Showing papers on "Spin-½ published in 1991"

Higher spin algebras and quantization on the sphere and hyperboloid

Abstract: The oscillator-type realization is proposed for the continuous set of infinite-dimensional algebras of quantum operators on the two-dimensional sphere and hyperboloid. This realization is typical for infinite-dimensional higher spin algebras related to higher spin gauge theories. It involves the Klein-type operator that emerges nontrivially in the Heisenberg-type commutation relations for the oscillators. The invariant trace and bilinear form are constructed. The latter is shown to degenerate for all odd-integer values of the continuous parameter ν, which parametrizes the class of algebras under investigation. The degeneration points are shown to correspond to ordinary finite-dimensional matrix algebras and superalgebras. Possible applications of these results to higher spin gauge theories are discussed. In particular, it is noted that the deformation parameter ν can be interpreted as a vacuum value of some auxiliary scalar field in an appropriate higher spin gauge theory.

A hierarchically constrained kinetic Ising model

Abstract: A concrete model for hierarchically constrained dynamics in the sense proposed by Palmer et al. (Phys. Rev. Lett.53, 958 (1984)) is presented. The model is a kinetic Ising chain with an asymmetric kinetic constraint, allowing a spin to flip only if its neighbour to the right is in the up spin state. The spin autocorrelation function is obtained by numerically exact calculation for finite chain length up toL=9 and by Monte Carlo simulation for effectively infinite chain length. The Kohlrausch-Williams-Watts formula is found to fit the results only with limited accuracy, and within limited time intervals. We also performed an analytical calculation using an effective-medium approximation. The approximation leads to a spurious blocking transition at a critical up spin concentrationc=0.5.

Large N Expansion for Frustrated and Doped Quantum Antiferromagnets

Abstract: A large N expansion technique, based on symplectic (Sp(N)) symmetry, for frustrated magnetic systems is studied. The phase diagram of a square lattice, spin S, quantum antiferromagnet with first, s...

Generalized Thue-Morse chains and their physical properties

Abstract: We study the physical properties of the Thue-Morse chain and its generalizations. After a preliminary discussion of its basic features (e.g., structure factor, location, and relative magnitude of spectral gaps), we focus on (1) the trace maps of generalized Thue-Morse lattices, (2) a detailed analysis of the attractor of the associated dynamical system, (3) the electronic spectra through the trace-map approach, (4) spin excitations in a quantum Ising model in a transverse magnetic field, (5) light transmission through a multilayer, and (6) the diamagnetic properties of Thue-Morse superconducting wire networks and Josephson-junction arrays.

The magnetic field dependence of proton spin relaxation in tissues.

Abstract: The magnetic field dependence of water-proton relaxation is reported for a simple protein solution, a cross-linked protein solution, and a series of rat tissues, fresh, dried and rehydrated. The shape of the magnetic field dependence associated with water proton relaxation in tissues is accounted for by magnetic dipole-dipole interactions between the mobile water spins and the immobile spin populations of the nonrotating components of the tissue coupling the behavior of the immobilized spin system to that of the mobile water spin system. The effect of this coupling is to impart the field dependence of the relaxation associated with the immobilized spin population to that of the mobile water spins that are observed in most relaxation and imaging experiments. © 1991 Academic Press, Inc.

Algebraic structure of translation-invariant spin-1/2 xxz and q-Potts quantum chains.

Abstract: Spin-1/2 xxz and q-Potts quantum chains with translation-invariant boundary conditions are analyzed as representations of the periodic Temperley-Lieb-Jones algebra. A connection with the affine Hecke algebra is established and used to find the irreducible content. This analysis provides an explanation for both the degeneracies and the overlap in the spectra of these models.

On the Electron Transport through a Quantum Dot

Abstract: Electron transport through a quantum dot is discussed from the point of view of the Friedel sum rule. When an odd number of electrons are in the dot, the localized moment may be formed because of the Coulomb repulsion between the electrons. In this situation, it is predicted that the transmission probability of an electron through the dot is almost unity if the temperature is lower than the Kondo temperature, i.e., the characteristic energy of the spin fluctuations divided by Boltzmann constant.

Neutrino helicity flip from gravity-spin coupling.

Abstract: It is suggested that the rotation-spin coupling predicted by Mashhoon may lead, in the case of neutrinos, to a helicity flip that has implications for astrophysical objects such as rotating neutron stars and supernovae. The coupling is generalized here to include gravitational fields and total angular momentum and is derived by solving the covariant Dirac and Maxwell-Proca equations exactly to first order in the metric deviation ${\ensuremath{\gamma}}_{\mathrm{\ensuremath{\mu}}\ensuremath{ u}}$. For fermions the spin part of the effect also applies to gravitational fields of arbitrary strength.

Spin tunnelling: a perturbative approach

Abstract: It is shown that the tunnelling splitting of the energy levels of the easy-axis spin system in a small transverse magnetic field can be calculated perturbationally for arbitrary S. The results are exact, in contrast to those obtained previously in the same limit by indirect and rather difficult methods.

On the dynamics of the radially symmetric Heisenberg ferromagnetic spin system

Abstract: By considering the geometrical equivalence of the radially symmetric Heisenberg ferromagnetic spin system in n‐arbitrary spatial dimensions and the generalized nonlinear Schrodinger equation (GNLSE) with radial symmetry, it is shown that they possess the Painleve property only for the (n=2) circularly (planar radially) symmetric case. For the circularly symmetric case, suitable (2×2) matrix eigenvalue equations are constructed, involving nonisospectral flows and their gauge equivalence is shown. The connection with inhomogeneous systems and, in particular, the linearly x‐dependent system is pointed out. Appropriate Backlund transformations (BT) and explicit soliton solutions for both the spin systems and the GNLSEs are also derived.

Phase space approach to quantum dynamics

Abstract: Replaces the Schrodinger equation for the time propagation of states of a quantized 2D spherical phase space by the dynamics of a system of N particles lying in phase space. This is done through factorization formulae of an analytic function theory arising in a coherent-state representation, the 'particles' being the zeroes of the quantum state. For linear Hamiltonians, like a spin in a uniform magnetic field, the motion of the particles is classical. However, nonlinear terms induce interactions between the particles. Their time propagation is studied and it is shown that, contrary to integrable systems, for chaotic maps they tend to fill, as their classical counterpart, the whole phase space in a uniform way.

Quasiparticle properties in ferromagnetic CeRu2Ge2

Abstract: A detailed de Haas-van Alphen study of high-quality crystals of ferromagnetic CeRu2Ge2 (Tc ≈ 8 K) is presented. All expected Fermi surface sheets have been observed, including an extraordinarily large surface with a cross-sectional area bordering on the size of the Brillouin zone itself. A comparison to band structure calculations allows the formulation of a model for the Fermi surface consisting of five spin split sheets. For the first time in one of these systems the completeness of the de Haas-van Alphen data allows a rigorous analysis of the heat capacity and its accountability in terms of the observed quasiparticles. Analysis of the observed spin splitting yields values for the 4f to conduction electron interaction parameters for each sheet and enables a self-consistent understanding of the mass enhancement. A comparison to the related heavy-fermion system CeRu2Si2 provides new insight into the underlying nature of its quasiparticle properties.

Spin Dependence of the AHARONOV—BOHM Effect

Abstract: The problem of the proper inclusion of spin in Aharonov—Bohm scattering is considered. It is proposed that this should be accomplished by imposing the requirement that all singularities arising from the presence of spin in the associated wave equations be interpreted as limits of physically realizable flux distributions. This leads to results which confirm the usual cross section in the spinless case but imply nontrivial modifications for the scattering of a polarized spin one-half beam. By applying the technique to a calculation of the virial coefficient for a collection of flux carrying spin one-half particles, some severe obstacles to conventional views of the flux as a parameter which interpolates between bosonic and fermionic statistics are shown to occur. Although similar results for the scattering of arbitrary spin particles obtain in the Galilean limit, it is found that when spin one is considered in the context of a relativistic wave equation the singularity structure is too pathological to yield a consistent interpretation. The exact equivalence of the spin one-half Aharonov-Bohm effect to the Aharonov-Casher effect is also demonstrated and corresponding results for polarized beams are presented. Finally, it is shown that the Aharonov-Bohm effect for arbitrary spin in the Galilean limit is the exact solution in the two-particle sector of a Galilean covariant field theory.

Analysis of Normal State Properties of High-Tc Superconductors on the Basis of Fermi Liquid Theory

Abstract: Fermi liquid theory· is developed to discuss normal state properties of high- Tc superconductors (HTSC). On the basis of a microscopic model composed of d- and p-electrons, we derive the expressions for the specific heat, spin susceptibility, spin-lattice relaxation time T, and T2-term of electrical resistivity. By insisting consistency among these quantities, we can conclude that spin fluctuations in HTSC are localized in the momentum space in sharp contrast to heavy fermion systems, where spin fluctuations are localized in the real space. Starting with the rigorous expres­ sions derived above, and assuming large antiferromagnetic spin fluctuations in HTSC, we can naturally explain the temperature dependence ~f the resistivity and T,-' observed in the normal state of HTSC.

Melosh rotation: source of the proton's missing spin

Abstract: It is shown that the observed small value of the integrated spin structure function for protons could be naturally understood within the naive quark model by considering the effect from Melosh rotation. The key to this problem lies in the fact that the deep inelastic process probes the light-cone quarks rather than the instant-form quarks, and that the spin of the proton is the sum of the Melosh rotated light-cone spin of the individual quarks rather than simply the sum of the light-cone spin of the quarks directly.

Charge Gap, Charge Susceptibility and Spin Correlation in the Hubbard Model on a Square Lattice

Abstract: Quantum Monte Carlo study of the Hubbard model on a square lattice in the ground state is reported. For the on-site interaction U =4 scaled by the transfer, the charge excitation gap at the half-filling is estimated to be Δ c =0.58±0.08. Near half-filling, the charge compressibility κ follows the form κ∝δ -1 for the doping concentration δ, indicating a divergent behavior as the system approaches half-filling, while κ=0 at the half-filling. The incommensurate spin correlation length ξ scales as ξ∝1/\(\sqrt{\delta}\).

Microscopic theory of spin arrangements and spin waves in very thin ferromagnetic films

Abstract: We present theoretical studies of the classical ground-state spin configuration and spin waves, in very thin ferromagnetic films, with thickness that ranges from a monolayer to a few tens of layers. The analyses are based on a microscopic model that includes dipolar and exchange interactions between the spins, surface (or interface) anisotropy of single-site character quadratic and quartic in the spin components, along with an external magnetic field applied at an arbitrary direction with respect to the film normal. Issues explored include the nature of spin canting induced by surface anisotropy in ultrathin (few-atomic-layer) films, and in films with thicknesses of up to 100 layers. Also, we explore the nature of spin waves in ultrathin films, in the presence of spin canting, and in thicker films with attention to the interplay between dipolar and exchange contributions to the excitation energy. Most particularly, in the thicker films, we examine the transition from the dipole-dominated Damon-Eshbach waves to the exchange-dominated surface spin waves that emerge from the Heisenberg model.

Wave functions and other properties of spin-reversed quasiparticles at ν=1/m Landau-level occupation

Abstract: A family of wave functions appropriate for arbitrary-spin quasiparticles of the fully polarized, \ensuremath{ u}=1/m incompressible fluid is constructed. The spectrum with spin degrees of freedom included, becomes more complex, and in particular, is shown to be massively degenerate (no Zeeman energy). As a result, for finite systems in the absence of Zeeman energy the absolute ground states for two sectors differing by one flux quantum are spin singlet and maximally polarized. I study the spectrum with two reversed spins near \ensuremath{ u}=1 for up to 160 electrons and find the signature of this trend to persist in the thermodynamic limit. I also find that for all experimentally accessible magnetic field values, the single spin-reversed quasiparticle at \ensuremath{ u}=1 is irrelevant and is preempted by quasiparticles having additional reversed spins.