The Mathematical Structure of Arrangement Channel Quantum Mechanics

A non-Hermitian matrix Hamiltonian H appears in the wavefunction form of a variety of many-body scattering theories. This operator acts on an arrangement channel Banach or Hilbert space 1(;\u27 = Ell ncr where ,r is the N-particle Hilbert space and a are certain arrangement channels. Various aspects of the spectral and semigroup theory for H are considered. The normalizable and weak (wavelike) eigenvectors ofH are naturally characterized as either physical or spurious. Typically H is scalar spectral and equivalent to H on an H-invariant subspace of physical solutions. If the eigenvectors form a basis, by constructing a suitable biorthogonal system, we show that H is scalar spectral on \u27C. Other concepts including the channel space observables, trace class and trace, density matrix and Moller operators are developed. The sense in which the theory provides a representation of N-particle quantum mechanics and its equivalence to the usual Hilbert space theory is clarified

Representations for Three-Body T-Matrix on Unphysical Sheets: Proofs

A proof is given for the explicit representations which have been formulated in the author's previous work (nucl-th/9505028) for the Faddeev components of three-body T-matrix continued analytically on unphysical sheets of the energy Riemann surface. Also, the analogous representations for analytical continuation of the three-body scattering matrices and resolvent are proved. An algorithm to search for the three-body resonances on the base of the Faddeev differential equations is discussed.Comment: 98 Kb; LaTeX; Journal-ref was added (the title changed in the journal

The charge ordered state in half-doped Bi-based manganites studied by 17^{17}O and 209^{209}Bi NMR

We present a $^{209}$Bi and $^{17}$O NMR study of the Mn electron spin correlations developed in the charge ordered state of Bi$_{0.5}$Sr$_{0.5}$MnO$_{3}$ and Bi$_{0.5}$Ca$_{0.5}$MnO$_{3}$. The unusually large local magnetic field $^{209}H_{loc}$ indicates the dominant $6s^{2}$ character of the lone electron pair of Bi$^{3+}$-ions in both compounds. The mechanism connecting the $s$ character of the lone pairs to the high temperature of charge ordering $T_{CO}$ is still not clarified. The observed difference in $^{209}H_{loc}$ for Bi$_{0.5}$Sr$_{0.5}$MnO$_{3}$ to Bi$_{0.5}$Ca$_{0.5}$MnO$_{3}$ is probably due to a decrease in the canting of the staggered magnetic moments of Mn$^{3+}$-ions from. The modification of the $^{17}$O spectra below $T_{CO}$ demonstrates that the line due to the apical oxygens is a unique local tool to study the development of the Mn spin correlations. In the AF state the analysis of the $^{17}$O spectrum of Pr$_{0.5}$Ca$_{0.5}$MnO$_{3}$ and Bi$_{0.5}$Sr$_{0.5}$MnO$_{3}$ prompts us to try two different theoretical descriptions of the charge-ordered state, a site-centered model for the first manganite and a bond-centered model for the second one.Comment: 10 pages, 7 figure

Representations for Three-Body T-Matrix on Unphysical Sheets

Explicit representations are formulated for the Faddeev components of three-body T-matrix continued analytically on unphysical sheets of the energy Riemann surface. According to the representations, the T-matrix on unphysical sheets is obviously expressed in terms of its components taken on the physical sheet only. The representations for T-matrix are used then to construct similar representations for analytical continuation of three-body scattering matrices and resolvent. Domains on unphysical sheets are described where the representations obtained can be applied.Comment: 123 Kb; LaTeX; Journal-ref was added (the title changed in the journal

Structure of boson systems beyond the mean-field

We investigate systems of identical bosons with the focus on two-body correlations. We use the hyperspherical adiabatic method and a decomposition of the wave function in two-body amplitudes. An analytic parametrization is used for the adiabatic effective radial potential. We discuss the structure of a condensate for arbitrary scattering length. Stability and time scales for various decay processes are estimated. The previously predicted Efimov-like states are found to be very narrow. We discuss the validity conditions and formal connections between the zero- and finite-range mean-field approximations, Faddeev-Yakubovskii formulation, Jastrow ansatz, and the present method. We compare numerical results from present work with mean-field calculations and discuss qualitatively the connection with measurements.Comment: 26 pages, 6 figures, submitted to J. Phys. B. Ver. 2 is 28 pages with modified figures and discussion

Charge and Orbital Ordering in Pr_{0.5} Ca_{0.5} MnO_3 Studied by ^{17}O NMR

The charge and orbital ordering in Pr_{0.5} Ca_{0.5} MnO_3 is studied for the first time by ^{17}O NMR. This local probe is sensitive to spin, charge and orbital correlations. Two transitions exist in this system: the charge and orbital ordering at T_{CO} = 225 K and the antiferromagnetic (AF) transition at T_N = 170 K. Both are clearly seen in the NMR spectra measured in a magnetic field of 7T. Above T_{CO} there exists only one NMR line with a large isotropic shift, whose temperature dependence is in accordance with the presence of ferromagnetic (FM) correlations. This line splits into two parts below T_{CO}, which are attributed to different types of oxygen in the charge/orbital ordered state. The interplay of FM and AF spin correlations of Mn ions in the charge ordered state of Pr_{0.5} Ca_{0.5} MnO_3 is considered in terms of the hole hopping motion that is slowed down with decreasing temperature. The developing fine structure of the spectra evidences, that there still exist charge-disordered regions at T_{CO} > T > T_N and that the static (t > 10^{-6}s) orbital order is established only on approaching T_N. The CE-type magnetic correlations develop gradually below T_{CO}, so that at first the AF correlations between checkerboard ab-layers appear, and only at lower temperature - CE correlations within the ab-planes

73Ge NMR spectra in germanium single crystals with different isotopic composition

We have studied the influence of isotopic disorder on the local deformations in Ge single crystals from both experimental and calculation points of view. The nuclear magnetic resonance (NMR) spectra of 73Ge nuclei (the nuclear spin equals 9/2) in perfect single crystals of germanium with different isotopic content were measured at temperatures 80, 300 and 450 K. Abnormal broadening of the spectrum was found to occur when the magnetic field was aligned along the [111] axis of a crystal. The observed specific angular dependence of the quadrupole broadening was attributed to isotopic disorder among atoms of germanium sited around the 73Ge NMR probe. Local lattice deformations in germanium crystal lattice due to isotopic impurity atoms were calculated in the framework of the adiabatic bond charge model. The results obtained were applied to study random noncubic crystal field interactions with the nuclear quadrupole moments and corresponding effects in NMR spectra. Simulated second and fourth moments of resonance frequency distributions caused by the magnetic dipole-dipole and electric quadrupole interactions are used to analyze the lineshapes, theoretical predictions agree qualitatively with the experimental data. © Springer-Verlag 1999

Magnetic relaxation in La0.250Pr0.375Ca0.375MnO3 with varying phase separation

We have studied the magnetic relaxation properties of the phase-separated manganite compound La0.250Pr0.375Ca0.375MnO3 . A series of polycrystalline samples was prepared with different sintering temperatures, resulting in a continuous variation of phase fraction between metallic (ferromagnetic) and charge-ordered phases at low temperatures. Measurements of the magnetic viscosity show a temperature and field dependence which can be correlated to the static properties. Common to all the samples, there appears to be two types of relaxation processes - at low fields associated with the reorientation of ferromagnetic domains and at higher fields associated with the transformation between ferromagnetic and non-ferromagnetic phases.Comment: 30 pages with figures, PDF, accepted to be published in Physical Review