Parallel spinors on pseudo-riemannian spin(q) manifolds

We study simply-connected irreducible non-locally symmetric pseudo-Riemannian Spin(q) manifolds admitting parallel quaternionic spinors.

Approximation algorithms for two-state anti-ferromagnetic spin systems on bounded degree graphs

In a seminal paper [10], Weitz gave a deterministic fully polynomial approximation scheme for counting exponentially weighted independent sets (which is the same as approximating the partition function of the hard-core model from statistical physics) in graphs of degree at most d, up to the critical activity for the uniqueness of the Gibbs measure on the innite d-regular tree. ore recently Sly [8] (see also [1]) showed that this is optimal in the sense that if here is an FPRAS for the hard-core partition function on graphs of maximum egree d for activities larger than the critical activity on the innite d-regular ree then NP = RP. In this paper we extend Weitz's approach to derive a deterministic fully polynomial approximation scheme for the partition function of general two-state anti-ferromagnetic spin systems on graphs of maximum degree d, up to the corresponding critical point on the d-regular tree. The main ingredient of our result is a proof that for two-state anti-ferromagnetic spin systems on the d-regular tree, weak spatial mixing implies strong spatial mixing. his in turn uses a message-decay argument which extends a similar approach proposed recently for the hard-core model by Restrepo et al [7] to the case of general two-state anti-ferromagnetic spin systems.

A new all-round density functional based on spin states and SN2 barriers

We report here a new empirical density functional that is constructed based on the performance of OPBE and PBE for spin states and SN 2 reaction barriers and how these are affected by different regions of the reduced gradient expansion. In a previous study [Swart, Sol̀, and Bickelhaupt, J. Comput. Methods Sci. Eng. 9, 69 (2009)] we already reported how, by switching between OPBE and PBE, one could obtain both the good performance of OPBE for spin states and reaction barriers and that of PBE for weak interactions within one and the same (SSB-sw) functional. Here we fine tuned this functional and include a portion of the KT functional and Grimme's dispersion correction to account for π- π stacking. Our new SSB-D functional is found to be a clear improvement and functions very well for biological applications (hydrogen bonding, π -π stacking, spin-state splittings, accuracy of geometries, reaction barriers)

Spin and density longitudinal response of quantum dots in the time-dependent local-spin-density approximation

The longitudinal dipole response of a quantum dot has been calculated in the far-infrared regime using local-spin-density-functional theory. We have studied the coupling between the collective spin and density modes as a function of the magnetic field. We have found that the spin dipole mode and single-particle excitations have a sizable overlap, and that the magnetoplasmon modes can be excited by the dipole spin operator if the dot is spin polarized. The frequency of the dipole spin edge mode presents an oscillation which is clearly filling factor (v) related. We have found that the spin dipole mode is especially soft for even-n values. Results for selected numbers of electrons and confining potentials are discussed.

Transverse dipole spin modes in quantum dots

We have carried out a systematic analysis of the transverse dipole spin response of a large-size quantum dot within time-dependent current density functional theory. Results for magnetic fields corresponding to integer filling factors are reported, as well as a comparison with the longitudinal dipole spin response. As in the two-dimensional electron gas, the spin response at high-spin magnetization is dominated by a low-energy transverse mode.

Wave-vector dependence of spin and density multipole excitations in quantum dots

We have employed time-dependent local-spin density-functional theory to analyze the multipole spin and charge density excitations in GaAs-AlxGa1-xAs quantum dots. The on-plane transferred momentum degree of freedom has been taken into account, and the wave-vector dependence of the excitations is discussed. In agreement with previous experiments, we have found that the energies of these modes do not depend on the transferred wave vector, although their intensities do. Comparison with a recent resonant Raman scattering experiment [C. Schüller et al., Phys. Rev. Lett. 80, 2673 (1998)] is made. This allows us to identify the angular momentum of several of the observed modes as well as to reproduce their energies

Vertically coupled quantum dots in the local spin-density functional theory

We have investigated the structure of double quantum dots vertically coupled at zero magnetic field within local-spin-density functional theory. The dots are identical and have a finite width, and the whole system is axially symmetric. We first discuss the effect of thickness on the addition spectrum of one single dot. Next we describe the structure of coupled dots as a function of the interdot distance for different electron numbers. Addition spectra, Hund's rule, and molecular-type configurations are discussed. It is shown that self-interaction corrections to the density-functional results do not play a very important role in the calculated addition spectra

Multipole modes and spin features in the Raman spectrum of nanoscopic quantum rings

We present a systematic study of ground state and spectroscopic properties of many-electron nanoscopic quantum rings. Addition energies at zero magnetic field (B) and electrochemical potentials as a function of B are given for a ring hosting up to 24 electrons. We find discontinuities in the excitation energies of multipole spin and charge density modes, and a coupling between the charge and spin density responses that allow to identify the formation of ferromagnetic ground states in narrow magnetic field regions. These effects can be observed in Raman experiments, and are related to the fractional Aharonov-Bohm oscillations of the energy and of the persistent current in the ring

Optimal generalized quantum measurements for arbitrary spin systems

Positive-operator-valued measurements on a finite number of N identically prepared systems of arbitrary spin J are discussed. Pure states are characterized in terms of Bloch-like vectors restricted by a SU(2J+1) covariant constraint. This representation allows for a simple description of the equations to be fulfilled by optimal measurements. We explicitly find the minimal positive-operator-valued measurement for the N=2 case, a rigorous bound for N=3, and set up the analysis for arbitrary N.

Hysteresis and avalanches in the T=0 random field ising model with 2-spin flip dynamics

We study the nonequilibrium behavior of the three-dimensional Gaussian random-field Ising model at T=0 in the presence of a uniform external field using a two-spin-flip dynamics. The deterministic, history-dependent evolution of the system is compared with the one obtained with the standard one-spin-flip dynamics used in previous studies of the model. The change in the dynamics yields a significant suppression of coercivity, but the distribution of avalanches (in number and size) stays remarkably similar, except for the largest ones that are responsible for the jump in the saturation magnetization curve at low disorder in the thermodynamic limit. By performing a finite-size scaling study, we find strong evidence that the change in the dynamics does not modify the universality class of the disorder-induced phase transition.

Spin-orbit effects in GaAs quantum wells: Interplay between Rashba, Dresselhaus, and Zeeman interactions

The interplay between Rashba, Dresselhaus, and Zeeman interactions in a quantum well submitted to an external magnetic field is studied by means of an accurate analytical solution of the Hamiltonian, including electron-electron interactions in a sum-rule approach. This solution allows us to discuss the influence of the spin-orbit coupling on some relevant quantities that have been measured in inelastic light scattering and electron-spin resonance experiments on quantum wells. In particular, we have evaluated the spin-orbit contribution to the spin splitting of the Landau levels and to the splitting of charge- and spin-density excitations. We also discuss how the spin-orbit effects change if the applied magnetic field is tilted with respect to the direction perpendicular to the quantum well.

Optical response of two-dimensional few-electron concentric double quantum rings: A local-spin-density-functional theory study

We have investigated the dipole charge- and spin-density response of few-electron two-dimensional concentric nanorings as a function of the intensity of a erpendicularly applied magnetic field. We show that the dipole response displays signatures associated with the localization of electron states in the inner and outer ring favored by the perpendicularly applied magnetic field. Electron localization produces a more fragmented spectrum due to the appearance of additional edge excitations in the inner and outer ring.