Exchange energy and generalized polarization in the presence of spin-orbit coupling in two dimensions

We discuss a general form of the exchange energy for a homogeneous system of interacting electrons in two spatial dimensions which is particularly suited in the presence of a generic spin-orbit interaction. The theory is best formulated in terms of a generalized fractional electronic polarization. Remarkably we find that a net generalized polarization does not necessarily translate into an increase in the magnitude of the exchange energy, a fact that in turn favors unpolarized states. Our results account qualitatively for the findings of recent experimental investigations

Non perturbative Adler-Bardeen Theorem

The Adler-Bardeen theorem has been proved only as a statement valid at all orders in perturbation theory, without any control on the convergence of the series. In this paper we prove a nonperturbative version of the Adler-Bardeen theorem in $d=2$ by using recently developed technical tools in the theory of Grassmann integration.Comment: 28 pages, 14 figure

Froth-like minimizers of a non local free energy functional with competing interactions

We investigate the ground and low energy states of a one dimensional non local free energy functional describing at a mean field level a spin system with both ferromagnetic and antiferromagnetic interactions. In particular, the antiferromagnetic interaction is assumed to have a range much larger than the ferromagnetic one. The competition between these two effects is expected to lead to the spontaneous emergence of a regular alternation of long intervals on which the spin profile is magnetized either up or down, with an oscillation scale intermediate between the range of the ferromagnetic and that of the antiferromagnetic interaction. In this sense, the optimal or quasi-optimal profiles are "froth-like": if seen on the scale of the antiferromagnetic potential they look neutral, but if seen at the microscope they actually consist of big bubbles of two different phases alternating among each other. In this paper we prove the validity of this picture, we compute the oscillation scale of the quasi-optimal profiles and we quantify their distance in norm from a reference periodic profile. The proof consists of two main steps: we first coarse grain the system on a scale intermediate between the range of the ferromagnetic potential and the expected optimal oscillation scale; in this way we reduce the original functional to an effective "sharp interface" one. Next, we study the latter by reflection positivity methods, which require as a key ingredient the exact locality of the short range term. Our proof has the conceptual interest of combining coarse graining with reflection positivity methods, an idea that is presumably useful in much more general contexts than the one studied here.Comment: 38 pages, 2 figure

Model-independent Limits from Spin-dependent WIMP Dark Matter Experiments

Spin-dependent WIMP searches have traditionally presented results within an odd group approximation and by suppressing one of the spin-dependent interaction cross sections. We here elaborate on a model-independent analysis in which spin-dependent interactions with both protons and neutrons are simultaneously considered. Within this approach, equivalent current limits on the WIMP-nucleon interaction at WIMP mass of 50 GeV/c$^{2}$ are either $\sigma_{p}\leq0.7$ pb, $\sigma_{n}\leq0.2$ pb or $|a_{p}|\leq0.4$, $|a_{n}|\leq0.7$ depending on the choice of cross section or coupling strength representation. These limits become less restrictive for either larger or smaller masses; they are less restrictive than those from the traditional odd group approximation regardless of WIMP mass. Combination of experimental results are seen to produce significantly more restrictive limits than those obtained from any single experiment. Experiments traditionally considered spin-independent are moreover found to severely limit the spin-dependent phase space. The extension of this analysis to the case of positive signal experiments is explored.Comment: 12 pages, 12 figures, submitted to Phys. Rev.

Striped periodic minimizers of a two-dimensional model for martensitic phase transitions

In this paper we consider a simplified two-dimensional scalar model for the formation of mesoscopic domain patterns in martensitic shape-memory alloys at the interface between a region occupied by the parent (austenite) phase and a region occupied by the product (martensite) phase, which can occur in two variants (twins). The model, first proposed by Kohn and Mueller, is defined by the following functional: $${\cal E}(u)=\beta||u(0,\cdot)||^2_{H^{1/2}([0,h])}+ \int_{0}^{L} dx \int_0^h dy \big(|u_x|^2 + \epsilon |u_{yy}| \big)$$ where $u:[0,L]\times[0,h]\to R$ is periodic in $y$ and $u_y=\pm 1$ almost everywhere. Conti proved that if $\beta\gtrsim\epsilon L/h^2$ then the minimal specific energy scales like $\sim \min\{(\epsilon\beta/L)^{1/2}, (\epsilon/L)^{2/3}\}$, as $(\epsilon/L)\to 0$. In the regime $(\epsilon\beta/L)^{1/2}\ll (\epsilon/L)^{2/3}$, we improve Conti's results, by computing exactly the minimal energy and by proving that minimizers are periodic one-dimensional sawtooth functions.Comment: 29 pages, 3 figure

Heavy Superheated Droplet Detectors as a Probe of Spin-independent WIMP Dark Matter Existence

At present, application of Superheated Droplet Detectors (SDDs) in WIMP dark matter searches has been limited to the spin-dependent sector, owing to the general use of fluorinated refrigerants which have high spin sensitivity. Given their recent demonstration of a significant constraint capability with relatively small exposures and the relative economy of the technique, we consider the potential impact of heavy versions of such devices on the spin-independent sector. Limits obtainable from a $\mathrm{CF_{3}I}$-loaded SDD are estimated on the basis of the radiopurity levels and backgrounds already achieved by the SIMPLE and PICASSO experiments. With 34 kgd exposure, equivalent to the current CDMS, such a device may already probe to below 10$^{-6}$ pb in the spin-independent cross section.Comment: 9 pages, 4 figures, accepted Phys. Rev.

Behind the dust curtain: the spectacular case of GRB 160623A

We report on the X-ray dust-scattering features observed around the afterglow of the gamma ray burst GRB 160623A. With an XMM-Newton observation carried out ~2 days after the burst, we found evidence of at least six rings, with angular size expanding between ~2 and 9 arcmin, as expected for X-ray scattering of the prompt GRB emission by dust clouds in our Galaxy. From the expansion rate of the rings, we measured the distances of the dust layers with extraordinary precision: 528.1 +\- 1.2 pc, 679.2 +\- 1.9 pc, 789.0 +\- 2.8 pc, 952 +\- 5 pc, 1539 +\- 20 pc and 5079 +\- 64 pc. A spectral analysis of the ring spectra, based on an appropriate dust-scattering model (BARE-GR-B from Zubko et al. 2004}) and the estimated burst fluence, allowed us to derive the column density of the individual dust layers, which are in the range 7x10^20-1.5x10^22 cm^-2. The farthest dust-layer (i.e. the one responsible for the smallest ring) is also the one with the lowest column density and it is possibly very extended, indicating a diffuse dust region. The properties derived for the six dust-layers (distance, thickness, and optical depth) are generally in good agreement with independent information on the reddening along this line of sight and on the distribution of molecular and atomic gas.Comment: 9 pages, 10 figures, 1 table; accepted for publication in MNRA