Helmholtz decomposition theorem and Blumenthal's extension by regularization

Helmholtz decomposition theorem for vector fields is usually presented with too strong restrictions on the fields and only for time independent fields. Blumenthal showed in 1905 that decomposition is possible for any asymptotically weakly decreasing vector field. He used a regularization method in his proof which can be extended to prove the theorem even for vector fields asymptotically increasing sublinearly. Blumenthal's result is then applied to the time-dependent fields of the dipole radiation and an artificial sublinearly increasing field.Comment: 11 pages. arXiv admin note: text overlap with arXiv:1506.0023

Critical dynamics of diluted relaxational models coupled to a conserved density (diluted model C)

We consider the influence of quenched disorder on the relaxational critical dynamics of a system characterized by a non-conserved order parameter coupled to the diffusive dynamics of a conserved scalar density (model C). Disorder leads to model A critical dynamics in the asymptotics, however it is the effective critical behavior which is often observed in experiments and in computer simulations and this is described by the full set of dynamical equations of diluted model C. Indeed different scenarios of effective critical behavior are predicted.Comment: 4 pages, 5 figure

Static and dynamic structure factors in three-dimensional randomly diluted Ising models

We consider the three-dimensional randomly diluted Ising model and study the critical behavior of the static and dynamic spin-spin correlation functions (static and dynamic structure factors) at the paramagnetic-ferromagnetic transition in the high-temperature phase. We consider a purely relaxational dynamics without conservation laws, the so-called model A. We present Monte Carlo simulations and perturbative field-theoretical calculations. While the critical behavior of the static structure factor is quite similar to that occurring in pure Ising systems, the dynamic structure factor shows a substantially different critical behavior. In particular, the dynamic correlation function shows a large-time decay rate which is momentum independent. This effect is not related to the presence of the Griffiths tail, which is expected to be irrelevant in the critical limit, but rather to the breaking of translational invariance, which occurs for any sample and which, at the critical point, is not recovered even after the disorder average.Comment: 43 page

Model C critical dynamics of random anisotropy magnets

We study the relaxational critical dynamics of the three-dimensional random anisotropy magnets with the non-conserved n-component order parameter coupled to a conserved scalar density. In the random anisotropy magnets the structural disorder is present in a form of local quenched anisotropy axes of random orientation. When the anisotropy axes are randomly distributed along the edges of the n-dimensional hypercube, asymptotical dynamical critical properties coincide with those of the random-site Ising model. However structural disorder gives rise to considerable effects for non-asymptotic critical dynamics. We investigate this phenomenon by a field-theoretical renormalization group analysis in the two-loop order. We study critical slowing down and obtain quantitative estimates for the effective and asymptotic critical exponents of the order parameter and scalar density. The results predict complex scenarios for the effective critical exponent approaching an asymptotic regime.Comment: 8 figures, style files include

Large spin-orbit effects in small quantum dots

We consider small ballistic quantum dots weakly coupled to the leads in the chaotic regime and look for significant spin-orbit effects. We find that these effects can become quite prominent in the vicinity of degeneracies of many-body energies. We illustrate the idea by considering a case where the intrinsic exchange term -JS^2 brings singlet and triplet many-body states near each other, while an externally tunable Zeeman term then closes the gap between the singlet and the one of the triplet states (with spin projection parallel the external field). Near this degeneracy, the spin-orbit coupling leads to a striking temperature dependence of the conductance, with observable effects of order unity at temperatures lower than the strength of the spin-orbit coupling. Under favorable circumstances, spelled out in the paper, these order unity effects in the conductance persist to temperatures much higher than the spin-orbit coupling strength. Our conclusions are unaffected by the presence of non-universal perturbations. We suggest a class of experiments to explore this regime.Comment: 13 pages, 8 figure

Superfluid state of magnetoexcitons in double layer graphene structures

The possibility of realization of a superfluid state of bound electron-hole pairs (magnetoexcitons) with spatially separated components in a graphene double layer structure (two graphene layers separated by a dielectric layer) subjected by a strong perpendicular to the layers magnetic field is analyzed. We show that the superfluid state of magnetoexcitons may emerge only under certain imbalance of filling factors of the layers. The imbalance can be created by an electrostatic field (external gate voltage). The spectrum of elementary excitations is found and the dependence of the Berezinskii-Kosterlitz-Thouless transition temperature on the interlayer distance is obtained. The advantages of use graphene double layer systems instead of double quantum well GaAs heterostructures are discussed

Defect-induced condensation and central peak at elastic phase transitions

Static and dynamical properties of elastic phase transitions under the influence of short--range defects, which locally increase the transition temperature, are investigated. Our approach is based on a Ginzburg--Landau theory for three--dimensional crystals with one--, two-- or three--dimensional soft sectors, respectively. Systems with a finite concentration $n_{\rm D}$ of quenched, randomly placed defects display a phase transition at a temperature $T_c(n_{\rm D})$, which can be considerably above the transition temperature $T_c^0$ of the pure system. The phonon correlation function is calculated in single--site approximation. For $T>T_c(n_{\rm D})$ a dynamical central peak appears; upon approaching $T_c(n_{\rm D})$, its height diverges and its width vanishes. Using an appropriate self--consistent method, we calculate the spatially inhomogeneous order parameter, the free energy and the specific heat, as well as the dynamical correlation function in the ordered phase. The dynamical central peak disappears again as the temperatur is lowered below $T_c(n_{\rm D})$. The inhomogeneous order parameter causes a static central peak in the scattering cross section, with a finite $k$ width depending on the orientation of the external wave vector ${\bf k}$ relative to the soft sector. The jump in the specific heat at the transition temperatur of the pure system is smeared out by the influence of the defects, leading to a distinct maximum instead. In addition, there emerges a tiny discontinuity of the specific heat at $T_c(n_{\rm D})$. We also discuss the range of validity of the mean--field approach, and provide a more realistic estimate for the transition temperature.Comment: 11 pages, 11 ps-figures, to appear in PR

Low-temperature illumination and annealing of ultra-high quality quantum wells

The effects of low temperature illumination and annealing on fractional quantum Hall (FQH) characteristics of a GaAs/AlGaAs quantum well are investigated. Illumination alone, below 1 K, decreases the density of the 2DEG electrons by more than an order of magnitude and resets the sample to a repeatable initial state. Subsequent thermal annealing at a few Kelvin restores the original density and dramatically improves FQH characteristics. A reliable illumination and annealing recipe is developed that yields an energy gap of 600 mK for the 5/2 state