Field Hamiltonian Research Articles

Numerical analysis of tunneling paths in constant field SU(2) lattice gauge theory

We present results of a computer analysis of euclidean solutions of the SU(2) lattice gauge theory Hamiltonian for constant fields. The accumulation of tunneling solutions in a certain region of phase space is investigated because it is expected to give a strong contribution to the path integral. Our analysis shows, that an infinite set of classical trajectories with finite action exists, and describes how they cluster.

Study of crystal field splitting of PrAl 2 through reduced level scheme models

Under the action of the crystal field, the 4 f-shell of the light rare-earth intermetallics is split into a series of levels that may be degenerate or not. The location of these levels in the overall crystal field splitting scheme is not well determined in the literature for several light rare-earth intermetallics, including PrAl 2. For many authors, the ground level of PrAl 2 is a singlet while for others it is a doublet. In this work, we will try to determine the level scheme of the ground multiplet of PrAl 2 using two models in which the crystal field and magnetic Hamiltonians are simplified, i.e. we keep in both models only the two lowest levels of the ground multiplet of PrAl 2. In the first model, the ground and the first excited levels are, respectively, singlet and triplet (singlet-triplet model) and in the second one they are, respectively, doublet and triplet (doublet-triplet model). The exchange, of the Heisenberg-type between the rare-earth ions, is treated in mean field approximation. Using these approaches, we construct, in matrix notation, the model Hamiltonians corresponding to the models mentioned above and from them we derive the magnetic state equations of interest. The theoretical curves of magnetic entropy temperature of PrAl 2 are compared with the corresponding experimental curves given in the literature and we conclude that the ground level of this compound is a doublet.

Field-induced phase transitions in rare-earth compounds with a singlet ground state

Field-induced phase transitions are studied for rare earth compounds. The spin wave spectrum is calculated for the ground state of the mean field Hamiltonian. The anisotropy of the crystal field states has the consequence that the magnetic polarization does not commute with the Hamiltonian. This leads to an energy gap in the spectrum and to zero-point reduction of the magnetic moments.

Effect of the Tb 3+ crystal field on the positive muon precession frequency in TbNi 5

We have recorded positive muon spectra on a single crystal of the ferromagnetic ( T c = 23K) hexagonal compound TbNi 5 for T<T c. Only one muon precession frequency is observed. Its temperature dependence is well described by an Hamiltonian which is the sum of the molecular field and the crystal field Hamiltonian. Our results suggest that μSR spectroscopy can be used to get information on the Hamiltonian which describes the magnetic and electric interactions in 4f intermetallics.

Semiempirical Crystal Field Calculations for fN-Systems. I. Many-Electron Formalism of Crystal Field Effect in fN-Configurations

A new many-electron crystal field formalism for the fN-configuration in lanthanide and actinide ions is presented. An effective crystal field Hamiltonian is obtained by projecting the original electronic Hamiltonian of an f-cluster (fN-ion + ligand environment) on the subspace of [J, M] > functions of the fN-configuration of the central ion. On the basis of this formalism a semiempirical many-electron method is developed that allows for a practical ab initio calculation of crystal field energies in fN-systems. The important role of many-electron crystal field effects in fN-systems with significant covalent contributions is discussed. [Russian Text Ignored].

Symmetries of the nuclear average field hamiltonian and a search for possible exotic equilibrium deformations in superdeformed nuclei

Symmetry properties of the general average-field hamiltonian-matrix resulting from the geometrical symmetries of the hamiltonian itself are derived and discussed. The corresponding numerical algorithms are constructed. Total energy calculations for superdeformed nuclei are then extended to include the usually neglected deformation modes α λ = 3 μ ≠ 0 in the expansion of the nuclear surface expression R(ϑ, ϕ; {α}) = c ({α}) R 0 1+ ∑ λ ∑ μ=−λ λ α λμ ∗Y λμ(ϑφ) . The general trends in the shell-energy dependence on α λ = 3 μ and the implied instabilities in the superdeformed configurations of the rare earth nuclei are studied using the Strutinsky formula with the macroscopic part taken in the form of the folded-Yukawa plus exponential interaction. A possibility of new (double superdeformed minimum) structures coexisting in some nuclei and resulting from the proton shell effects is predicted and illustrated. No signficant neutron effects are found in the rare superdeformed nuclei considered.

Classical limit of (1 + 1)-dimensional string theory

We find the general classical solution of the Das-Jevicki collective field theory, corresponding to a tachyon background in (1 + 1)-dimensional string theory. The solution has a simple interpretation in the equivalent free Fermi theory, as a state with a dynamical Fermi surface. In terms of the variables corresponding to the upper and lower Fermi momenta, the collective field hamiltonian separates into right- and left-moving pieces. As one application, we discuss the tree-level S- matrix . We also describe briefly a number of interesting particular solutions.

The role of induction forces in infra-red matrix shifts: quantum chemical calculations with reaction field model hamiltonian

The equilibrium structure, charge distribution and vibrational harmonic force constants of the HF molecule and of the hydrogen-bonded complexes HF⋯HF, HF⋯HCl, HCl⋯HF and HCl⋯HCl were calculated using the 6-31G ∗∗ basis. The properties of the isolated (in vacuo) systems were compared to those obtained in different rare gas matrices. The inductive effect of the matrix was represented by a quantum chemical average reaction field hamiltonian. The reaction field response function has been calculated from a microscopic model of the matrix, using the experimental dipole polarizabilities. Comparison of the calculated vibrational frequencies with the experimental matrix shifts indicates that differences in various rare gas matrices (Ne, Ar, Kr, Xe) can probably be attributed to the differences in repulsive and dispersion forces, which should be added to the uniform shift due to the inductive (reaction field) interactions.

INTERACTIONS AND SCATTERING IN d = 1 STRING THEORY

We discuss two results: (i) we calculate the two-point function of the density fluctuations to [Formula: see text] in the fermonic formulation of the d = 1 string theory and compare with the [Formula: see text] result from the candidate collective field Hamiltonian. The latter result is divergent, showing the inequivalence of the two theories. We find out the corrections to the collective field Hamiltonian (both in the form of infinite counterterms and additional finite pieces) needed to match with the fermion theory. (ii) We study tree-level scattering processes between bosons due to the localized interaction near the boundary (in a region of order [Formula: see text]). The reflection problem at the boundary is treated by an analytic continuation of the time-of-flight variable.

Theoretical intensities of 4f-4f transitions between stark levels of the Eu 3+ ion in crystals

We report a theoretical calculation of the intensities of the 4f-4f transitions between Stark levels of the Eu 3+ ion in KY 3F 10, LiYF 4 and LaOCl hosts. A ligand field Hamiltonian, described by a simple overlap model, is initially applied to oxychlorides, oxybromides and fluorides doped with the Eu 3+ ion. Since for the even rank ligand field parameters, there is a significant improvement with respect to the crude electrostatic approximation, this model is also used in the evaluation of the odd rank parameters required in the intensity calculations. The average energy denominator method used by Bebb and Gold to treat multi-photon ionization processes in hydrogen and rare gas atoms is used here as an alternative procedure to evaluate the electric dipole matrix elements. The results are in good agreement with those given by the standard Judd-Ofelt theory. Only the forced electric dipole mechanism up to second order and the dynamic coupling are taken into account. Emphasis is given to the fact that these two mechanisms should contribute with the same sign to the B λtp intensity parameters, in contrast with theoretical calculations currently found in the literature. Comparison with experimental values points to the neglect of higher order corrections to these two mechanisms, and the use of a still incomplete representation of the ligand field as the reason for the discrepancies between theory and experiment.

ELECTRON SPIN RESONANCE INVESTIGATION OF Eu2+ IN BaCl2

The ESR spectra of BaCl2: Eu powder showed that Eu2+ ion substituting the ion Ba2+ is situated in a crystal field of the orthorhcmbic symmetry. By fitting the ESR experimental data to the axial symmetric spin Hamiltonian and the crystal field Hamiltonian, the spin Hamiltonian parameters were obtained. In addition, based on variation of ESR peak-hight versus doping concentration of Eu, the doping value Cs for saturated substitution of Eu2+ was found to be 0.34 mol%.

Quantum mechanics of anyons on a torus

We study a system of anyons on a torus, which are defined as nonrelativistic particles, and can be either bosons or fermions, coupled to a U(1) Chern-Simons field representing the dynamics of an intermediate statistics superposed to the original one. In the case of bosons we find the exact ground state for given total momentum, in the case of fermions we succeed in finding all the momentum and energy eigenstates of a translationally invariant mean field hamiltonian, which approximates the exact one for high densities. In the latter case we find particular momentum eigenstates, for which the energy has a sharp minimum, representing macroscopically quantized motions of the anyon fluid along a handle, which have the features of supercurrents. We also compute the corresponding magnetic field.

Field induced phase transitions in Pr compounds

Level crossing of crystalline field states is predicted to occur in some Pr compounds by an applied field. Phase transition associated with it is studied. That the Zeeman term is not commutable with the crystalline field Hamiltonian gives variety to the nature of the phase transition.

Are direct reaction field methods appropriate for describing dispersion interactions?

Direct reaction field (DRF) model Hamiltonians are used in various fields of quantum chemistry, for example in core polarization potentials and in solvent effect theories. The DRF method is usually claimed to be appropriate to describe the correlation (dispersion interaction) with other electron groups, which are not included explicitly in the calculation. It is shown that the C 6 coefficients resulting from the DRF theory are erroneous by a factor of 2 to 15 in a series of simple systems. The source of the error can be attributed to the unjustified assumption that the mean excitation energy of the explicitly treated subsystem is negligible with respect to the excitation energies of the other one. A more appropriate reaction field Hamiltonian is proposed which includes both “average” (nonlinear) and “direct” (linear) terms for polar solutes.

Self-fields in semiclassical radiation theory.

The interaction of an atomic system with an unquantized electromagnetic field is studied by means of the Heisenberg-operator equations of motion. The electromagnetic fields created by the atom are taken into account by assuming that the charge and probability current densities are the actual charge and current source terms in Maxwell's equation. When Ehrenfest's theorem is written to order (1/c${)}^{2}$, the equations of motion are found to have a constant of motion that can be interpreted as stating that the sum of the atomic energy, energy of interaction, and energy stored in the electromagnetic field is constant. This constant of integration can be expressed as an expectation of a new semiclassical Hamiltonian that now includes the effects of the atomic self-fields to order 1/${\mathit{c}}^{2}$. This Hamiltonian is related to the classical Darwin Lagrangian. Since the new approximate Hamiltonian is the sum of an atomic and a field Hamiltonian, it provides a formulation of semiclassical radiation theory that is formally close to the usual formulation of quantum electrodynamics. A Schr\"odinger equation can be derived by applying the variational principle to the expectation of the new Hamiltonian. The result is a nonlinear integro-differential equation, in \ensuremath{\Psi}, which is somewhat similar to Hartree's self-consistent equation for a multielectron atom.When the Heisenberg equations are written to include the next-higher-order terms, 1/${\mathit{c}}^{3}$, it is found that the total energy of the atom and the electromagnetic field in the vicinity of the atom decreases at a rate that is given by the Larmor power formula (2${\mathit{e}}^{2}$/3${\mathit{c}}^{3}$)(d〈v〉/dt${)}^{2}$, where 〈v〉 is the quantum-mechanical expectation of the electron's velocity operator. This approximate formulation of semiclassical radiation theory is applied to semiclassical calculations of atomic radiative shifts. It is then shown that, if some retardation effects are included to all orders of 1/c in the vector potential, the semiclassical analysis provides a formula for radiative energy-level shifts that are time dependent and that contain coefficients similar to the starting point of the Bethe calculation of the Lamb shift. The incorporation of mass renormalization in semiclassical theory is then discussed.

159Tb NMR in TbNi3and Related Compounds

159 Tb spin echo NMR measurements have been done on TbNi 3 , Tb 1- x Y x Ni 3 for x ≤0.4, Tb(Ni 1- x Cu x ) 3 for x ≤0.1 and Tb(Ni 0.96 Al 0.04 ) 3 . The NMR spectrum becomes rather broad with substituting Ni by Cu, while that for Tb(Ni 0.96 Al 0.04 ) 3 shows a well-resolved satellite structure. The magnetic moment of Tb in TbNi 3 is deduced to be 8.1 µ B for site I and 7.8 µ B for site II from an analysis of the electric quadrupole interaction of 159 Tb on the basis of a molecular field Hamiltonian.

Microwave multiphoton ionization and excitation of helium Rydberg atoms.

We study experimentally and theoretically the detailed field-amplitude dependence of the multiphoton ionization and excitation probability of highly excited ${\mathit{n}}_{0}$ $^{3}$S helium atoms in a 9.924-GHz linearly polarized microwave electric field. For ionization, with principal quantum numbers in the range ${\mathit{n}}_{0}$=25\char21{}32, we use a quasistatic analysis that employs integration of the time-dependent Schr\odinger equation using basis states of the static field Hamiltonian. The calculated results are used to interpret the observed ionization threshold structure. For excitation, the results of ${\mathit{n}}_{0}$ $^{3}$S\ensuremath{\rightarrow}${\mathit{n}}_{0}$ $^{3}$L, Lg2 excitation experiments are explained quantitatively and precisely using a theory of multiphoton resonances. We present maps of quasienergy levels that allow the study of the dynamics of the field-switching transients. These transient effects are analyzed along the lines of standard atomic collision theory and are shown to determine the shape of the observed resonances.

Affine fields and operator representations for the nonlinear σ model

The problem of operator representations and associated Hamiltonians for quantum fields and their conjugates appropriate to the nonlinear σ model is discussed. To respect the target‐space constraints, canonical field momenta are rejected in favor of alternative affine conjugate fields that serve to generate constraint‐preserving group transformations in the target space. Various operator representations are discussed at length, some of which do not admit canonically conjugate fields. After establishing certain general properties for Hamiltonians, there is an analysis of how operator field representations and Hamiltonians can be linked.

THE CORRESPONDENCE PRINCIPLE IN QUANTUM FIELD THEORY AND RELATIVISTIC BOSON STRING THEORY

The author constructs the Schrodinger representation in the quantum theory of fields, strings, and membranes on a mathematical level of rigor. This representation is based on the theory of pseudodifferential operators on an infinite-dimensional superspace, developed by the author within the framework of functional superanalysis. In the Schrodinger representation, the author realizes all the basic operators of quantum mechanics with fermion-boson coordinates, the operators of quantum field theory (including supersymmetric field theory), and the operators of the quantum and field theory of strings and membranes (Hamiltonians of fields with polynomial self-action in a space of arbitrary dimension. Virasoro operators, the BRST charge operator which forms the basis of boson string gauge theory, the gauge-invariant Hamiltonian of a boson string, and the Hamiltonian of a supermembrane). It should be noted that the representation constructed here does not satisfy the canonical axiomatics of quantum theory — the state space is not Hilbert space. Bibliography: 45 titles.

Magnetic properties of the hexagonal CeAlGa compound

Magnetic properties of the hexagonal CeAlGa compound studied by resistivity, neutron diffraction and inelastic neutron scattering on polycrystals as well as magnetization measurements on a single crystal are presented. Below T N = 6 K it orders in an incommensurate modulated structure ( Q = (0.156, 0.156, 0) and M Q | Q ). In the paramagnetic range all the observed properties are well accounted for by crystal field which was determined quantitatively. The existence of a B 3 4 O 3 4 term in the crystal field Hamiltonian has been evidenced. As a consequence the true crystallographic structure is not of AlB 2-type (space group P6/mmm) as derived from X-ray or neutron diffraction patterns but it belongs to a space group of lower symmetry.