Energy-momentum Space Research Articles

Synthesis, characterization and theoretical interpretation of vibrational spectra of poly(2-methylbut-2-enyl thiophene-3-carboxylate)

Electroactive thiophene substituted polyacetylene derivative, namely poly(2-methylbut-2-enyl thiophene-3-carboxylate) (PMT) was synthesized. First, novel acetylene monomer was synthesized by the reaction of 3-thiophenecarboxylic acid with propargyl bromide and then polymerized with a Rh catalyst to give the corresponding polymer. FTIR and FT-Raman spectra were recorded experimentally and used for complete normal mode analysis using Wilson’s GF matrix method and Phonon dispersion of poly(2-methylbut-2-enyl thiophene-3-carboxylate). The simple non-redundant set of internal coordinates and a simplified Urey–Bradley force-field approximation was employed in normal coordinate analysis and to calculate the potential energy distribution (PED) for each fundamental vibration. The PED contribution corresponding to each of the observed frequencies shows the reliability and accuracy of the spectral analysis. Apart from detailed assignments of modes, various characteristic features of dispersion curves have also been explained as arising due to internal symmetry in energy momentum space. Predicted values of intramolecular contribution to the heat capacity of this polymer calculated by density-of-states are also being reported.

Broad structures inγ-ray multiplicity gatedpandαspectra in low energy12C+93Nb and16O+89Y reactions

Gamma ray multiplicity gated proton spectra have been measured in the reactions 12 C+93 Nb at E(12 C)= 40 and 45.5 MeV and 16 O+89 Y at E(16 O)= 51 and 54 MeV populating the CN 105 Ag at EX between 35 and 40 MeV. Broad structures are seen in all spectra at high gamma ray multiplicities. The present data, along with those from our earlier work on the former reaction at E(12 C)= 42.5 MeV, establish the compound nuclear origin of the structures. The data can be explained by incorporating a localised enhancement of nuclear level density in the excitation energy and angular momentum space. Multiplicity gated Iś spectra have also been measured in the same reaction at E(12 C)= 37.5 – 45 MeV. Broad structures seen in these spectra seem to have contribution from other reaction mechanisms also.

Vibrational spectroscopic investigation of poly(p‐phenylene sulfide)

AbstractPoly(p‐phenylene sulfide) (PPS) is an important polymer of engineering interest particularly useful in the electronics and automotive industries. Normal mode analysis including phonon dispersion has been performed to understand completely the vibrational spectra of this polymer. Various characteristic features of the dispersion curves have been reported. Crossing/Repulsion between various pairs of modes at certain phase values have been explained as arising due to internal symmetry in the energy momentum space. The heat capacity is calculated as a function of temperature via density‐of‐states in the range 220–360 K. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 2353–2367, 2009

First Demonstration of Novel Method for Inelastic Neutron Scattering Measurement Utilizing Multiple Incident Energies

We succeeded in experimentally demonstrating that a series of two-dimensional maps of a dynamical structure factor in momentum–energy space with multiple incident energies can be simultaneously obt...

A study of vibrational dynamics of poly (a-n-butyl-b-l-aspartate) (panbla)

Poly(-N-butyl--L-aspartate) (PANBLA) is nylon-3 derivative in which an alcoxycarbonyl group has been stereoregularly attached to -carbon of the repeating unit. Like poly(-isobutyl--L-aspartate) (PAIBLA) exists in two helical forms, namely hexagonal form (13/4 helix) and tetragonal form (4/1 helix), were characterized by X-ray diffraction. The hexagonal form appears to be poorly crystalline and it could not be obtained well oriented. On the other hand tetragonal form turns to be highly crystalline. Both molecular mechanics calculations and the linked-atom least square (LALS) methodology using X-ray diffraction data have revealed that an antiparallel packing of 13/4 helices with a right handed (2R) scheme of hydrogen bonds is most favourable for hexagonal form of PANBLA. Regarding tetragonal form the above techniques favour a parallel arrangement of 4/1 helices according to right handed 4R model. IR dichroism studies also support the above results. Although the vibrational dynamics of both forms of PAIBLA has been studied, no such study has been performed for PANBLA. In the present communication the vibrational dynamics of PANBLA in tetragonal form (4/1 helix) has been studied through the dispersion of normal modes. The effect of side chain nature on the dynamical behaviour has also been analyzed. Apart from detailed assignments of modes, various characteristic features of dispersion curves have been explained as arising due to internal symmetry in energy momentum space. Finally, the density of states has been used to calculate heat capacity of this polymer.

Low-energy spin-polarized two-electron spectroscopy: a powerful tool for studying exchange correlation and spin-orbit interaction on surfaces

Spin-polarized two-electron spectroscopy-in-reflection has been proven to be a very efficient technique for studying the exchange correlation and spin-orbit interaction on magnetic and non-magnetic surfaces and thin ferromagnetic films. The essence of the technique is the detection of two time-correlated electrons emitted from the sample surface upon an impact of a single incident electron and measurements of their momenta. The coincidence technique has been combined with a time-of-flight electron energy analysis to measure momentum distributions of correlated electron pairs for various orientations of the electron beam polarization relative to the scattering plane and magnetization of the sample. This set of measurements allows to extract the information on exchange correlation and spin-orbit interaction from measured spectra. Energy- and momentum-conservation in the electron-electron scattering allows the valence electron involved into collision to be located in the energy-momentum space of the valence band of the sample. In this way the energy and momentum location of the exchange and SOI can be established. A few examples of the application of this technique for studying ferromagnetic and non-magnetic surfaces are presented.

ALTERNATING DIRECTION IMPLICIT METHOD FOR TWO-DIMENSIONAL FOKKER-PLANCK EQUATION OF DENSE SPHERICAL STELLAR SYSTEMS

The Fokker-Planck (FP) model is one of the commonly used methods for studies of the dynamical evolution of dense spherical stellar systems such as globular clusters and galactic nuclei. The FP model is numerically stable in most cases, but we find that it encounters numerical difficulties rather often when the effects of tidal shocks are included in two-dimensional (energy and angular momentum space) version of the FP model or when the initial condition is extreme (e.g., a very large cluster mass and a small cluster radius). To avoid such a problem, we have developed a new integration scheme for a two-dimensional FP equation by adopting an Alternating Direction Implicit (ADI) method given in the Douglas-Rachford split form. We find that our ADI method reduces the computing time by a factor of <TEX>${\sim}2$</TEX> compared to the fully implicit method, and resolves problems of numerical instability.

Coulomb potential in one dimension with minimal length: A path integral approach

We solve the path integral in momentum space for a particle in the field of the Coulomb potential in one dimension in the framework of quantum mechanics with the minimal length given by (ΔX)0=ℏβ, where β is a small positive parameter. From the spectral decomposition of the fixed energy transition amplitude, we obtain the exact energy eigenvalues and momentum space eigenfunctions.

Theory of high-energy features in single-particle spectra of hole-doped cuprates

The recent angle-resolved photoemission measurements performed up to binding energies of the order of $1\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ reveal a very robust feature: The nodal quasiparticle dispersion breaks up around $0.3--0.4\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ and reappears around $0.6--0.8\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$. The intensity map in the energy-momentum space shows a waterfall-like feature between these two energy scales. We demonstrated that these experimental features may follow naturally from the strong correlation effects built in the familiar $t\text{\ensuremath{-}}J$ model, and the waterfall reflects the fact that the low energy quasiparticles are pulled out of the soft lower Hubbard band at higher binding energies.

Electronic structure of thin cobalt film on W(1 1 0) by spin-polarized two-electron spectroscopy

The spin-dependent electronic structure of a 3 monolayer (ML) Co film on W(1 1 0) was studied using low-energy spin-polarized two-electron spectroscopy. The primary electron with spin projection perpendicular to the scattering plane impinged onto the sample and two-electrons resulting from its collision with a valence electron of the target were detected in coincidence using position sensitive detectors and time-of-flight technique for measuring momenta of both electrons. The momentum distributions I( k 0, k 1, k 2) of correlated electrons were measured for parallel ( I +) and anti-parallel ( I −) orientations of the majority spin projection of the sample and for the incident beam polarization at various primary energies in the range (9 − 27) eV. Energy – and momentum-conservation laws in the scattering event allow the valence electron involved in the collision to be located in the energy–momentum space of the valence band. The measured distributions are presented in the form of the asymmetry A = ( I + − I −)/( I + + I −). For symmetric detection of correlated electron pairs the asymmetry of the binding energy spectrum represents the spin-asymmetry of the Bloch spectral function in the centre of the Brillouin zone. This asymmetry reaches −26% just below the Fermi energy and indicates the dominance of the minority states in this region. The measurements at two opposite magnetizations perpendicular to the scattering plane were performed to map the exchange correlation and spin–orbit interaction in energy–momentum space of the cobalt film valence band.

Reciprocal relativity of noninertial frames: quantum mechanics

Noninertial transformations on time–position–momentum–energy space {t, q, p, e} with invariant Born–Green metric and the symplectic metric −de ∧ dt + dp ∧ dq are studied. This group of transformations contains the Lorentz group as the inertial special case and, in the limit of small forces and velocities, reduces to the expected Hamilton transformations leaving invariant the symplectic metric and the nonrelativistic line element ds2 = −dt2. The transformations bound relative velocities by c and relative forces by b. Spacetime is no longer an invariant subspace but is relative to noninertial observer frames. In the limit of b → ∞, spacetime is invariant. Born was lead to the metric by a concept of reciprocity between position and momentum degrees of freedom and for this reason we call this reciprocal relativity. For large b, such effects will almost certainly only manifest in a quantum regime. Wigner showed that special relativistic quantum mechanics follows from the projective representations of the inhomogeneous Lorentz group. Projective representations of a Lie group are equivalent to the unitary representations of its central extension. The same method of projective representations for the inhomogeneous group is used to define the quantum theory in the noninertial case. The central extension of the inhomogeneous group is the cover of the quaplectic group . is the Weyl–Heisenberg group. The group, and the associated Heisenberg commutation relations central to quantum mechanics, results directly from requiring projective representations. A set of second-order wave equations result from the representations of the Casimir operators.

Normal Modes and Their Dispersion in α Form of Nylon-6 (αNY6)

Nylon-6 [-(CH2)5–NHCO-]n (αNY6) is a synthetic polymer widely used in industrial applications. It has a planar zigzag conformation. A comprehensive study of the normal modes and their dispersion in αNY6 using Urey Bradley force field is being reported. Crossing between the various pairs of modes of dispersion curves have been explained as arising due to internal symmetry in the energy momentum space. The heat capacity derived from the dispersion curves via the density-of-states, is in good agreement with the experimental measurements obtained from the Athas data bank.

Turbulence and Coherent Structures in Two-Component Bose Condensates

We elucidate the self-evolution of two Bose gases from a strongly non - equilibrium initial state. Large scale numerical simulations of the coupled nonlinear Schrödinger (NLS) equations are used to follow the evolution of the system from weak turbulence to strong turbulence to superfluid turbulence in the long-wavelength region of energy space with a formation of a tangle of topological defects. The addition of the second gas increases the number of condensed particles in the first gas. It is shown that the large wavelength part of the fields evolves into coherent structures identified as solitary wave complexes of the coupled nonlinear Schrödinger equations. The families of the solitary waves moving on uniform background or along the topological defects are obtained as solutions of the coupled Gross–Pitaevskii equations. It is shown that there exist three continuous families of such solutions with or without the cusp in energy-momentum space.

Energy- and Momentum-Resolved Exchange and Spin-Orbit Interaction in Cobalt Film by Spin-Polarized Two-Electron Spectroscopy

Spontaneous ordering of electronic spins in ferromagnetic materials is one of the best known and most studied examples of quantum correlations. Exchange correlations are responsible for long range spin order and the spin-orbit interaction (SOI) can create preferred crystalline directions for the spins, i.e., magnetic anisotropy. Presented experimental data illustrate how novel spin-polarized two-electron spectroscopy in-reflection mode allows observation of the localization of spin-dependent interactions in energy-momentum space. Comparison of spin-orbit asymmetries in spectra of Co film and clean W(110) may indicate the presence of interface specific proximity effects providing important clues to the formation of preferred orientations for the magnetic moment of the Co film. These results may help to understand the microscopic origin of interface magnetic anisotropy.

ARPES on high-temperature superconductors: Simplicity vs. complexity (Review Article)

A notable role in understanding of the microscopic electronic properties of high-temperature superconductors (HTSC) belongs to angle-resolved photoemission spectroscopy (ARPES). This technique supplies a direct window into the reciprocal space of solids: the momentum-energy space where quasiparticles (electrons dressed in clouds of interactions) dwell. Any interaction in the electronic system, e.g., superconducting pairing, leads to modification of the quasiparticle spectrum—to redistribution of the spectral weight over the momentum-energy space probed by ARPES. Continued development of the technique had the effect that the picture seen through the ARPES window became clearer and sharper until the complexity of the electronic band structure of the cuprates had been resolved. Now, in the doping range optimal for superconductivity, the cuprates much resemble a normal metal with well-predicted electronic structure, though with rather strong electron-electron interaction. This principal disentanglement of the complex physics from complex structure reduced the mystery of HTSC to the tangible problem of the interaction responsible for quasiparticle formation. Here we present a short overview of recent ARPES results, which, we believe, suggest a way to resolve the HTSC puzzle.

Relation between High Ionic Conductivity and Low-energy Dynamics in Superionic Conducting Glass

The mechanism of high ionic conductivity in superionic conducting glass still constitutes an unsolved problem in the field of science. We performed the inelastic neutron scattering measurements of superionic glass system (AgI)x(Ag2S)x(AgPO3)1-2x using the chopper spectrometer at high flux neutron spallation source. The dynamical properties over the wide range momentum-energy space were precisely compared between superionic glass and insulator glass. We found that the superionic glass shows larger intensity in low-energy region compared with undoped insulator glass, and the increase of low-energy intensity is undoubtedly correlated with the dc ionic conductivity. We also found the peculiar Q dynamics of low-energy excitation in superionic glass indicating the in-phase dynamical correlations. These characteristic features in low-energy dynamics must provide the new insight on the mechanism of superionic glass.

Spin-half fermions with mass dimension one: theory, phenomenology, and darkmatter

We provide the first details on the unexpected theoretical discovery of a spin-one-halfmatter field with mass dimension one. It is based upon a complete set of dual-helicityeigenspinors of the charge conjugation operator. Due to its unusual properties withrespect to charge conjugation and parity, it belongs to a non-standard Wignerclass. Consequently, the theory exhibits non-locality with . We briefly discuss its relevance to the cosmological ‘horizon problem’. Because theintroduced fermionic field is endowed with mass dimension one, it can carry a quarticself-interaction. Its dominant interaction with known forms of matter is via Higgs, and withgravity. This aspect leads us to contemplate the new fermion as a prime darkmatter candidate. Taking this suggestion seriously we study a supernova-likeexplosion of a galactic-mass dark matter cloud to set limits on the mass of the newparticle and present a calculation on relic abundance to constrain the relevantcross-section. The analysis favours light mass (roughly 20 MeV) and relevant cross-sectionof about 2 pb. Similarities and differences with the WIMP and mirror matterproposals for dark matter are enumerated. In a critique of the theory we reveal ahint on non-commutative aspects of spacetime, and energy–momentum space.

Quantum Mechanics and Quantum Field Theories in the Quantized Space. II: -- Quantum Mechanics --

Some examples in new quantum mechanics with the Riemannian energy-momentum space are described.

The effective mass of a free-electron-like surface state of the Si(111)-Ag surface investigated by photoemission and scanning tunneling spectroscopies

A small electron pocket composed of a metallic and parabolic surface-state band of Si(1 1 1)3×3-Ag was investigated in detail by high-resolution angle-resolved photoemission spectroscopy (ARPES) and scanning tunneling spectroscopy (STS). The Fermi surface was a complete circle (Fermi ring), and the band dispersion was determined three dimensionally in energy–momentum space. The effective mass (m*) was extracted by a new method, two-dimensional (2D) fitting to the band dispersion, and compared with the results of conventional analyses of energy and momentum distribution curves (EDC and MDC). The EDC (MDC) analysis gave a m* value larger (smaller) than that obtained by the 2D fitting method by about 20%. The m* obtained by the 2D fitting was in good agreement with the value obtained by the STS measurements of electron standing waves, giving the most plausible value of m*=(0.13±0.03)me (me is the free-electron mass) for the parabolic band.

Quantum Mechanics and Quantum Field Theories in the Quantized Space. I: -- Basic Formalism --

The Riemannian phase space theory is developed here. It is a generalization of the usual Lorentz invariant theory. Its basic formulation is given in order to apply quantum physics, i.e., quantum mechanics (QM) and quantum field theories (QFT). It is one of the theories of general relativity and the rest system of cosmic background radiation plays a specific role, in which the Riemannian energy-momentum space is isotropic and homogeneous, the 3 dimensional surface of the 4 dimensional sphere (radius K) in E 4 . If desirable the space (spatial part in the space-time of the Big Bang universe) can be quantized. Its application to (examples in) QM and QFT shall be presented here and in the forthcoming paper.