Contour Rotation Research Articles

Angle-resolved photoemission spectroscopy with an in situ tunable magnetic field.

Angle-resolved photoemission spectroscopy (ARPES) is a powerful tool for probing the momentum-resolved single-particle spectral function of materials. Historically, in situ magnetic fields have been carefully avoided as they are detrimental to the control of photoelectron trajectory during the photoelectron detection process. However, magnetic field is an important experimental knob for both probing and tuning symmetry-breaking phases and electronic topology in quantum materials. In this paper, we introduce an easily implementable method for realizing an in situ tunable magnetic field at the sample position in an ARPES experiment and analyze magnetic-field-induced artifacts in the ARPES data. Specifically, we identified and quantified three distinct extrinsic effects of a magnetic field: constant energy contour rotation, emission angle contraction, and momentum broadening. We examined these effects in three prototypical quantum materials, i.e., a topological insulator (Bi2Se3), an iron-based superconductor (LiFeAs), and a cuprate superconductor (Pb-Bi2Sr2CuO6+x), and demonstrate the feasibility of ARPES measurements in the presence of a controllable magnetic field. Our studies lay the foundation for the future development of the technique and interpretation of ARPES measurements of field-tunable quantum phases.

Three-body resonances in pionless effective field theory

We investigate the appearance of resonances in three-body systems using pionless effective field theory at leading order. The Faddeev equation is analytically continued to the unphysical sheet adjacent to the positive real energy axis using a contour rotation. We consider both, the three-boson system and the three-neutron system. For the former, we calculate the trajectory of Borromean three-body Efimov states turning into resonances as they cross the three-body threshold. For the latter, we find no sign of three-body resonances or virtual states at leading order. This result is validated by exploring the level structure of three-body states in a finite volume approach.

Интегральное представление функции Миттаг-Леффлера

Generalization of the integral representation of the gamma function has been obtained, which shows that the Hankel contour assumes rotation in the complex plane. The range of admissible values for the contour rotation angle is set. Using this integral representation, generalization of the integral representation of the Mittag-Leffler function has been obtained that expresses the value of this function in terms of the contour integral.

Principles of constructing gyroscopes based on photonic crystal (band-gap) fibers

The gyroscope is a device that makes it possible to measure the change in the orientation angles associated rotation of the body relative to an inertial coordinate system. Photonic crystal fiber gyroscopes are a kind of optical gyroscopes that offer many new features beyond that conventional fiber optic gyroscopes can offer. In any case, the properties of the optical fiber can play a large role in determining the characteristics of the gyroscope. The principle of operation of most optical gyroscopes is based on the Sagnac effect or the Sagnac interferometer, the essence of which is as follows. If two light waves propagate in a closed optical circuit in opposite directions, then in the case of an immovable circuit, the phase incursions of both waves that have passed the entire circuit in opposite directions will be the same. When the contour rotates around an axis normal to the contour plane, the phase incursions of the waves become unequal, and their difference in the general case will be proportional to the angular velocity of the contour rotation, the area covered by the contour, and the frequency of the electromagnetic wave (EMW). Since the area and frequency of the EMW remain unchanged during the operation of the gyroscope, the phase shift will be proportional only to the angular velocity. The use of photonic crystal fiber to increase the sensitivity is very promising; it significantly reduces the drift through thermal polarization, resistance, and the Kerr effect. This article suggests the use of photonic-crystal (hollow-core) fiber in optical gyroscope instead of conventional fibers.

Geotechnical properties of 3D-printed transparent granular soil

This paper proposes a 3D-printed transparent granular soil technique based on the contour rotation interpolation method, 3D printing and transparent soil technologies. Laboratory tests, including one-dimensional compression, direct shear and triaxial compression tests, are assessed for mechanical properties of 3D-printed transparent granular soil. The results show that 3D-printed transparent granular soil can be used to consider the effect of shape on macromechanical soil properties, which is an advantage that cannot be achieved by the previously presented transparent soil techniques. Subsequently, a simple model test of rigid flat plate penetration into transparent granular soil is performed. The obtained soil displacements using the PIV technique are compared with the classical shallow strain path method solution. This comparison indicates that the proposed 3D-printed transparent granular soil can capture the soil deformation pattern, although the accuracy needs to be further improved. The proposed 3D-printed transparent granular soil technique could be used for model test that needs to consider the shape of sand particle.

Revealing Controllable Anisotropic Magnetoresistance in Spin–Orbit Coupled Antiferromagnet Sr2IrO4

AbstractAntiferromagnetic spintronics actively introduces new principles of magnetic memory, in which the most fundamental spin‐dependent phenomena, i.e., anisotropic magnetoresistance effects, are governed by an antiferromagnet instead of a ferromagnet. A general scenario of the antiferromagnetic anisotropic magnetoresistance effects mainly stems from the magnetocrystalline anisotropy related to spin–orbit coupling. Here magnetic field driven contour rotation of the fourfold anisotropic magnetoresistance in bare antiferromagnetic Sr2IrO4/SrTiO3 (001) thin films hosting a strong spin–orbit coupling induced Jeff = 1/2 Mott state is demonstrated. Concurrently, an intriguing minimal in the magnetoresistance emerges. Through first principles calculations, the bandgap engineering due to rotation of the Ir isospins is revealed to be responsible for these emergent phenomena, different from the traditional scenario where relatively more conductive state is obtained usually when magnetic field is applied along the magnetic easy axis. These findings demonstrate a new efficient route, i.e., via the novel Jeff = 1/2 state, to realize controllable anisotropic magnetoresistance in antiferromagnetic materials.

Conjecture: A PossiblennΛ Resonance

We address the question of whether there might exist a resonance in the nn Λ system, using a rank one separable potential formulation of the Hamiltonian. We explore the eigenvalues of the kernel of the Faddeev equation in the complex energy plane using contour rotation to allow us to analytically continue the kernel onto the second energy sheet. We follow the largest eigenvalue as the n Λ potentials are scaled and the nn Λ continuum is turned into a resonance and then into a bound state of the system.

Resonances in theΛnnsystem

Background: A bound state of the $\mathrm{\ensuremath{\Lambda}}nn$ system has been reported, but at least three theoretical papers question the existence of such a bound state.Purpose: We address the alternative question of whether there might exist a resonance in the $\mathrm{\ensuremath{\Lambda}}nn$ system, using a rank-one separable potential formulation of the Hamiltonian.Methods: We examine the eigenvalues of the kernel of the Faddeev equation in the complex energy plane using contour rotation to allow us to analytically continue the kernel onto the second energy sheet. The model $\mathrm{\ensuremath{\Lambda}}n$ interaction is fitted to the $\mathrm{\ensuremath{\Lambda}}p$ scattering length and effective range.Results: We follow the largest eigenvalue as the $\mathrm{\ensuremath{\Lambda}}n$ potentials are scaled and the $\mathrm{\ensuremath{\Lambda}}nn$ continuum is turned first into a resonance, and then into a bound state of the system.Conclusions: Because a change in the strength of the $\mathrm{\ensuremath{\Lambda}}n$ potential of as little as 5% will produce a $\mathrm{\ensuremath{\Lambda}}nn$ resonance, we infer that an experiment of the $^{3}\text{H}(\text{e},{\text{e}}^{\ensuremath{'}}{\text{K}}^{+})_{\mathrm{\ensuremath{\Lambda}}}^{3}\text{n}$ type at JLAB could be used to constrain the properties of the $\mathrm{\ensuremath{\Lambda}}n$ interaction.

Evaluation of two-photon exchange graphs for highly charged heliumlike ions.

Contributions of one-loop ladder and crossed-ladder graphs to the ground-state energy of heliumlike ions are calculated in Furry representation QED. With the aid of a contour rotation, the graphs are evaluated to all orders in Z\ensuremath{\alpha} in the range Z=10--110. Particular attention is given to the relation of this work to recent many-body perturbation theory and configuration-interaction calculations.

A computer‐aided measuring system for the characterization of yeast populations combining 2D‐image analysis, electronic particle counter, and flow cytometry

An integrated measuring system was developed that directly compares the shape of size distributions of Saccharomyces cerevisiae populations obtained from either microscopic measurements, electronic particle counter, or flow cytometer. Because of its asymmetric mode of growth, a yeast population consists of two different subpopulations, parents and daughters. Although electronic particle counter and flow cytometer represent fast methods to assess the growth state of the population as a whole, the determination of important cell cycle parameters like the fraction of daughters or budded cells requires microscopic observation. We therefore adapted a semiautomatic and interactive 2D-image processing program for rapid and accurate determination of volume distributions of the different sub-populations. The program combines the capacity of image processing and volume calculation by contour-rotation, with the potential of visual evaluation of the cells. High-contrast images from electron micrographs are well suited for image analysis, but the necessary air drying caused the cells to shrink to 35% of their hydrated volume. As an alternative, hydrated cells overstained with the fluorochrome calcofluor and visualized by fluorescence light microscopy were used. Cell volumes calculated from length, and diameter measurements with the assumption of an ellipsoid cell shape were underestimated as compared to volumes derived from 2D-image analysis and contour rotation, because of a deviating cell shape, especially in the older parent cells with more than one bud scar. The bimodal volume distribution obtained from microscopic measurements was identical to the protein distribution measured with the flow cytometer using cells stained with dansylchloride, but differed significantly from the size distribution measured with the electronic particle counter. Compared with the flow cytometer, 2-D image analysis can thus provide accurate distributions with important additional information on, for instance, the distributions of subpopulations like parents, daughters, or budded cells.

Non-perturbative calculation of correlators in 2D quantum gravity

The “fifth-time” action provides a truly non-perturbative definition of 2D quantum gravity. We show that it can be used for numerical calculation of correlators. We compare with the results obtained by defining 2D gravity by contour rotation in the functional integral. The two non-perturbative definitions give different results for correlators. The method of contour rotation leads to complex correlators, while the results using the fifth-time action are always real.

Elliptic Fourier analysis of cell and nuclear shapes

The elliptic Fourier analysis (EFA) is proposed to characterize the cell and nuclear shape. The principal feature of this method is that it decomposes shapes with a closed contour into subshapes each of which maintains a closed contour. A set of homogeneous, nonredundant descriptors, independent of the contour rotation and translation, is computed from the elliptic Fourier coefficients. These descriptors also account for the contour size and resolution. The paired analysis of the cell and nuclear shape provides an exhaustive and accurate definition of the nucleoplasmic configuration.

Conformal rotation in perturbative gravity.

The classical Euclidean action for general relativity is unbounded below; therefore Euclidean functional integrals weighted by this action are manifestly divergent. However, as a consequence of the positive-energy theorem, physical amplitudes for asymptotically flat spacetimes can indeed be expressed as manifestly convergent Euclidean functional integrals formed in terms of the physical degrees of freedom. From these integrals, we derive expressions for these same physical quantities as Euclidean integrals over the full set of variables for gravity computed as metric perturbations off a flat background. These parametrized Euclidean functional integrals are weighted by manifestly positive actions with rotated conformal factors. They are similar in form to Euclidean functional integrals obtained by the Gibbons-Hawking-Perry prescription of contour rotation.

Splines and a three-body separable expansion for scattering problems

This paper investigates an energy-dependant finite rank approximation to the three-body amplitude at scattering energies both below and above the breakup threshold. The expansion method is one proposed by Adhikari and Sloan as an approximation method for solving few-body integral equations. Cubic spline functions are used to evaluate the expansion terms without contour rotation. Numerical results are obtained for a system of three identical bosons and the utility of this expansion method in a numerical treatment of the integral equations for four-body scattering is briefly discussed. Due to logarithmic singularities in the off-shell three-body amplitude at positive energies, no pointwise agreement is found between the separable expansion and the exact three-body amplitude at energies above the breakup threshold.

FIELD INVESTIGATION OF LONGSHORE TRANSPORT DISTRIBUTION

Following a change in wave direction, the active contours in an idealized pocket beach respond by rotating such that they approach a perpendicular orientation relative to the incoming wave rays. Assuming that cross-shore sediment transport does not contribute to this contour rotation, and that the contours are in the early stages of this equilibration process, the amount of contour rotation can be interpreted as the cross-shore distribution of the longshore sediment transport. As part of the Nearshore Sediment Transport Study, detailed nearshore profile measurements were conducted at Santa Barbara, California. Twenty-two of these profile lines were located on Leadbetter Beach, which is a quasi-pocket beach. To explore the concept described above, two of the nine intersurvey periods were selected due to their strong indications of wave direction change. Analysis of these data sets yielded two estimates of cross-shore distribution of longshore sediment transport which were compared with those presented by Komar, Fulford and Tsuchiya. Although these three distributions differ significantly, the effect of the tidal variations is to "smear" the differences in the inferred distributions as evident in the contour displacements. It was found that none of the relationships for longshore transport distribution predicted the amount of transport inferred in water depths greater than one meter. It is possible, especially for one of the intersurvey periods that the changes in contour locations were so extreme that substantial crossshore sediment transport was induced and would be interpreted as longshore transport occurring in water depths greater than had actually occurred. The method introduced here should be useful in other field and laboratory programs to investigate the cross-shore distribution of longshore sediment transport.

On the application of contour rotation to three-body amplitudes

Three-body scattering amplitudes based on the Amado-Lovelace version of the Faddeev equations are studied by means of the theory of L 2 kernels. It is shown by application of contour deformation techniques that the Fredholm representation of the solutions for physical scattering energies are rigorously justified. The theory developed is further used to give a new proof of the rotation-of-contours method and a method to calculate the eigenvalue spectrum of the equations for physical energies.

Solution of the Faddeev integral equation without contour rotation

We present a new method of solution of the Faddeev equations for three-particle scattering above the breakup threshold using separable two-body potentials. No contour deformation is required with our method. The numerical techniques involved are explained in detail, and a justification for these techniques is given. A comparison is made to earlier calculations which used the contour-deformation technique.

On analytic nonlocal potentials. I. A forward dispersion relation

We propose a class of analytic short-ranged nonlocal potentials, and we obtain dispersion relations for the forward scattering amplitude. We use the Fredholm method for the Lippman-Schwinger equation for the scattering solution, and contour rotation in the analytic continuation of the forward scattering amplitude.

Electromagnetic mass differences and inelastic electron scattering

The Cottingham expression for the electromagnetic mass splitting within a given isomultiplet is studied with a particular emphasis on possible subtractions and divergences. Necessary and sufficient conditions for the convergence of the integration over the photon mass and for the validity of the contour rotation in the ν-plane are derived. The mass differences are expressed in terms of measurable inelastic electron scattering cross sections both in the subtracted and in the unsubtracted case. The subtraction function for ΔI = 1 mass differences is expressed in terms of the A 2 residue function. The latter can be computed from the low energy data using finite energy sum rules, thus leading to a representation of ΔM in terms of low energy data alone. A naive application of this representation fails and the A 2 -exchange alone is unable to yield the necessary correction for ΔI = 1 mass differences. Possible reasons for this failure are discussed.