polarization preserving selection rules. The selection rules may find explanation by different coupling mechanisms of inter-Landau level transitions with free charge carrier magneto-optic plasma oscillations

Modeling and Simulation of Multi-Lane Traffic Flow

A most important aspect in the field of traffic modeling is the simulation of bottleneck situations. For their realistic description a macroscopic multi-lane model for uni-directional freeways including acceleration, deceleration, velocity fluctuations, overtaking and lane-changing maneuvers is systematically deduced from a gas-kinetic (Boltzmann-like) approach. The resulting equations contain corrections with respect to previous models. For efficient computer simulations, a reduced model delineating the coarse-grained temporal behavior is derived and applied to bottleneck situations.Comment: For related work see http://www.theo2.physik.uni-stuttgart.de/helbing.htm