Matrix Poles Research Articles

Trajectories ofS-matrix poles in a new finite-range potential

The trajectories of $S$-matrix poles are calculated in the finite-range phenomenological potential introduced recently by Salamon and Vertse [Phys. Rev. C 77, 037302 (2008)] (SV). The potential is similar to a Woods-Saxon (WS) interaction, but it is exactly zero beyond a radius, without any cutoff. The trajectories of the resonance poles in this SV potential are compared to the corresponding trajectories in a cutoff WS potential for $l>0$. The dependence on the cutoff radius is demonstrated. The starting points of the trajectories turn out to be related to the average ranges of the two terms in the SV potential.

Model independent analysis of gluonic pole matrix elements and universality of transverse-momentum-dependent fragmentation functions

Gluonic pole matrix elements explain the appearance of single spin asymmetries (SSA) in high-energy scattering processes. They involve a combination of operators which are odd under time reversal (T-odd). Such matrix elements appear in principle both for parton distribution functions and parton fragmentation functions. We show that for parton fragmentation functions these gluonic pole matrix elements vanish as a consequence of the analytic structure of scattering amplitudes in Quantum Chromodynamics. This result is important in the study of the universality of transverse momentum dependent (TMD) fragmentation functions.

ANALYTIC PROPERTIES OF MULTI-PARTON POLE MATRIX ELEMENTS AND UNIVERSALITY OF FRAGMENTATION FUNCTIONS

Gluonic pole matrix elements explain the appearance of single spin asymmetries (SSA) in high-energy scattering processes. They involve a combination of operators which are odd under time reversal (T-odd). Such matrix elements appear in principle both for parton distribution functions and parton fragmentation functions. We show that for parton fragmentation functions these gluonic pole matrix elements vanish as a consequence of the analytic structure of scattering amplitudes in Quantum Chromodynamics. We extend this analysis to the case of multi-partonic pole matrix elements. This result is important in the study of the universality of transverse momentum dependent (TMD) fragmentation functions.

Green functions of the spectral ball and symmetrized polydisk

The Green function of the spectral ball is constant over the isospectral varieties, is never less than the pullback of its counterpart on the symmetrized polydisk, and is equal to it in the generic case where the pole is a cyclic (non-derogatory) matrix. When the pole matrix is derogatory, the inequality is always strict, and the difference between the two functions depends on the multiplicity of the eigenvalues as roots of the minimal polynomial of that matrix. In particular, the Green function of the spectral ball is not symmetric in its arguments. Additionally, some estimates are given for invariant functions in the symmetrized polydisc, e.g. (infinitesimal versions of) the Carathéodory distance and the Green function, that show that they are distinct in dimension greater or equal to 3.

Bound, virtual, and resonanceS-matrix poles from the Schrödinger equation

A general method, which we call the potential $S$-matrix pole method, is developed for obtaining the $S$-matrix pole parameters for bound, virtual and resonant states based on numerical solutions of the Schr\"odinger equation. This method is well-known for bound states. In this work we generalize it for resonant and virtual states, although the corresponding solutions increase exponentially when $r\to\infty$. Concrete calculations are performed for the $1^+$ ground and the $0^+$ first excited states of $^{14}\rm{N}$, the resonance $^{15}\rm{F}$ states ($1/2^+$, $5/2^+$), low-lying states of $^{11}\rm{Be}$ and $^{11}\rm{N}$, and the subthreshold resonances in the proton-proton system. We also demonstrate that in the case the broad resonances their energy and width can be found from the fitting of the experimental phase shifts using the analytical expression for the elastic scattering $S$-matrix. We compare the $S$-matrix pole and the $R$-matrix for broad $s_{1/2}$ resonance in ${}^{15}{\rm F}$

Multichannel calculation of excited vectorϕresonances and theϕ(2170)

A multichannel calculation of excited ${J}^{PC}={1}^{--}\ensuremath{\phi}$ states is carried out within a generalization of the resonance-spectrum expansion, which may shed light on the classification of the $\ensuremath{\phi}(2170)$ resonance, discovered by BABAR and originally denoted $X(2175)$. In this framework, a complete spectrum of bare $s\overline{s}$ states is coupled to those Okubo-Zweig-Iizuka--allowed decay channels that should be most relevant for the considered energy range. The included $S$- and $P$-wave two-meson channels comprise the lowest pseudoscalar, vector, scalar, and axial-vector mesons, while in the $q\overline{q}$ sector both the $^{3}S_{1}$ and $^{3}D_{1}$ states are coupled. The only two free parameters are tuned so as to reproduce mass and width of the $\ensuremath{\phi}(1020)$, but come out reasonably close to previously used values. Among the model's $T$-matrix poles, there are good candidates for observed resonances, as well as other ones that should exist according to the quark model. Besides the expected resonances as unitarized confinement states, a dynamical resonance pole is found at $(2186\ensuremath{-}i246)\text{ }\text{ }\mathrm{MeV}$. The huge width makes its interpretation as the $\ensuremath{\phi}(2170)$ somewhat dubious, but further improvements of the model may change this conclusion.

Partonic Pole Matrix Elements for Fragmentation

A model-independent analysis of collinear three-parton correlation functions for fragmentation is performed. By investigating their support properties it is shown, in particular, that the so-called partonic pole matrix elements vanish. This sheds new light on the understanding of transverse single spin asymmetries in various hard semi-inclusive reactions. Moreover, it gives additional strong evidence for the universality of transverse-momentum-dependent fragmentation functions.

Electron-induced bond breaking at low energies in HCOOH and glycine: The role of very short-livedσ∗anion states

Cross sections for dissociative electron attachment (DEA) to formic acid and glycine are calculated by the resonant $R$-matrix theory. A model with one effective reaction coordinate close to the O-H stretch motion is employed. The choice of the anion $R$-matrix pole and the surface amplitude as functions of the reaction coordinate for formic acid are based on scattering phase-shift calculations using the finite element discrete model. For glycine the input parameters are adjusted to reproduce experimental data. The results show that the mechanism of DEA in these molecules is similar to that for the hydrogen halides and involves electron capture into a ${\ensuremath{\sigma}}^{\ensuremath{\ast}}(\text{OH})$ orbital so that no ${\ensuremath{\sigma}}^{\ensuremath{\ast}}/{\ensuremath{\pi}}^{\ensuremath{\ast}}$ coupling is required. Nonlocal effects play an important role for both molecules. In particular, pronounced steps and cusps are seen at the vibrational excitation thresholds. A sharp threshold peak in glycine is interpreted as a vibrational Feshbach resonance.

Resonance parameters fromK-matrix andT-matrix poles

We extract $K$ matrix poles from our fits to elastic pion-nucleon scattering and eta-nucleon production data in order to test a recently proposed method for the determination of resonance properties, based on the trace of the $K$ matrix. We have considered issues associated with the separation of background and resonance contributions, the correspondence between $K$ matrix and $T$ matrix poles, and the complicated behavior of eigenphases.

Feshbach projection-operator formalism applied to resonance scattering on Bargmann-type potentials

The projection-operator formalism of Feshbach is applied to resonance scattering in a single-channel case. The method is based on the division of the full function space into two segments, internal (localized) and external (infinitely extended). The spectroscopic information on the resonances is obtained from the non-Hermitian effective Hamilton operator ${H}_{\mathrm{eff}}$ appearing in the internal part due to the coupling to the external part. As is well known, additional so-called cutoff poles of the $S$ matrix appear, generally, due to the truncation of the potential. We study the question of spurious $S$ matrix poles in the framework of the Feshbach formalism. The numerical analysis is performed for exactly solvable potentials with a finite number of resonance states. These potentials represent a generalization of Bargmann-type potentials to accept resonance states. Our calculations demonstrate that the poles of the $S$ matrix obtained by using the Feshbach projection-operator formalism coincide with both the complex energies of the physical resonances and the cutoff poles of the $S$ matrix.

Dynamics of the spindle pole matrix protein NuMA and dynactin during human oocyte and zygote development

OBJECTIVE: The nature of the meiotic spindle differs between species. In particular, its transformation during the progression through the meiotic cell cycle up to the zygote stage after fertilization is poorly understood in humans. This work focuses on the study of the assembly of the nuclear mitotic apparatus protein (NuMA), α/β tubulins and dynactin during human female meiosis and fertilization. DESIGN: Immunofluorescence microscopy and pharmacological inhibition studies. MATERIALS AND METHODS: Confocal microscopy was used to determine the spatial distribution of NuMA and α/β tubulins from GV oocytes to pronuclear stage zygotes after fertilization. A total of 86 oocytes and discarded supernumerary pronuclear stage zygotes were analyzed. The material were fixed and permeabilized with a combination of 2% formaldehyde and 1%Triton X-100 previously described. Incubation with primary and secondary antibodies was done over night at room temperature and for one hour at 37°C respectively. DNA was labeled using TOTO-3. Inhibition of phosphatases and ATPases activity (dynein dependent transport) was carried out during 1 and 2 hs in 400 μM Sodium-Orthovanadate (SOV). After treatment, the distribution of NuMA and dynactin was analyzed. RESULTS: At GV stage, NuMA was evenly spread across the nucleoplasm. Before GVBD, some discrete NuMA foci were detected close to chromosomes but most of the NuMA protein was still diffusely localized in the nucleus. After GVBD, NuMA became tightly associated with the chromosome cluster. Metaphase I and II oocytes show NuMA localized at the spindle poles as discrete spots. After fertilization, all normal (2PNs) and abnormal (≥3PNs) pronuclear stage zygotes show NuMA translocated to the interphase nuclei. SOV treatment during 2hs of human oocyte maturation induces the formation of DNA spread, ectopic localization of NuMA and lower maturation rate compared to controls. CONCLUSIONS: The study of NuMA in germ cells and zygotes is relatively new and largely unexplored in humans. The identification of NuMA in different stages of matured oocytes and zygotes suggests its importance during bipolar spindle assembly. Further investigation of NuMA in abnormal oocytes and embryos, will enhance our understanding of its contribution during the assembly of microtubule spindle and the segregation of chromosomes during meiosis and mitosis.

Spectral analysis of gluonic pole matrix elements for fragmentation

The nonvanishing of gluonic pole matrix elements can explain the appearance of single spin asymmetries in high-energy scattering processes. We use a spectator framework approach to investigate the spectral properties of quark-quark-gluon correlators and use this to study gluonic pole matrix elements. Such matrix elements appear in principle both for distribution functions such as the Sivers function and fragmentation functions such as the Collins function. We find that for a specific class of spectator models, the contribution of the gluonic pole matrix element in fragmentation functions vanishes. This outcome is important in the study of universality for fragmentation functions and confirms findings using a different approach.

Shape optimization of double-chamber side mufflers with extended tube by using four-pole matrix, boundary element method and genetic algorithm

As the excellent noise reduction in dealing with most of the industrial venting noise in lower frequencies, reactive silencer has been prevailing and widely discussed, according. Most researchers explored the noise reduction effects due to flowing rate and temperature gradient based on pure plane wave theory; however, the effect of high degree wave was rarely addressed. Moreover, the maximum of silencer noise reduction under space constraint, in which frequently occurred in engineering problem, are hardly mentioned. Most of the optimal assessments were oriented with a slower optimizer, the mathematic gradient method. An issue by using a precise and quick optimizer to access the optimal noise reduction of a complicated silencer under limited space becomes essential and obligatory. In this paper, the optimal design of a double–chamber side muffler connected with internal extended tube under limited space is presented; in addition, the genetic algorithm is selected as the optimizer in searching for the best design set. In theoretical derivation, on the basis of one–dimensional plane wave theory, the system four-pole matrices under flowing effect have been established and furthermore deduced to a scalar noise reduction function. To verify the accuracy of four–pole transfer matrices, one set of silencer shape parameter has been used to construct and further acoustic test in laboratory and noise simulated in boundary element method (high degree of sound wave) have be performed individually. The results reveal that all of the four–pole matrix theory, experimental data and boundary element method are in agreement. To verify the accuracy of GA solution during optimization, an optimal design of noise reduction onto pure tone with 300 Hz is pre–run. The result reveals that the maximized STL is precisely located at 300 Hz. Consequently, a numerical case of optimal noise reduction to broadband noise source under space constraint is exemplified.

The brachistochrone problem in open quantum systems

Recently, the quantum brachistochrone problem has been discussed in the literature by using non-Hermitian Hamilton operators of different types. Here, it is demonstrated that the passage time is tunable in realistic open quantum systems due to the biorthogonality of the eigenfunctions of the non-Hermitian Hamilton operator. As an example, the numerical results obtained by Bulgakov et al for the transmission through microwave cavities of different shapes are analyzed from the point of view of the brachistochrone problem. The passage time is shortened in the crossover from the weak-coupling to the strong-coupling regime where the resonance states overlap and many branch points (exceptional points) in the complex plane exist. The effect can not be described in the framework of the standard quantum mechanics with the Hermitian Hamilton operator and consideration of S matrix poles.

Fano resonances in stubbed quantum waveguides with impurities

We consider T–shaped, two–dimensional quantum waveguides containing attractive or repulsive impurities with a smooth, realistic shape, and study how the resonance behavior of the total conductance depends upon the strength of the defect potential and the geometry of the device. The resonance parameters are determined locating the relevant S–matrix poles in the Riemann energy surface. The total scattering operator is obtained from the S–matrices of the various constituent segments of the device through the $\bigstar$ –product composition rule. This allows for a numerically stable evaluation of the scattering matrix and of the resonance parameters.

S-matrix poles close to thresholds in confined geometries

We have studied the behavior of the S–matrix poles near threshold for quantum waveguides coupled to a cavity with a defect. We emphasize the occurrence of both dominant and shadow poles on the various sheets of the energy Riemann surface, and show that the changes of the total conductivity near threshold as the cavity's width changes can be explained in terms of dominant to shadow pole transitions.

Strange dibaryon resonance in theK¯NN-πYNsystem

Three-body resonances in the $\overline{K}\mathit{NN}$ system have been studied within a framework of the $\overline{K}\mathit{NN}$-$\ensuremath{\pi}YN$ coupled-channel Faddeev equation. By solving the three-body equation, the energy dependence of the resonant $\overline{K}N$ amplitude is fully taken into account. The $S$-matrix pole has been investigated from the eigenvalue of the kernel with the analytic continuation of the scattering amplitude on the unphysical Riemann sheet. The $\overline{K}N$ interaction is constructed from the leading order term of the chiral Lagrangian using relativistic kinematics. The $\ensuremath{\Lambda}(1405)$ resonance is dynamically generated in this model, where the $\overline{K}N$ interaction parameters are fitted to the data of scattering length. As a result we find a three-body resonance of the strange dibaryon system with binding energy $B~79$ MeV and width $\ensuremath{\Gamma}~74$ MeV. The energy of the three-body resonance is found to be sensitive to the model of the $I=0$ $\overline{K}N$ interaction.

Gluonic pole cross sections and single spin asymmetries in hadron-hadron scattering

The gauge-links connecting the parton field operators in the hadronic matrix elements appearing in the transverse momentum dependent distribution functions give rise to T-odd effects. Due to the process-dependence of the gauge-links the T-odd distribution functions appear with different pre-factors. A consequence is that in the description of single spin asymmetries the parton distribution and fragmentation functions are convoluted with gluonic pole cross sections rather than the basic partonic cross sections. In this paper we calculate the gluonic pole cross sections encountered in single spin asymmetries in hadron-hadron scattering. The case of back-to-back pion production in polarized proton-proton scattering is worked out explicitly. It is shown how T-odd gluon distribution functions originating from gluonic pole matrix elements appear in twofold.

ANALYTICITY AND THE Nc COUNTING RULE OF S MATRIX POLES

By studying ππ scattering amplitudes in the large-N c limit, we clarify the N c dependence of the S matrix pole position. It is demonstrated that analyticity and the N c counting rule exclude the existence of S-matrix poles with [Formula: see text]. Especially the properties of σ and f0(980) with respect to the 1/N c expansion are discussed. We point out that in general tetra-quark resonances do not exist.

Ab initioelectron propagator theory of molecular wires: I. Formalism

Ab initio electron propagator methodology may be applied to the calculation of electrical current through a molecular wire. A new theoretical approach is developed for the calculation of the retarded and advanced Green functions in terms of the electron propagator matrix for the bridge molecule. The calculation of the current requires integration in a complex half plane for a trace that involves terminal and Green's-function matrices. Because the Green's-function matrices have complex poles represented by matrices, a special scheme is developed to express these "matrix poles" in terms of ordinary poles. An expression for the current is derived for a terminal matrix of arbitrary rank. For a single terminal orbital, the analytical expression for the current is given in terms of pole strengths, poles, and terminal matrix elements of the electron propagator. It is shown that Dyson orbitals with high pole strengths and overlaps with terminal orbitals are most responsible for the conduction of electrical current.