Physical Sheet Research Articles

Analytic continuation ofs matrix in multichannel problems

The analytic continuation of thet ands matrices to the Riemann surface in multichannel problems is investigated. Explicit representations for the continuedt ands matrices on all sheets are obtained in terms of thet ands matrices on the physical sheet.

Primary chemical and physical characterization of acute toxic components in wastewaters

A chemical and physical primary characterization work sheet was developed based on the Microtox test, a bacterial bioluminescence system used as a rapid estimate of acute quatic toxic effects. Measurements of the variation in light reduction upon different pretreatments provided information about the chemical and physical properties of the main toxic component(s) in test wastewater samples. This primary characterization of a wastewater sample was performed within 1 day. Tests of pure toxic chemical compounds and wastewaters with known and unknown primary toxicants are presented. Outlines to the chemical analysis and identification of toxic components may be deduced from the primary characterization. The provisional characterization may also provide information on wastewater treatment techniques.

Dads, Docs, Drugs, and Decisions

To the Editor. —I could not agree with the conclusions of Drs LaPuma and Priest 1 any more strongly. It is common for us to treat our own family members, particularly our children, for what we consider routine exams, especially when this involves filling out forms for athletic, school, or employment physicals. Recently, my oldest daughter, a healthy-looking 21-year-old and a senior in college, needed a physical examination as part of postgraduate pursuit. In bold letters on the top of the physical examination sheet was printed May Not Be Completed by a Family Member. With this, my daughter went to our family physician who performed a thorough examination. He found a very small lump at the base of her neck. I found the lump difficult to even feel, and I am quite sure I would have discounted it on my examination. After a few weeks, definitive diagnosis of stage II

Remarks on unitarization methods.

It is shown that the unitarized {ital P}-wave Nambu-Goldstone scattering amplitude, constructed from the one-loop chiral perturbation theory by the {ital K}-matrix method, does not have a resonant behavior, but has instead one nearby pair of complex-conjugate poles on the physical sheet and should be rejected. This result is in constrast with other unitarization schemes such as the Pade, the inverse amplitude, and the {ital N}/{ital D} methods, which produce a {ital P}-wave resonance and have the correct analytic property.

Integrable systems away from critically: The Toda field theory and S-matrix of the tricritical Ising model

The tricritical Ising model, considered as coset construction with the exceptional group E 7, is analyzed away from criticality. The additional conserved currents of the corresponding Toda system imply the factorization of the S-matrix, explicitly computed. We discuss the origin of higher-order poles on the physical sheet of the scattering amplitudes and their relevance to the three-point couplings of the theory.

Observable effects of poles and shadow poles in coupled-channel systems.

Using separable potentials in a coupled-channel Lippmann-Schwinger equation, we investigate the motion of poles on the different Riemann sheets and their observable effects as the coupling strength is varied. Only in the weak-coupling limit can one determine in which uncoupled channel the pole originated by the sheet on which it lies. Cusp structure versus resonance peak as one crosses a threshold is found to depend on the distance of the pole from the physical sheet. Resonance poles in each uncoupled channel can produce double-loop Argand plots similar to those seen in \ensuremath{\pi}N ${P}_{11}$ amplitude analysis.

Propagating, damped, and leaky surface waves on the corrugated traction-free boundary of an elastic half-space

The dispersion relation for surface waves on the corrugated boundary (periodic in one direction and constant in the other) of an elastic half-space is derived using a modal approach, and the result is shown to be equivalent to that derived by the null-field approach. The dispersion relation is solved numerically for roots on all Riemann sheets for varying corrugation heights, frequencies, and angles of propagation. Many of the roots move on several sheets, and this leads to zero, one, or two roots residing on the physical sheet.

アセチル化によるＴＭＰの改質とアセチル化がシート強度に及ぼす影響

In order to modify the mechanical properties of high-yield pulps, thermomechanical pulp (TMP) and the other pulps were acetylated by a acetic acid/acetic anhydride/sulfuric acid mixture under the swelling condition (method A) or by a toluene/acetic anhydride/perchloric acid mixture (method B), and then the physical properties and sheet strengths of acetylated pulps were measured.The water retention value (WRV) of acetylated TMP did not depend solely on the degree of acetyl substitution. TMP acetylated by method A produced sample having high WRV up to 402%, while acetylation of TMP by method B gave pulp with less WRV than the value of the original pulp (108%).The total heat of wetting (THW) of acetylated TMP also was determined calorimetrically. The change in THW was markedly affected by the methods of acetylation. The THW of acetylated TMP having lower acetyl contents up to 20%, which was prepared by method A, was almost same with the value of original TMP. But, the THW of acetylated TMP with higher acetyl content and all acetylated TMP prepared by method B decreased sharply with an increase in acetyl content.The sheet strengths, such as, tensile strength, tear factor and burst factor of sheet from TMP acetylated by method A showed maxima at 20% of acetyl content, while these strengths of the pulp sheets acetylated by method B decreased gradually with an increase in acetyl content.From the change in morphological structure of acetylated TMP, it is indicated that swelling occurs only in TMP acetylated by method A and that interfiber contact area increases in the sheets from the TMP.

The time-local view of nonequilibrium statistical mechanics. I. Linear theory of transport and relaxation

The various approaches to nonequilibrium statistical mechanics may be subdivided into convolution and convolutionless (time-local) ones. While the former, put forward by Zwanzig, Mori, and others, are used most commonly, the latter are less well developed, but have proven very useful in recent applications. The aim of the present series of papers is to develop the time-local picture (TLP) of nonequilibrium statistical mechanics on a new footing and to consider its physical implications for topics such as the formulation of irreversible thermodynamics. The most natural approach to TLP is seen to derive from the Fourier-Laplace transform\(\widetilde{C}(z)\)) of pertinent time correlation functions, which on the physical sheet typically displays an essential singularity at z=∞ and a number of macroscopic and microscopic poles in the lower half-plane corresponding to long- and short-lived modes, respectively, the former giving rise to the autonomous macrodynamics, whereas the latter are interpreted as doorway modes mediating the transfer of information from relevant to irrelevant channels. Possible implications of this doorway mode concept for socalled extended irreversible thermodynamics are briefly discussed. The pole structure is used for deriving new kinds of generalized Green-Kubo relations expressing macroscopic quantities, transport coefficients, e.g., by contour integrals over current-current correlation functions obeying Hamiltonian dynamics, the contour integration replacing projection. The conventional Green-Kubo relations valid for conserved quantities only are rederived for illustration. Moreover,\(\widetilde{C}(z)\) may be expressed by a Laurent series expansion in positive and negative powers ofz, from which a rigorous, general, and straightforward method is developed for extracting all macroscopic quantities from so-called secularly divergent expansions of\(\widetilde{C}(z)\) as obtained from the application of conventional many-body techniques to the calculation of\(\widetilde{C}(z)\). The expressions are formulated as time scale expansions, which should rapidly converge if macroscopic and microscopic time scales are sufficiently well separated, i.e., if lifetime (“memory”) effects are not too large.

A numerical method of analytical continuation of Green-function-like expressions

Green functions, being the basic entities of a great part of condensed matter theory, are 'Herglotz', i.e. they can be analytically continued into the open half-planes forming the physical sheet of complex energy. On the real-energy axis they are usually nonanalytic and may even be distributions, which makes their numerical calculation there hard to perform. On the contrary, being smooth functions in the complex plane, they may easily be computed numerically there, provided closed formal expressions are given. The problem of a numerical analytical continuation towards the singularities (deconvolution) has been treated rather empirically in recent literature. Here a systematic analysis of the extrapolation error propagation is given, and an optimised deconvolution procedure is proposed. The focus is on the spectral function, the density of states and integrated density of states problems. Examples are given demonstrating the power of the procedure.

Efimov states for three 4He atoms?

The system of three 4He atoms interacting through the intermolecular potential HFDHE2 is solved exactly within the Faddeev scheme. We find that the trimer has two bound states at E=−0.11 K and E=−0.16(−2) K, where the excited state shows the property of an Efimov state. It is overrun by the two-body fragmentation threshold for an artificially enhanced overall interaction strength. Uncertainties in the potential parameters, possibly combined with solvent effects, may allow a slightly weaker force, which supports a second Efimov state. In any case dynamical effects of the Efimov states will be the same whether it lies close to E=0 on the physical or unphysical sheet.

Effects of Coulomb interaction in relativistic N/D equations with allowance for inelasticity

The quasipotential approach is used to investigate the analytic properties of the partial-wave S matrix in the relativistic Coulomb-nuclear scattering problem of particles having charges of the same kind. A procedure for separating the Coulomb singularities of the partial-wave amplitudes is considered, and it is shown that in the complex plane of the square of the relative momentum nu of the particles the matrix tauCH(nu) of the partial-wave amplitudes renormalized in a certain manner has on the physical sheet an analytic structure analogous to that of the matrix of partial-wave amplitudes when the Coulomb interaction is switched off. In the multichannel case, a system of modified N/D equations is formulated with allowance for inelasticity and the Coulomb effects.

Discrete symmetry for bound and virtual levels

Proceeding from the analytic continuation of the Lippmann-Schwinger integral equation onto the unphysical energy sheet, a new simple formula for the residue of the t-matrix in the pole on the unphysical sheet is derived. The formula expresses the residue in terms of the partial scattering amplitude at the corresponding energy point on the physical sheet. For the Yukawa type potential a new symmetry theorem for bound and virtual levels is proved. The theorem makes it possible to indicate the points on level trajectories which are mirror-symmetrical with respect to zero momentum.

On the gravitational lagrangian with R2-terms

Abstract A new gravitational quantum lagrangian with logarithmic dependence on R is suggested. The resulting propagator seems to have no tachyon or unphysical state poles, nor complex conjugate poles on the physical sheet.

Singularities in the scattering of a very slow electron by a weakly polar molecule

A simple one-electron potential with a dipole tail is used to study the tracks of poles of the scattering amplitude in the complex momentum plane, close to the origin, and for states with a large s-wave component. Several Riemann sheets have to be considered, because the dipole tail leads to a branch point at the origin. On the 'physical' sheet, there is a single track in the upper half-plane; it follows the positive imaginary axis down to the origin and stops there. On other Riemann sheets, there are two distinct tracks in the lower half-plane, which are mirror images of one another in the negative imaginary axis. They meet the track on the physical sheet at the origin. The tracks in the lower half-plane exist only if the dipole moment is less than 1.19 D, and collapse to the negative imaginary axis if the dipole moment vanishes.

Analysis of some pseudo-discrete spatial decay modes of the two- and three-group neutron transport equations by analytic continuation

The nature and location of the poles of the dispersion function of the frequency-dependent two- and three-group neutron transport equations for an infinite 3-D homogeneous multiplying medium with constant cross sections and isotropic scattering is investigated. It is shown that on the right half of the complex plane, only one pole exists on the physical sheet of the Riemann surface, which is almost identical to the one obtained in two- and three-group frequency-dependent diffusion theory, and gives rise to the well-known, in neutron noise, long attenuation length global component of the detector response. In contrast to diffusion theory, in transport theory no other pole exists on the physical sheet; the poles associated with the short spatial relaxation length ‘local component’ in homogeneous diffusion theories approaches are bifurcated and are to be found on the adjacent ‘unphysical’ sheets of the Riemann surface of the generic multivalued dispersion function. Although not on the physical sheet, the bifurcated poles are located very close to it and give rise to pseudo-discrete spatial decay modes with very similar characteristics to the local component of the detector response in homogeneous diffusion theories.

Positron-atom dispersion relations

The singularity structure of the forward positron-atom scattering amplitude is studied within the framework of perturbation theory with the use of the Landau rules. The unphysical and anomalous regions in the positron-atom forward dispersion relations are discussed. It is shown that the unphysical region starts at E/sub 0/ = -Vertical BarE(Ps)Vertical Bar+Vertical BarE/sub 1/Vertical Bar and the anomalous region at E/sub a/ = -(..sqrt..2Vertical BarE(Ps)Vertical Bar - ..sqrt..Vertical BarE/sub 1/Vertical Bar )/sup 2/, where E(Ps) and E/sub 1/ are correspondingly the positronium and the atomic-electron binding energies. The anomalous region is on the physical sheet if Vertical BarE(Ps)Vertical Bar/2>Vertical BarE/sub 1/Vertical Bar.

Perturbation of resonances

Resonances are often treated under the assumption that they are simple poles of the resolvent kernel (Green's function). There are no physical or mathematical reasons which exclude the existence of multiple poles of Green's functions even in the case when the potential is real valued. In this case the poles in the physical sheet are simple since the Schrödinger operator is selfadjoint but the poles on the unphysical sheet are not necessarily simple. We prove that sufficiently small perturbations of the potential (or boundary in diffraction problems) do not increase the multiplicity of the resonances on any fixed compact domain of the complex plane. We also observe that a knowledge of the set of the Green's function poles does not determine the potential uniquely.

Surface waves and the heating of the corona

Abstract The Sun's atmosphere is highly structured by magnetic fields, and this modifies the nature of the usual Alfvén waves which propagate in an everywhere uniform medium. Two simple magnetic field structures are considered: the interface profile (for which a discontinuity separates two media with different, but uniform, unidirectional magnetic fields), and the monotonic profile (for which the magnetic field is unidirectional and continuous but not everywhere constant). An initial-value problem is formulated in ideal MHD, and the perturbations from equilibrium are written in terms of a Bromwich integral. It is well known that the poles of the Bromwich kernel lead to the usual discrete normal mode solutions, and the branch-cuts of the kernel lead to a continuum. An analysis reveals that the interface profile supports Alfvén surface and body waves, whilst the monotonic profile allows only a continuous spectrum of waves. However, by suitably deforming the contour, spectral poles (not related to normal modes) can be located off the physical (principal) Riemann sheet. The residues from these poles yield solutions resembling the interfacial surface waves, but they decay on a timescale T. This property of temporal decay in a non-dissipative system has led lonson (1978) and Wentzel (1979b) to suggest that the spectral residues show the behaviour of a surface wave when the interface is made continuous, and they have interpreted T as the time-scale for dissipation of such a wave in a non-ideal medium. Here we argue that, on the contrary, the time T is in fact the scale for the build-up of the continuous spectrum of oscillations; the spectral residues indicate restructuring of wave motions. It is shown that the process of phase-mixing causes motions along the magnetic field to build-up, whilst those transverse to the field decay. However, the status of wave propagation in a highly structured medium as a means of heating the corona, by dissipating through irreversible processes in non-ideal MHD, remains open until a fully dissipative investigation of their character becomes available.

Prototype models for particle structure in gauge supersymmetry

Particle content in prototype models of gauge supersymmetry is examined. The properties of the prototype models which are in common with those of gauge supersymmetries are the initial non-diagonality of the quadratic part of the action, global supersymmetry invariance and the existence of a mass parameter in the quadratic part of the action. The analysis exhibits the particle content of prototype models to consist of normal poles and sets of complex conjugate poles on the physical sheet. Diagonalization of the hamiltonian can be carried out for such systems (in contrast to the prototype model of conformal supergravity where dipole ghosts arose). Essentially the pole structure observed in the prototype models of gauge supersymmetry is the supersymmetric analogue of the Lee-Wick phenomenon where the normal and the complex conjugate poles form global multiplets.