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

High density limit of the two-dimensional electron liquid with Rashba spin-orbit coupling

We discuss by analytic means the theory of the high-density limit of the unpolarized two-dimensional electron liquid in the presence of Rashba or Dresselhaus spin-orbit coupling. A generalization of the ring-diagram expansion is performed. We find that in this regime the spin-orbit coupling leads to small changes of the exchange and correlation energy contributions, while modifying also, via repopulation of the momentum states, the noninteracting energy. As a result, the leading corrections to the chirality and total energy of the system stem from the Hartree-Fock contributions. The final results are found to be vanishing to lowest order in the spin-orbit coupling, in agreement with a general property valid to every order in the electron-electron interaction. We also show that recent quantum Monte Carlo data in the presence of Rashba spin-orbit coupling are well understood by neglecting corrections to the exchange-correlation energy, even at low density values.Comment: 11 pages, 5 figure

Data Mining to Uncover Heterogeneous Water Use Behaviors From Smart Meter Data

Knowledge on the determinants and patterns of water demand for different consumers supports the design of customized demand management strategies. Smart meters coupled with big data analytics tools create a unique opportunity to support such strategies. Yet, at present, the information content of smart meter data is not fully mined and usually needs to be complemented with water fixture inventory and survey data to achieve detailed customer segmentation based on end use water usage. In this paper, we developed a data‐driven approach that extracts information on heterogeneous water end use routines, main end use components, and temporal characteristics, only via data mining existing smart meter readings at the scale of individual households. We tested our approach on data from 327 households in Australia, each monitored with smart meters logging water use readings every 5 s. As part of the approach, we first disaggregated the household‐level water use time series into different end uses via Autoflow. We then adapted a customer segmentation based on eigenbehavior analysis to discriminate among heterogeneous water end use routines and identify clusters of consumers presenting similar routines. Results revealed three main water end use profile clusters, each characterized by a primary end use: shower, clothes washing, and irrigation. Time‐of‐use and intensity‐of‐use differences exist within each class, as well as different characteristics of regularity and periodicity over time. Our customer segmentation analysis approach provides utilities with a concise snapshot of recurrent water use routines from smart meter data and can be used to support customized demand management strategies.TU Berlin, Open-Access-Mittel - 201

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

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

To what extent can dynamical models describe statistical features of turbulent flows?

Statistical features of "bursty" behaviour in charged and neutral fluid turbulence, are compared to statistics of intermittent events in a GOY shell model, and avalanches in different models of Self Organized Criticality (SOC). It is found that inter-burst times show a power law distribution for turbulent samples and for the shell model, a property which is shared only in a particular case of the running sandpile model. The breakdown of self-similarity generated by isolated events observed in the turbulent samples, is well reproduced by the shell model, while it is absent in all SOC models considered. On this base, we conclude that SOC models are not adequate to mimic fluid turbulence, while the GOY shell model constitutes a better candidate to describe the gross features of turbulence.Comment: 14 pages, 4 figures, in press on Europhys. Lett. (may 2002

Many-body effective mass enhancement in a two-dimensional electron liquid

Motivated by a large number of recent magnetotransport studies we have revisited the problem of the microscopic calculation of the quasiparticle effective mass in a paramagnetic two-dimensional (2D) electron liquid (EL). Our systematic study is based on a generalized $GW$ approximation which makes use of the many-body local fields and takes advantage of the results of the most recent QMC calculations of the static charge- and spin-response of the 2D EL. We report extensive calculations for the many-body effective mass enhancement over a broad range of electron densities. In this respect we critically examine the relative merits of the on-shell approximation, commonly used in weak-coupling situations, {\it versus} the actual self-consistent solution of the Dyson equation. We show that already for $r_s \simeq 3$ and higher, a solution of the Dyson equation proves here necessary in order to obtain a well behaved effective mass. Finally we also show that our theoretical results for a quasi-2D EL, free of any adjustable fitting parameters, are in good qualitative agreement with some recent measurements in a GaAs/AlGaAs heterostructure.Comment: 12 pages, 3 figures, CMT28 Conference Proceedings, work related to cond-mat/041226

Dynamical polarization of graphene under strain

We study the dependence of the plasmon dispersion relation of graphene on applied uniaxial strain. Besides electron correlation at the RPA level, we also include local field effects specific for the honeycomb lattice. As a consequence of the two-band character of the electronic band structure, we find two distinct plasmon branches. We recover the square-root behavior of the low-energy branch, and find a nonmonotonic dependence of the strain-induced modification of its stiffness, as a function of the wavevector orientation with respect to applied strain.Comment: Phys. Rev. B, accepte

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.