A Proof of Tarski’s Fixed Point Theorem by Application of Galois Connections

Two examples of Galois connections and their dual forms are considered. One of them is applied to formulate a criterion when a given subset of a complete lattice forms a complete lattice. The second, closely related to the first, is used to prove in a short way the Knaster-Tarski’s fixed point theore

Radiative transitions of DsJ∗(2317)D^*_{sJ}(2317) and DsJ(2460)D_{sJ}(2460)

We study radiative decays of $D^*_{sJ}(2317)$ and $D_{sJ}(2460)$ using light-cone QCD sum rules. In particular, we consider the decay modes $D^*_{sJ}(2317)\to D_s^* \gamma$ and $D_{sJ}(2460)\to D_s^{(*)} \gamma, D^*_{sJ}(2317) \gamma$ and evaluate the hadronic parameters in the transition amplitudes analyzing correlation functions of scalar, pseudoscalar, vector and axial-vector quark currents. In the case of $D^*_{sJ}(2317)\to D_s^* \gamma$ we also consider determinations based on two different correlation functions in HQET. The decay widths turn out to be different than previous estimates obtained by other methods; the results favour the interpretation of $D^*_{sJ}(2317)$ and $D_{sJ}(2460)$ as ordinary $\bar c s$ mesons.Comment: RevTex, 23 pages, 9 eps figure

Quantitative analysis of pedestrian counterflow in a cellular automaton model

Pedestrian dynamics exhibits various collective phenomena. Here we study bidirectional pedestrian flow in a floor field cellular automaton model. Under certain conditions, lane formation is observed. Although it has often been studied qualitatively, e.g., as a test for the realism of a model, there are almost no quantitative results, neither empirically nor theoretically. As basis for a quantitative analysis we introduce an order parameter which is adopted from the analysis of colloidal suspensions. This allows to determine a phase diagram for the system where four different states (free flow, disorder, lanes, gridlock) can be distinguished. Although the number of lanes formed is fluctuating, lanes are characterized by a typical density. It is found that the basic floor field model overestimates the tendency towards a gridlock compared to experimental bounds. Therefore an anticipation mechanism is introduced which reduces the jamming probability.Comment: 11 pages, 12 figures, accepted for publication in Phys. Rev.

Tuning of the spin-orbit interaction in a quantum dot by an in-plane magnetic field

Using an exact diagonalization approach we show that one- and two-electron InAs quantum dots exhibit avoided crossing in the energy spectra that are induced by the spin-orbit coupling in the presence of an in-plane external magnetic field. The width of the avoided crossings depends strongly on the orientation of the magnetic field which reveals the intrinsic anisotropy of the spin-orbit coupling interactions. We find that for specific orientations of the magnetic field avoided crossings vanish. Value of this orientation can be used to extract the ratio of the strength of Rashba and Dresselhaus interactions. The spin-orbit anisotropy effects for various geometries and orientations of the confinement potential are discussed. Our analysis explains the physics behind the recent measurements performed on a gated self-assembled quantum dot [S. Takahashi et al. Phys. Rev. Lett. 104, 246801 (2010)].Comment: Corrected according to referees comment

Monte Carlo Simulation of Ising Models with Dipole Interaction

Recently, a new memory effect was found in the metamagnetic domain structure of the diluted Ising antiferromagnet $Fe_x Mg_{1-x} Cl_2$ by domain imaging with Faraday contrast. Essential for this effect is the dipole interaction. We simulate the low temperature behavior of diluted Ising-antiferromagnets by a Monte Carlo simulation considering long range interaction. The metamagnetic domain structure occurring due to the dipole interaction is investigated by graphical representation. In the model considered the antiferromagnetic state is stable for an external magnetic field smaller than a lower boundary $B_{c1}$ while for fields larger than an upper boundary $B_{c2}$ the system is in the saturated paramagnetic phase, where the spins are ferromagnetically polarized. For magnetic fields in between these two boundaries a mixed phase occurs consisting of ferromagnetic domains in an antiferromagnetic background. The position of these ferromagnetic domains is stored in the system: after a cycle in which the field is first removed and afterwards applied again the domains reappear at their original positions. The reason for this effect can be found in the frozen antiferromagnetic domain state which occurs after removing the field.Comment: Latex, 10 pages; 3 postsript-figures, compressed tar-file, uuencoded, report 10109

Constrained Monte Carlo Method and Calculation of the Temperature Dependence of Magnetic Anisotropy

We introduce a constrained Monte Carlo method which allows us to traverse the phase space of a classical spin system while fixing the magnetization direction. Subsequently we show the method's capability to model the temperature dependence of magnetic anisotropy, and for bulk uniaxial and cubic anisotropies we recover the low-temperature Callen-Callen power laws in M. We also calculate the temperature scaling of the 2-ion anisotropy in L10 FePt, and recover the experimentally observed M^2.1 scaling. The method is newly applied to evaluate the temperature dependent effective anisotropy in the presence of the N'eel surface anisotropy in thin films with different easy axis configurations. In systems having different surface and bulk easy axes, we show the capability to model the temperature-induced reorientation transition. The intrinsic surface anisotropy is found to follow a linear temperature behavior in a large range of temperatures

A coarse grained model of granular compaction and relaxation

We introduce a theoretical model for the compaction of granular materials by discrete vibrations which is expected to hold when the intensity of vibration is low. The dynamical unit is taken to be clusters of granules that belong to the same collective structure. We rigourously construct the model from first principles and show that numerical solutions compare favourably with a range of experimental results. This includes the logarithmic relaxation towards a statistical steady state, the effect of varying the intensity of vibration resulting in a so-called `annealing' curve, and the power spectrum of density fluctuations in the steady state itself. A mean-field version of the model is introduced which shares many features with the exact model and is open to quantitative analysi

Factorization of Numbers with the temporal Talbot effect: Optical implementation by a sequence of shaped ultrashort pulses

We report on the successful operation of an analogue computer designed to factor numbers. Our device relies solely on the interference of classical light and brings together the field of ultrashort laser pulses with number theory. Indeed, the frequency component of the electric field corresponding to a sequence of appropriately shaped femtosecond pulses is determined by a Gauss sum which allows us to find the factors of a number

Resonant harmonic generation and collective spin rotations in electrically driven quantum dots

Spin rotations induced by an AC electric field in a two-electron double quantum dot are studied by an exact numerical solution of the time dependent Schroedinger equation in the context of recent electric dipole spin resonance experiments based on the Pauli blockade. We demonstrate that the splitting of the main resonance line by the spin exchange coupling is accompanied by the appearance of fractional resonances and that both these effects are triggered by interdot tunnel coupling. We find that the AC driven system generates residual but distinct harmonics of the driving frequency which are amplified when tuned to the main transition frequency. The mechanism is universal for electron systems in electrically driven potentials and works also in the absence of electron-electron interaction or spin-orbit coupling.Comment: Corrected version accepted for PR