First-order Matrix Elements Research Articles

Differential Mueller matrix imaging of partially depolarizing optically anisotropic biological tissues

Since recently, a number of innovative polarization-based optical imaging modalities have been introduced and extensively used in various biomedical applications, with an ultimate aim to attain the practical tool for the optical biopsy and functional characterization of biological tissues. The techniques utilize polarization properties of light and Mueller matrix mapping of microscopic images of histological sections of biological tissues or polycrystalline films of biological fluids. The main drawback of currently developed laser polarimetry approaches and Mueller matrix mapping techniques is poor reproducibility of experimental data. This is due to azimuthal dependence of polarization and ellipticity values of most matrix elements to sample orientation in respect to incidence light polarization. Current study aims to generalize the methods of laser polarimetry for diagnosis of partially depolarizing optically anisotropic biological tissues. A method of differential Mueller matrix mapping for reconstruction of linear and circular birefringence and dichroism parameter distributions of partially depolarizing layers of biological tissues of different morphological structure is introduced and practically implemented. The coordinate distributions of the value of the first-order differential matrix elements of histological sections of brain tissue with spatially structured, optically anisotropic fibrillar network, as well as of parenchymatous tissue of the rectum wall with an “islet” polycrystalline structure are determined. Within the statistical analysis of polarization reproduced distributions of the averaged parameters of phase and amplitude anisotropy, the significant sensitivity of the statistical moments of the third and fourth orders to changes in the polycrystalline structure of partially depolarizing layers of biological tissue is observed. The differentiation of female reproductive sphere connective tissue is realized with excellent accuracy. The differential Mueller matrix mapping method for reconstruction of distributions of linear and circular birefringence and dichroism parameters of partially depolarizing layers of biological tissues of different morphological structures is proposed and substantiated. Differential diagnostics of changes in the phase (good balanced accuracy) and amplitude (excellent balanced accuracy) of the anisotropy of the partially depolarizing layers of the vagina wall tissue with prolapse of the genitals is realized. The maximum diagnostic efficiency of the first-order differential matrix method was demonstrated in comparison with the traditional methods of polarization and Mueller matrix mapping of histological sections of light-scattering biological tissues.

Mixture of Electromagnetically Induced Transparency and Autler–Townes Splitting in a Five-Level Atomic System**Supported by the National Natural Science Foundation of China under Grant Nos. 11274132, 11547208, and the Science Foundation of China Three Gorges University

Discerning electromagnetically induced transparency (EIT) from Autler–Townes splitting (ATS) is a significant issue in quantum optics and has attracted wide attention in various three-level configurations. Here we present a detailed study of EIT and ATS in a five-level atomic system considered to be composed of a four-level Y-type subsystem and a three-level Λ-type subsystem. In our theoretical calculations with standard density matrix formalism and steady-state approximation, we obtain the general analytical expression of the first-order matrix element responsible for the probe-field absorption. In light of the well-known three-level EIT and ATS criteria, we numerically show an intersection of EIT with ATS for the Y-type subsystem. Furthermore, we show that an EIT dip is sandwiched between two ATS dips (i.e., multi-dip mixture of EIT and ATS) in the absorption line for the five-level system, which can be explained by the dressed-state theory and Fano interference.

Switching from positive to negative absorption with electromagnetically induced transparency in circuit quantum electrodynamics

We present a theoretical study of electromagnetically induced transparency (EIT) in a superconducting quantum circuit with a tunable V-shaped energy spectrum derived from two superconducting Josephson charge qubits coupled with each other through a superconducting quantum interference device. Using the density matrix formalism and the steady-state approximation, we obtain the analytical expressions of the first-order matrix element associated with the absorption and dispersion of the probe field for two different V-type schemes. Our results show that, for this superconducting quantum system, it is possible to realize a remarkable phenomenon that dynamic conversion between EIT and EIT with amplification without population inversion. Such a unique optical feature has potential applications in quantum optical devices and quantum information processing.

New hadronic currents in TAUOLA: for confrontation with the experimental data

The status of implementation of new hadronic currents into the Monte Carlo system for simulation of τ -lepton production and decay in high-energy accelerator experiments is reviewed. Since the τ -lepton conference in 2010 substantial progress was achieved: (i) For the TAUOLA Monte Carlo generator of τ -lepton decays, automated and simultaneous use of many versions of form factors for the calculation of optional weights for fits was developed and checked to work in the Belle and BaBar software environment. Alternative parameterizations of hadronic currents based on the Resonance Chiral approach are available now. This was achieved for more than 88% of the total τ hadronic width. (ii) the TAUOLA universal interface based on HepMC (the C++ event record) is available. This is the case for C++ users of PHOTOS Monte Carlo for radiative corrections in decays, as well. An algorithm for weighted events to explore spin effects in analysis of hard processes was prepared. (iii) Kernels featuring a complete first-order matrix element are available now for PHOTOS users interested in decays of Z and W bosons. New tests with different options of matrix elements for those and for K l 3 decays are available as well. Presented results illustrate the status of the projects performed in collaboration with Zofia Czyczula, Nadia Davidson, Tomasz Przedziński, Olga Shekhovtsova, Elżbieta Richter-Wąs, Pablo Roig, Qingjun Xu and others.

Second-order achromat design based on FODO cell

Two dipole doglegs are widely used to translate the beam axis horizontally or vertically. Quadrupoles are placed between the two consecutive dipoles to match first-order dispersion and provide betatron focusing. Similarly, a four dipole chicane is usually employed to form a bypass region, where the beam axis is transversely shifted first, then translated back to the original axis. In order to generate an isochronous section, quadrupoles are again needed to tune the first-order transfer matrix element ${R}_{56}$ equaling zero. Usually sextupoles are needed to correct second-order dispersion in the bending plane, for both the dogleg optics and the chicane (with quad) optics. In this paper, an alternative optics design is introduced, which is based on a simple FODO cell and does not need sextupole assistance to form a second-order achromat. It may provide a similar function of either a dogleg or a bypass, by using two or four of such combined supercells.

Density-functional expansion methods: evaluation of LDA, GGA, and meta-GGA functionals and different integral approximations.

We extend the Kohn-Sham potential energy expansion (VE) to include variations of the kinetic energy density and use the VE formulation with a 6-31G* basis to perform a "Jacob's ladder" comparison of small molecule properties using density functionals classified as being either LDA, GGA, or meta-GGA. We show that the VE reproduces standard Kohn-Sham DFT results well if all integrals are performed without further approximation, and there is no substantial improvement in using meta-GGA functionals relative to GGA functionals. The advantages of using GGA versus LDA functionals becomes apparent when modeling hydrogen bonds. We furthermore examine the effect of using integral approximations to compute the zeroth-order energy and first-order matrix elements, and the results suggest that the origin of the short-range repulsive potential within self-consistent charge density-functional tight-binding methods mainly arises from the approximations made to the first-order matrix elements.

A simulation of QCD radiation in top quark decays

In this paper we describe a theoretical framework and algorithms for implementing QCD corrections to top quark decays in the Herwig++ event generator. The dominant corrections, due to soft and collinear emissions, are summed to all orders through the coherent parton branching formalism. In addition, unenhanced first-order matrix-element corrections are included to account for large transverse momentum emissions.

Incorporating next-to-leading order matrix elements for hadronic diboson production in showering event generators

A method for incorporating information from next-to-leading order QCD matrix elements for hadronic diboson production into showering event generators is presented. In the hard central region (high jet transverse momentum) where perturbative QCD is reliable, events are sampled according to the first-order tree level matrix element. In the soft and collinear regions next-to-leading order corrections are approximated by calculating the differential cross section across the phase space accessible to the parton shower using the first-order (virtual graphs included) matrix element. The parton shower then provides an all-orders exclusive description of parton emissions. Events generated in this way provide a physical result across the entire jet transverse momentum spectrum, have next-to-leading order normalization everywhere, and have positive definite event weights. The method is generalizable without modification to any color singlet production process.

Two-effective center approximation for the single ionization of molecular hydrogen by fast electron impact

The triple differential cross section (3DCS) for the $(e,2e)$ ionization of diatomic hydrogen is determined using the first-order transition matrix element of the Born series. A two-effective center continuum wave function which takes into account the diatomic character of the target is introduced to describe the ejected electron in the exit channel. Vertical transitions from the equilibrium position of the ${}^{1}{\ensuremath{\Sigma}}_{g}^{+}$ ground electronic state of the target to the ${}^{2}{\ensuremath{\Sigma}}_{g}^{+}$ ground electronic state of the residual ${\mathrm{H}}_{2}^{+}$ are considered for relatively high incident electron energy values (\ensuremath{\sim}4 keV). This approach, which needs relatively small computational efforts to apply it to other diatomic systems, produces results that are in good agreement with existing experimental data. The influence on 3DCS of the screening of the nuclear charges produced by the residual bound electron in the exit channel is studied.

HERWIG 6: an event generator for hadron emission reactions with interfering gluons (including supersymmetric processes)

HERWIG is a general-purpose Monte Carlo event generator, which includes the simulation of hard lepton-lepton, lepton-hadron and hadron-hadron scattering and soft hadron-hadron collisions in one package. It uses the parton-shower approach for initial- and final-state QCD radiation, including colour coherence effects and azimuthal correlations both within and between jets. This article updates the description of HERWIG published in 1992, emphasising the new features incorporated since then. These include, in particular, the matching of first-order matrix elements with parton showers, a more correct treatment of heavy quark decays, and a wide range of new processes, including many predicted by the Minimal Supersymmetric Standard Model, with the option of R-parity violation. At the same time we offer a brief review of the physics underlying HERWIG together with details of the input and control parameters and the output data, to provide a self-contained guide for prospective users of the program. This version of the manual (version 3) is updated to HERWIG version 6.5, which is expected to be the last major release of Fortran HERWIG. Future developments will be implemented in a new C++ event generator, HERWIG++.

Computing matrix elements through inhomogeneous equations in multichannel problems

Matrix elements are closely connected with solutions of inhomogeneous Schrödinger equations. Based on the recently developed renormalized method for the solutions of multichannel inhomogeneous Schrödinger equations, simple procedures are derived for the calculation of first-order and second-order matrix elements in multichannel problems. First-order matrix elements are associated with the asymptotic outgoing solution of an inhomogeneous equation and their values are given by the renormalized method directly. For a second-order matrix element, by writing it first as an overlap integral with the outgoing solution of an inhomogeneous equation, recursion relations for two auxiliary quantities, which completely determine the overlap integral, are then derived. These recursion relations should be propagated together with the renormalized solution. The value of the second-order matrix element is given at the end of the propagation. The algorithms are illustrated by numerical examples.

Time-independent perturbation theory for quasinormal-mode solutions in quantum mechanics.

Quasinormal modes are characterized by complex energy eigenvalues and by eigenfunctions that are outgoing waves at infinity, and are therefore not normalizable in the usual sense. In the space of such wave functions, the operators of quantum mechanics are not Hermitian, and the familiar tools break down. We reformulate the time-independent perturbation theory for quasinormal modes and express the corrections to the complex energy in terms of matrix elements. One main feature of the results is the appearance of an alternative definition for the norm, which is finite for quasinormal modes. Explicit formulas are given for the real and imaginary parts of the first-order correction and for the imaginary part of the second-order correction, the latter in the approximation where the original quasinormal mode is extremely narrow. This restricted (but physically most useful) part of the perturbative formalism depends only on the first-order matrix elements, and the simple form of the second-order correction can be interpreted in terms of a generalized golden rule.

Variational expressions for first-order properties involving continuum wave functions.

We discuss methods for computing first-order matrix elements involving continuum wave functions variationally. Specifically, we show that the trial wave function obtained from the Kohn method will give a variational result for any first-order property. We also discuss a variational technique for computing the squared modulus of a first-order matrix element based on approximating the resolvent. We explain why the resolvent method will converge more slowly in certain cases and illustrate our remarks with calculations on a model problem.

Improved parton showers in ep interactions

A scheme for including the first-order matrix element in ep parton showers is presented. This is an important improvement since it applies to hard emission where the leading-log approximation is less reliable. The contributions from the initial-and final-state showers are treated on an equal footing, solving the potential problem of double-counting of emission. Kinematical constraints, relating the dynamics of the two separate showers, are also solved in this context. The choice of splitting variable in initial-state showers is furthermore discussed.

Charged-particle scattering in the presence of a magnetic and a laser field and multiphoton emissions

Charged-particle scattering by a static potential V(r) in the simultaneous presence of a magnetic and a laser field, both directed along the z axis, is studied within the Green's function formalism and the first Born approximation (FBA). For three types of scattering potential (screened Coulomb, pure Coulomb and exponential) the first-order matrix elements and the cross sections are calculated exactly and given in analytic closed form. The optical theorem is derived, with the result that the total scattering cross section is found to be expressed not through the imaginary part of the forward elastic scattering amplitude as is usually the case, but through the real part. The analytic structure of the cross sections in the presence of the two external fields is found to resemble the cross sections of collision processes involving particles with discrete internal structure. The analysis shows that the magnetic field assisted potential scattering is one of the physical processes where a beam of free electrons is found to amplify coherent radiation, especially in the low-frequency regions (infrared or less).

Collisional excitation of electron Landau levels in strong magnetic fields

The cross sections for the excitation and deexcitation of the quantized transverse energy levels of an electron in a magnetic field are calculated for electron-proton and electron-electron collisions in light of the importance of the cross sections for studies of X-ray pulsar emission. First-order matrix elements are calculated using the Dirac theory of the electron, thus taking into account relativistic effects, which are believed to be important in accreting neutron stars. Results for the collisional excitation of ground state electrons by protons are presented which demonstrate the importance of proton recoil and relativistic effects, and it is shown that electron-electron excitations may contribute 10 to 20% of the excitation rate from electron-proton scattering in a Maxwellian plasma. Finally, calculations of the cross section for electron-proton small-angle scattering are presented which lead to relaxation rates for the electron velocity distribution which are modified by the magnetic field, and to a possible increase in the value of the Coulomb logarithm.

Comments on charged particle scattering in the presence of a quantising magnetic field

Transition probabilities and scattering cross sections are derived for charged particle potential scattering in the presence of a quantising constant magnetic field. They are derived within the S-matrix and the Green's function approaches and found to differ significantly from the ones defined for spherical geometries. Three types of scattering potential are considered: screened Coulombic, pure Coulombic and exponential. For all of them the first-order matrix elements and accordingly, the transition probabilities and the cross sections are exactly calculated and given in analytic closed form. The optical theorem is derived, with the result that the total scattering cross section is found to be expressed through the real part of the elastic scattering amplitude. The transition probabilities and the scattering cross sections are found to have singularities and accordingly to exhibit giant growth (cyclotron resonances) at values of the incident particle energy (along the z axis) exactly matching the energy differences between the initial and the final state Landau levels.

Role of Relativistic Effects and Configuration Mixing on the 1s2s3p4P (J=5/2) State of Argon

The first-order matrix elements vanish for the energetic K and L x-rays and Auger transitions for the 1s2s3p4Po5/2 states due to the selection rules governing the spin quantum numbers. However, spin-for-bidden transitions are possible when considering higher order multipoles. Cascading to the 1s2p2 4pe levels is possible in the configuration mixing with the 1s2p3s4Po and 1s2p3d4Po terms. We present the results of our relativistic calculations and of the configuration mixing for the case of 1s2s3p 4po5/2 state in argon.

Exchange amplitudes and forward dispersion relations for electron-atomic hydrogen scattering

The analytic properties of the forward elastic exchange amplitude g(E) are studied as a function of the incident electron energy E for electron scattering by atomic hydrogen. The authors first prove that the bound-state of gB2(E), the second Born contribution to g(E), has an infinite number of singularities due to the analytic structure of the off-shell first-order exchange matrix element. These singularities are (i) poles of order (n-1) at E=-1/2n2 (n>or=2) associated with excited intermediate states of the target and (ii) cuts at E=-1/2n2 (n>or=1) coming from all intermediate states. In addition, the bound-state part of gB2(E) also exhibits poles and cuts at E=-2(1+1/2n)2, n>or=1, arising from the integration over the intermediate momentum of the projectile. They then show that the continuum contributions to gB2(E) lead to singularities having the same location as those coming from the bound states, so that the interplay between bound and continuum singularities is very important.

Rotational bands in 185Os and 187Os

The excited states of the odd-neutron nuclei 185Os and 187Os were investigated by in-beam γ-ray measurements using the reactions 183W(α, 2n), 187Re(d, 2n) and 187Re(p, n). High-resolution singles γ-ray spectra and γ-γ coincidence spectra were measured. In addition, excitation functions and angular distributions of the γ-rays were determined for 185Os. From the measurement of the delayed γ-radiation and the results of the γ-γ coincidence experiments, two isomers were found in 185Os at energies of 102.3 and 275.7 keV. They were interpreted, quite similar to the known isomers in 187Os, as being the Nilsson states 7 2 −[503] and 11 2 +[615] , respectively. Furthermore, in 185Os the rotational states built on the ground state 1 2 −[510] up to spin 25 2 as well as the rotational bands built on the two isomeric states and on the 9 2 +[624] configuration were found. Interband transitions between some members of the bands based on the configurations 1 2 −[510] and 7 2 −[503] in 185Os indicated a strong mixing of the two I = 13 2 rotational members which are very close in energy. This mixing of states with a difference of 3 units in the K quantum number was described by a Coriolis coupling calculation including only first-order matrix elements. Further calculations were performed to describe the 1 2 −[510] ground state band and the strongly perturbed 11 2 +[615] band. In 187Os, the rotational bands belonging to the Nilsson states 7 2 −[503] and 11 2 +[615] were followed up to spin values of 17 2 and 19 2 , respectively.