Full Theoretical Treatment Research Articles

An exactly solvable model of randomly pinned charge density waves in two dimensions

The nature of the interplay between fluctuations and quenched random disorder is a long-standing open problem, particularly in systems with a continuous order parameter. This lack of a full theoretical treatment has been underscored by recent advances in experiments on charge density wave materials. To address this problem, we formulate an exactly solvable model of a two-dimensional randomly pinned incommensurate charge density wave, and use the large-N technique to map out the phase diagram and order parameter correlations. Our approach captures the physics of the Berezinskii–Kosterlitz–Thouless phase transition in the clean limit at large N. We pay particular attention to the roles of thermal fluctuations and quenched random field disorder in destroying long-range order, finding a novel crossover between weakly- and strongly-disordered regimes.

Spatial correlations of dark energy from quantum fluctuations during inflation

This paper contains a detailed study of the properties of a simple model attempting to explain dark energy as originated from quantum fluctuations of a light spectator scalar field in inflation. In [1] we recently outlined how Starobinsky's stochastic formalism can be used to study the spatial correlations imprinted on dark energy by its quantum origin in this model and we studied their possible role in relieving the Hubble tension. Here we provide a more comprehensive derivation of the results in [1] and we refine some of our estimates, comparing to the approximate results obtained previously. Among the main results, we analyze the non-coincident correlators predicted by a full field theoretical treatment and their relation with those computed within the stochastic formalism. We find that in the region where stochastic theory predicts significant sub-Hubble correlators it is in disagreement with field theoretical predictions. However, agreement can be restored by introducing a reduced speed of sound for the scalar field. We also discuss an alternative approach to the problem of studying correlators within the stochastic formalism based directly on the evolution of probability distributions. We find that the two approaches give the same answer for 2-point functions of the field, but not for 4-point functions relevant to density correlators and we discuss the behaviour of the two methods with respect to Wick's theorem.

Approach-Avoidance Decisions Under Threat: The Role of Autonomic Psychophysiological States.

Acutely challenging or threatening situations frequently require approach-avoidance decisions. Acute threat triggers fast autonomic changes that prepare the body to freeze, fight or flee. However, such autonomic changes may also influence subsequent instrumental approach-avoidance decisions. Since defensive bodily states are often not considered in value-based decision-making models, it remains unclear how they influence the decision-making process. Here, we aim to bridge this gap by discussing the existing literature on the potential role of threat-induced bodily states on decision making and provide a new neurocomputational framework explaining how these effects can facilitate or bias approach-avoid decisions under threat. Theoretical accounts have stated that threat-induced parasympathetic activity is involved in information gathering and decision making. Parasympathetic dominance over sympathetic activity is particularly seen during threat-anticipatory freezing, an evolutionarily conserved response to threat demonstrated across species and characterized by immobility and bradycardia. Although this state of freezing has been linked to altered information processing and action preparation, a full theoretical treatment of the interactions with value-based decision making has not yet been achieved. Our neural framework, which we term the Threat State/Value Integration (TSI) Model, will illustrate how threat-induced bodily states may impact valuation of competing incentives at three stages of the decision-making process, namely at threat evaluation, integration of rewards and threats, and action initiation. Additionally, because altered parasympathetic activity and decision biases have been shown in anxious populations, we will end with discussing how biases in this system can lead to characteristic patterns of avoidance seen in anxiety-related disorders, motivating future pre-clinical and clinical research.

Distributed Acoustic Sensing Based on Pulse-Coding Phase-Sensitive OTDR

Phase-sensitive optical time-domain reflectometry ( ${\Phi }$ -OTDR), which utilizes the phase information of Rayleigh scattered lightwave inside optical fiber, could turn a fiber cable into a massive sensor array for distributed acoustic sensing (DAS), i.e., an emerging infrastructure for Internet of Things. Given a certain fiber length, there are tradeoffs among the sensing bandwidth, the sensitivity, and the spatial resolution. In this paper, the concept of linearization and Golay pulse-coding for heterodyne ${\Phi }$ -OTDR are proposed and experimentally verified for the first time. First, we gave a full theoretical treatment on how an intensity-coded yet phase-retrieved ${\Phi }$ -OTDR can be built up as a fully linear system, therefore a significant enhancement of signal-to-noise ratio becomes viable and the sensing bandwidth equals the four-times averaging case. Second in the proof-of-concept experiment, submeter gauge length and nano-strain resolution were realized with 10 km sensing range, in other words, more than ten thousand sensitive sensing units were realized along the fiber. This paper makes a significant step toward high-performance DAS with orders-of-magnitude performance enhancement.

Proof of the Splitting Mode of Compressive Brittle Failure and Integration With General Failure Theory

The problem of special interest is the nature of the mode of failure in uniaxial compression at the brittle limit. This problem is known by observation to undergo a splitting mode of failure. The present work gives a full theoretical treatment and proof for this mode of failure. The general failure theory of Christensen for isotropic materials provides the basis for the derivation. The solution demonstrates the depth of technical capability that is required from the failure theory to treat such a classically difficult problem.

Yang–Mills theory in the SO(2,3)⋆ model of noncommutative gravity

According to the standard cosmological model, thermodynamic conditions of the early Universe were such that nuclear matter existed in the state of quark–gluon plasma, rather than hadrons. On the other hand, it is generally believed that quantum gravity effects become ever more stronger as we approach the Big Bang, in particular, we expect that the phenomenon of space–time noncommutativity will be significant. Thus we are led to consider the properties of quarks and gluons in noncommutative space–time. For this, we employ the [Formula: see text] model of noncommutative gravity. As a first step towards the full theoretical treatment of the effects of noncommutativity on quark–gluon plasma, our main goal in this paper is to consistently incorporate Yang–Mills gauge fields in the [Formula: see text] framework and investigate their coupling to gravity that arises due to space–time noncommutativity. We construct an action that is invariant under deformed [Formula: see text] gauge transformations and expand it perturbatively in orders of the canonical deformation parameter [Formula: see text] via Seiberg–Witten map. In particular, we analyze the flat-space–time limit and demonstrate that residual noncommutativity induces various new couplings of quarks and gluons.

Anti-Stokes resonant x-ray Raman scattering for atom specific and excited state selective dynamics

Ultrafast electronic and structural dynamics of matter govern rate and selectivity of chemical reactions, as well as phase transitions and efficient switching in functional materials. Since x-rays determine electronic and structural properties with elemental, chemical, orbital and magnetic selectivity, short pulse x-ray sources have become central enablers of ultrafast science. Despite of these strengths, ultrafast x-rays have been poor at picking up excited state moieties from the unexcited ones. With time-resolved anti-Stokes resonant x-ray Raman scattering (AS-RXRS) performed at the LCLS, and ab initio theory we establish background free excited state selectivity in addition to the elemental, chemical, orbital and magnetic selectivity of x-rays. This unparalleled selectivity extracts low concentration excited state species along the pathway of photo induced ligand exchange of Fe(CO)5 in ethanol. Conceptually a full theoretical treatment of all accessible insights to excited state dynamics with AS-RXRS with transform-limited x-ray pulses is given—which will be covered experimentally by upcoming transform-limited x-ray sources.

Condenser-free contrast methods for transmitted-light microscopy.

Phase contrast microscopy allows the study of highly transparent yet detail-rich specimens by producing intensity contrast from phase objects within the sample. Presented here is a generalized phase contrast illumination schema in which condenser optics are entirely abrogated, yielding a condenser-free yet highly effective method of obtaining phase contrast in transmitted-light microscopy. A ring of light emitting diodes (LEDs) is positioned within the light-path such that observation of the objective back focal plane places the illuminating ring in appropriate conjunction with the phase ring. It is demonstrated that true Zernike phase contrast is obtained, whose geometry can be flexibly manipulated to provide an arbitrary working distance between illuminator and sample. Condenser-free phase contrast is demonstrated across a range of magnifications (4–100×), numerical apertures (0.13–1.65NA) and conventional phase positions. Also demonstrated is condenser-free darkfield microscopy as well as combinatorial contrast including Rheinberg illumination and simultaneous, colour-contrasted, brightfield, darkfield and Zernike phase contrast. By providing enhanced and arbitrary working space above the preparation, a range of concurrent imaging and electrophysiological techniques will be technically facilitated. Condenser-free phase contrast is demonstrated in conjunction with scanning ion conductance microscopy (SICM), using a notched ring to admit the scanned probe. The compact, versatile LED illumination schema will further lend itself to novel next-generation transmitted-light microscopy designs. The condenser-free illumination method, using rings of independent or radially-scanned emitters, may be exploited in future in other electromagnetic wavebands, including X-rays or the infrared.

Compton scattering fromLi6at 86 MeV

Cross sections for $^{6}\mathrm{Li}(\ensuremath{\gamma},\ensuremath{\gamma})^{6}\mathrm{Li}$ have been measured at the High Intensity Gamma-Ray Source $\mathrm{(HI}\stackrel{P\vec}{\ensuremath{\gamma}}\mathrm{S)}$ and the sensitivity of these cross sections to the nucleon isoscalar polarizabilities was studied. Data were collected using a quasimonoenergetic 86-MeV photon beam at photon scattering angles of ${40}^{\ensuremath{\circ}}--{160}^{\ensuremath{\circ}}$. These results are an extension of a previous measurement at a lower energy. The earlier work indicated that the $^{6}\mathrm{Li}(\ensuremath{\gamma},\ensuremath{\gamma})^{6}\mathrm{Li}$ reaction at 60 MeV provides a means of extracting the nucleon polarizabilities; this work demonstrates that the sensitivity of the cross section to the polarizabilities is increased at 86 MeV. A full theoretical treatment is needed to verify this conclusion and produce values of the polarizabilities.

Steady-state and non-steady state operation of counter-current chromatography devices

Different variants of separation processes based on steady-state (continuous sample loading) and non-steady state (batch) operating modes of CCC columns have been analyzed and compared. The analysis is carried out on the basis of the modified equilibrium cell model, which takes into account both mechanisms of band broadening – interphase mass transfer and axial mixing. A full theoretical treatment of the intermittent counter-current chromatography with short sample loading time is performed. Analytical expressions are presented allowing the simulation of the intermittent counter-current chromatography separations for various experimental conditions.Chromatographic and extraction separations have been compared and advantages and disadvantages of the two methods have been evaluated. Further technical development of the CCC machines to implement counter-current extraction separations is considered.

Electron-impact excitation of Cr ii

Context. Absorption or emission lines of Cr ii are observed in a wide variety of astrophysical spectra and accurate atomic data are urgently needed to interpret these lines. Many of these data are impossible to measure experimentally and a full theoretical treatment is the only means by which these data can be obtained. Aims. In this paper, we present collision strengths and effective collision strengths for electron-impact excitation of Cr ii for forbidden transitions among the lowest-lying 74 fine-structure levels. Effective collision strengths have been computed for 18 individual electron temperatures of astrophysical importance, ranging from 2000–100 000 K. Methods. The parallel suite of R-matrix packages, RMATRX II, which has recently been extended to allow for the inclusion of relativistic effects, has been used in the present work to compute the collision strengths and effective collision strengths for electronimpact excitation of Cr ii. We concentrate in this publication on low-lying forbidden lines among the lowest 74 jj fine-structure levels with configurations 3d 5 and 3d 4 4s, although atomic data has been evaluated for all 39 060 transitions among the 280 jj levels of configurations 3d 5 ,3 d 4 4s and 3d 4 4p. This work constitutes the largest evaluation ever performed for this ion involving 1932 coupled channels. Results. Collision and effective collision strengths are presented for all transitions among the lowest 74 Jπ states of Cr ii and comparisons made with the work of Bautista et al. (2009). While the effective collision strengths agree well for some transitions, significant discrepancies exist for others. We believe that the present atomic data represents the most accurate, most sophisticated and most complete data set for electron-impact excitation of Cr ii and we would recommend them to astrophysicists and plasma physicists in their application work. We would expect that the effective collision strengths presented for the important low-lying forbidden lines are accurate to within 15%.

Propagation of squeezed vacuum under electromagnetically induced transparency

We analyze the transmission of continuous-wave and pulsed squeezed vacuum through rubidium vapor under the conditions of electromagnetically induced transparency. Our analysis is based on a full theoretical treatment for a squeezed state of light propagating through temporal and spectral filters and detected using time and frequency-domain homodyne tomography. A model based on a three-level atom allows us to evaluate the linear losses and extra noise that degrade the nonclassical properties of the squeezed vacuum during the atomic interaction and eventually predict the quantum states of the transmitted light with a high precision.

Elution-extrusion countercurrent chromatography: theory and concepts in metabolic analysis.

Elution-extrusion countercurrent chromatography (EECCC) takes full advantage of the liquid nature of the stationary phase in CCC by combining regular chromatographic elution with stationary-phase extrusion. EECCC is shown to be a three-stage process consisting of classical elution (I), sweeping elution (II), and extrusion (III). After only two column volumes of solvent, it rapidly yields a high-resolution chromatogram that covers an extended polarity range of solutes. As hydrophilicity/lipophilicity balance is a crucial discriminatory property of analytes in highly complex mixtures such as metabolomic samples, the precise determination of CCC distribution constants (KD) is vital to the analysis of metabolomes and other complex biological matrixes. This work builds the EECCC concept by performing a full theoretical treatment and providing equations for retention volumes, peak widths, resolution factors, and distribution constants. Experimental validation utilizes natural products standards that resemble the zero to infinity range of the polarity continuum. EECCC extends the "sweet spot" of high resolution in CCC and provides access to the otherwise practically unapproachable high-KD portion of the high-resolution chromatograms in CCC. Its improved capabilities of KD targeting make EECCC a promising tool for the specific analysis of "small" molecules in complex samples such as in metabolomic fingerprinting and footprinting.

Surface-Plasmon-Mediated Single-Molecule Fluorescence Through a Thin Metallic Film

We demonstrate that fluorescence of single molecules in the nanometric vicinity of a thin gold film can be effectively excited and detected through the film with an epi-illumination scanning confocal microscope. A full theoretical treatment of the fluorescence signal indicates that both excitation and emission are surface-plasmon mediated. Remarkably, the number of photons detectable from chromophores perpendicular to the interface is enhanced by the presence of the metal.

State Selective Electron Capture in the Collision of S3+ Ions in Atomic Hydrogen and Helium

A full theoretical treatment including an ab-initio molecular calculation of the potential energy curves and couplings followed by a semi-classical collision dynamics has been performed for the one-electron capture by S3+ ions in collision with atomic hydrogen. The present paper completes a previous letter [9] and displays the full results concerning this process in order to provide a detailed understanding of the mechanism. These calculations show evidence of the predominance of the S2+(3s23p3d)3F° capture level, already pointed out by translational energy spectroscopy experiments and confirms experimental measurements. A compared study of the behaviour of the S3+ projectile colliding both hydrogen and helium targets is also presented.

Optimized second-harmonic generation in quantum cascade lasers

Optimized second-harmonic generation (SHG) in quantum cascade (QC) lasers with specially designed active regions is reported. Nonlinear optical cascades of resonantly coupled intersubband transitions with giant second-order nonlinearities were integrated with each QC-laser active region. QC lasers with three-coupled quantum-well (QW) active regions showed up to 2 /spl mu/W of SHG light at 3.75 /spl mu/m wavelength at a fundamental peak power and wavelength of 1 W and 7.5 /spl mu/m, respectively. These lasers resulted in an external linear-to-nonlinear conversion efficiency of up to 1 /spl mu/W/W/sup 2/. An improved 2-QW active region design at fundamental and SHG wavelengths of 9.1 and 4.55 /spl mu/m, respectively, resulted in a 100-fold improved external linear-to-nonlinear power conversion efficiency, i.e. up to 100 /spl mu/W/W/sup 2/. Full theoretical treatment of nonlinear light generation in QC lasers is given, and excellent agreement with the experimental results is obtained. For the best structure, a second-order nonlinear susceptibility of 4.7/spl times/10/sup -5/ esu (2/spl times/10/sup 4/pm/V) is calculated, about two orders of magnitude above conventional nonlinear optical materials and bulk III-V semiconductors.

Understanding the concept of representation within the context of local forest management decision making

Public involvement in forest management decision making has become more and more prevalent. With this growth, a large body of literature has emerged that examines ideal forms of public participation processes. Despite these scholarly advances, it is argued that the literature fails to account for the full concept of representation, which is relegated to a one-dimensional interpretation based on the correspondence of the representatives and their constituents, known as descriptive representation. In this paper, a statistical comparison of Alberta-based Public Resource Advisory Groups and the provincial general public is provided. The results are indicative of other similar studies where differences in socio-demographic characteristics and belief and values between the public and representative groups exist. However, in the second part of the paper, a full theoretical treatment of representation is given. In addition to descriptive representation, two other forms of representation are introduced: the representation of subjective interests and the representation of objective interests. Both provide a different interpretation of what constitutes representation and has important consequences for an understanding of forest-management decision making.

Photoelectron spectroscopic determination of the energy bandwidths of high-order harmonics (7th–55th) produced by an ultrafast laser in neon

The energy bandwidths of high-order harmonics of a Ti:sapphire ultrafast laser are extracted from electron kinetic-energy measurements of the photoionization of gas-phase atoms and molecules. High-order harmonics of the 70 fs, 800 nm laser are produced by focusing $\ensuremath{\approx}2.5 \mathrm{mJ}$ pulses into a jet of neon gas and are frequency-separated by a grazing-incidence grating. Photoelectrons resulting from the ionization of gaseous samples are energy-analyzed with a magnetic bottle time-of-flight spectrometer. Energy broadening of the photoelectron peaks at low kinetic energies are a direct result of the energy bandwidths of the harmonics. The energy bandwidths of the harmonics are found to increase from $0.11(\ifmmode\pm\else\textpm\fi{}0.03) \mathrm{eV}$ (7th harmonic) to $0.37(\ifmmode\pm\else\textpm\fi{}0.03) \mathrm{eV}$ (45th harmonic) in a gradual manner. The higher-order harmonics (47th--55th) appear to reach a plateau at a value of $\ensuremath{\approx}0.43 \mathrm{eV}.$ Though a full theoretical treatment of bandwidths of the harmonics for the 70 fs driving pulse regime does not exist, the theories developed for shorter pulses $(<~30 \mathrm{fs})$ can give insight into the observed results.

Exchange and anisotropy effects on spin waves in epitaxial Co films

Using Brillouin scattering we have investigated the effect of large in-plane anisotropy on magnetic excitations in $b$ axis-oriented epitaxial 50-nm Co films. For in-plane fields along the easy axis the magnon frequencies increase monotonically with increasing field. For in-plane fields along the hard axis, nonmonotonic behavior is observed in which the surface to bulk spin-wave character of one magnon mode changes as a function of applied field. Although fits to the data based on a full theoretical treatment are consistent with parameters in the literature and with parameters extracted from the magnetization data, we show that uncertainties in crystal orientation (as small as 1\ifmmode^\circ\else\textdegree\fi{}) can produce dramatic effects in the quantitative data interpretation.

Thermal diffusivity of anisotropic materials by photothermal methods

In this paper we analyze the possibility of extending the photothermal methods developed for thermal diffusivity measurements of isotropic materials [A. Salazar and A. Sánchez-Lavega, Rev. Sci. Instrum. 65, 2896 (1994)] to the case of anisotropic specimens. A full theoretical treatment of the photothermal signal generation for the case of an anisotropic sample with its principal axes aligned with the sample surface is presented. Three photothermal detection schemes have been studied: infrared radiometry, photothermal reflectance, and optical beam deflection (mirage effect). The fundamental result we have obtained is that when using infrared radiometry, photothermal reflectance and collinear mirage setups, the thermal magnitude retrieved is the resistivity to heat diffusion (a tensor defined as the inverse of the thermal diffusivity tensor). Only the perpendicular mirage experiment allows one to directly retrieve the thermal diffusivity along any direction of the material. Experimental measurements performed on two highly anisotropic materials confirm the above-mentioned results.