Next‐to‐next‐to‐leading order post‐Newtonian spin(1)‐spin(2) Hamiltonian for self‐gravitating binaries

We present the next‐to‐next‐to‐leading order post‐Newtonian (PN) spin(1)‐spin(2) Hamiltonian for two self‐gravitating spinning compact objects. If both objects are rapidly rotating, then the corresponding interaction is comparable in strength to a 4PN effect. The Hamiltonian is checked via the global Poincaré algebra with the center‐of‐mass vector uniquely determined by an ansatz.     

Next‐to‐next‐to‐leading order post‐Newtonian spin‐orbit Hamiltonian for self‐gravitating binaries

We present the next‐to‐next‐to‐leading order post‐Newtonian (PN) spin‐orbit Hamiltonian for two self‐gravitating spinning compact objects. If at least one of the objects is rapidly rotating, then the corresponding interaction is comparable in strength to a 3.5PN effect. The result in the present paper in fact completes the knowledge of the post‐Newtonian Hamiltonian for binary spinning black holes up to and including 3.5PN. The Hamiltonian is checked via known results for the test‐spin case and via the global Poincaré algebra with the center‐of‐mass vector uniquely determined by an ansatz.     

Precanonical quantization of Yang-Mills fields and the functional Schrödinger representation

Precanonical quantization of pure Yang-Mills fields, which is based on the covariant De Donder-Weyl (DW) Hamiltonian formulation, and its connection with the functional Schrödinger representation in the temporal gauge are discussed. The mass gap problem is related to the finite-dimensional spectral problem for a generalized Clifford-valued magnetic Schrödinger operator which represents the DW Hamiltonian operator.     

Next‐to‐next‐to‐leading order post‐Newtonian linear‐in‐spin binary Hamiltonians

The next‐to‐next‐to‐leading order post‐Newtonian spin‐orbit and spin(1)‐spin(2) Hamiltonians for binary compact objects in general relativity are derived. The Arnowitt‐Deser‐Misner canonical formalism and its generalization to spinning compact objects in general relativity are presented and a fully reduced matter‐only Hamiltonian is obtained. Several simplifications using integrations by parts are discussed. Approximate solutions to the constraints and evolution equations of motion are provided. Technical details of the integration procedures are given including an analysis of the short‐range behavior of the integrands around the sources. The Hamiltonian of a test‐spin moving in a stationary Kerr spacetime is obtained by rather simple approach and used to check parts of the mentioned results. Kinematical consistency checks by using the global (post‐Newtonian approximate) Poincaré algebra are applied. Along the way a self‐contained overview for the computation of the 3PN ADM point‐mass Hamiltonian is provided, too.     

THE DECAY ρ→ππ IN LATTICE GAUGE THEORY

The hadronic decays are studied by using an improved Hamiltonian including 2-link interactions. We find that the formulation is effective for studying hadronic decays as well as mass spectrum. In the intermediate coupling region,the decay width of ρ meson is found to be of the right order of magnitude.     

<Emphasis Type="Italic">P</Emphasis>-wave excitations of baryons within the field correlator method

I present the mass predictions of Λ(2880), Σ(2800) states in the Effective Hamiltonian method and discuss possible quantum numbers.     

On a possible interpretation of the X(3872) as a 1<Superscript>1</Superscript>D<Subscript>2</Subscript> state in a constituent-quark model based on a generalized Fermi-Breit equation

A recent experimental analysis suggested to represent the X(3872) -resonance as a c [`(c)] \bar{{c}} 1¹ D ₂ state but this attribution is being hotly debated. We calculate the mass values for that state by means of a previously studied constituent-quark model. The different contributions of the model Hamiltonian to the total mass are also explicitly shown.     

Exact Solutions of Schrödinger Equation for the Position-Dependent Effective Mass Harmonic Oscillator

A one-dimensional harmonic oscillator with position-dependent effective mass is studied. We quantize the oscillator to obtain a quantum Hamiltonian, which is manifestly Hermitian in configuration space, and the exact solutions to the corresponding Schrödinger equation are obtained analytically in terms of modified Hermite polynomials. It is shown that the obtained solutions reduce to those of simple harmonic oscillator as the position dependence of the mass vanishes.     

Symmetrized Hamiltonian versus ‘Foreman’ Hamiltonian for semiconductor valence band: an insight

A quantitative comparison of different k·p calculations of valence-band states in quantum-confined semiconductor heterostructures is presented. The importance of using the appropriate Hamiltonian form is studied quantitatively following a numerical method which enables discrimination between existing Hamiltonians. The correct form of the Hamiltonian appears to be the Foreman Hamiltonian, which gives physically reasonable results contrary to the symmetrized Hamiltonian.     

Theory of invariants‐based formulation of Hamiltonians with application to strained zinc‐blende crystals

Group theoretical methods and theory are combined to determine spin‐dependent contributions to the effective conduction band Hamiltonian. To obtain the constants in the effective Hamiltonian, in general all invariants of the Hamiltonian have to be determined. Hence, we present a systematic approach to keep track of all possible invariants and apply it to the Hamiltonian of crystals with zinc‐blende symmetry, in order to find all possible contributions to effective quantities such as effective mass, g‐factor and Dresselhaus constant. Additional spin‐dependent contributions to the effective Hamiltonian arise in the presence of strain. In particular, with regard to the constants C₃ and D which describe spin‐splitting linear in the components of k and ε , considering all possible terms allowed by symmetry is crucial.     

Effects of Mass Discontinuity on the Numerical Solutions to Quantum Wells Using the Effective Mass Equation

This paper investigates the effects of mass dicontinuity on the numerical solutions to quantum wells using the effective mass equation. The numerical methods utilized are the finite element method with first-order elements, and the finite difference method with the entire truncated solution domain discretized by equally spaced nodes. The three Hamiltonians explored are the convention Hamiltonian, the BenDaniel and Duke Hamiltonian, and the Bastard Hamiltonian. It is shown that the proper discretization patterns for both numerical schemes may drastically improve the solution accuracy. The finite difference representation of the BenDaniel and Duke Hamiltonian using the direct mass average is found more accurate than the one using the harmonic mass average. It is further pointed out that, at the mass profile discontinuities, the commonly accepted interface conditions for the Bastard Hamiltonian are not natural conditions. This observation is critical if the Bastard Hamiltonian is to be solved numerically.     

Effective Hamiltonian for scalar theories in the Gaussian approximation

We use a Gaussian wave functional for the ground state to reorder the Hamiltonian into a free part with a variationally determined mass and the rest. Once spontaneous symmetry breaking is taken into account, the residual Hamiltonian can, in principle, be treated perturbatively. In this scheme we analyze the O(1) and O(2) scalar models. For the O(2)-theory we first explicitly calculate the massless Goldstone excitation and then show that the one-loop corrections of the effective Hamiltonian do not generate a mass.     

Microscopic interacting boson model calculations for even-even <Superscript>128–138</Superscript>Ce nuclei

In this study, we determined the most appropriate Hamiltonian that is needed for the present calculations of energy levels and B(E2) values of ^128–138Ce nuclei which have a mass around A≅130 using the interacting boson model (IBM). Using the best-fitted values of parameters in the Hamiltonian of the IBM-2, we have calculated energy levels and B(E2) values for a number of transitions in ^{128,130,132,134,136,138}Ce. The results were compared with the previous experimental and theoretical (PTSM model) data and it was observed that they are in good agreement. Also some predictions of this model have better accuracy than those of PTSM model. It has turned out that the interacting boson approximation (IBA) is fairly reliable for calculating spectra in the entire set of ^{128,130,132,134,136,138}Ce isotopes and the quality of the fits presented in this paper is acceptable.      

Spectrum of <Superscript>10</Superscript>Be in the approximation of the leading irreducible representation of the <Emphasis Type="Italic">SU</Emphasis>(3) group

An algorithm for implementing the approximation of the leading irreducible representation of the SU(3) group is expounded for a microscopic Hamiltonian involving the potential energy of nucleon-nucleon interaction. An effective Hamiltonian is constructed that reproduces the results of calculations with nucleon-nucleon potentials used in the theory of light nuclei. It is shown that, in many respects, the structure of the effective Hamiltonian is similar to the structure of the Hamiltonian of a triaxial rotor and that, for the wave functions in the Elliott scheme, one can go over to a space where linear combinations of Wigner D functions appear to be the transforms of these functions, but where their normalization requires dedicated calculations.     

Spectroscopy of the Ωccb baryon in the hypercentral constituent quark model

We extract the mass spectrum of the triply heavy baryon Ω_ccb using the hypercentral constituent quark model. The first order correction is also added to the potential term of the Hamiltonian. The radial and orbital excited state masses are determined, and the Regge trajectories and magnetic moments for this baryon are also given.     

Constant of Motion,Lagrangian and Hamiltonian of the Gravitational Attraction of Two Bodies with Variable Mass

The Lagrangian, the Hamiltonian and the constant of motion of the gravitational attraction of two bodies when one of them has variable mass is considered. The relative and center of mass coordinates are not separated, and choosing the reference system in the body with much higher mass, it is possible to reduce the system of equations to 1-D problem. Then, a constant of motion, the Lagrangian, and the Hamiltonian are obtained. The trajectories found in the space position-velocity,(x,v), are qualitatively different from those on the space position-momentum,(x,p). PACS numbers: 03.20.+i     

Hamiltonian operators and ℓ-coverings

An efficient method to construct Hamiltonian structures for nonlinear evolution equations is described. It is based on the notions of variational Schouten bracket and ℓ^*-covering. The latter serves the role of the cotangent bundle in the category of nonlinear evolution PDEs. We first consider two illustrative examples (the KdV equation and the Boussinesq system) and reconstruct for them the known Hamiltonian structures by our methods. For the coupled KdV–mKdV system, a new Hamiltonian structure is found and its uniqueness (in the class of polynomial (x,t)-independent structures) is proved. We also construct a nonlocal Hamiltonian structure for this system and prove its compatibility with the local one.     

Inelastic neutron scattering study and Hubbard model description of the antiferromagnetic tetrahedral molecule Ni<Subscript>4</Subscript>Mo<Subscript>12</Subscript>

The tetrameric Ni(II) spin cluster Ni₄Mo₁₂ has been studied by INS. The data were analyzed extensively in terms of a very general spin Hamiltonian, which includes antiferromagnetic Heisenberg interactions, biquadratic 2-spin and 3-spin interactions, a single-ion magnetic anisotropy, and Dzyaloshinsky-Moriya interactions. Some of the experimentally observed features in the INS spectra could be reproduced, however, one feature at 1.65 meV resisted all efforts. This supports the conclusion that the spin Hamiltonian approach is not adequate to describe the magnetism in Ni₄Mo₁₂. The isotropic terms in the spin Hamiltonian can be obtained in a strong-coupling expansion of the Hubbard model at half-filling. Therefore detailed theoretical studies of the Hubbard model were undertaken, using analytical as well as numerical techniques. We carefully analyzed its abilities and restrictions in applications to molecular spin clusters. As a main result it was found that the Hubbard model is also unable to appropriately explain the magnetism in Ni₄Mo₁₂. Extensions of the model are also discussed.