Conservation laws in Bimetric gravitation theories

In the bimetric theory of gravitation with a flat-space background metric conservation laws for energy and momentum are considered in several different forms. In the bimetric theory with a constant-curvature background metric a previous error in the energy-momentum relation is corrected.     

Coordinate-free quantization of second-class constraints

The conversion of second-class constraints into first-class constraints is used to extend the coordinate-free path-integral quantization, achieved by a flat-space Brownian motion regularization of the coherent-state path-integral measure, to systems with second-class constraints.     

Remove Degeneracy in Relativistic Symmetries for Manning-Rosen Plus Quasi-Hellman Potentials by Tensor Interaction

The relativistic Dirac equation under spin and pseudo-spin symmetries is investigated for Manning-Rosen plus quasi-Hellman potentials with tensor interaction. For the first time we consider the Hulthen plus Yukawa for tensor interaction. The Formula method is used to obtain the energy eigen-values and wave functions. We also discuss about the energy eigen-values and the Dirac spinors for the Manning-Rosen plus quasi-Hellman potentials for the spin and pseudo-spin symmetry with Formula method. To show the accuracy of the present model, some numerical results are shown in both pseudo-spin and spin symmetry limits.     

Dimensionally reduced gravitational Chern-Simons term and its kink

When the gravitational Chern-Simons term is reduced from 3 to 2 dimensions, the lower dimensional theory supports a symmetry breaking solution and an associated kink. Kinks in general relativity bear a close relation to flat-space kinks, governed by identical potentials.     

Asymptotic behavior of fluctuations for the 1D Ising model in zero-temperature limit

Fluctuation of the average spin for one-dimensional Ising spins with nearest neighbor interactions are studied. The distribution function for the average spin is calculated for a finite volume, finite temperature, and finite magnetic field. As the volume increases and the temperature diminishes at zero magnetic field, there are two limits in which the probability distribution shows quite different behaviors: in the thermodynamic limit as the volume goes to infinity for finite temperature, small deviations of the fluctuations are described by a Gaussian distribution, and in the limit as the temperature vanishes for a finite volume, the ground states are realized with probability one. The crossover between these limits is analyzed via a ratio of the correlation length to the volume. The helix-coil transition in a polypeptide is discussed as an application.     

Exact Spin and Pseudospin Symmetry Solutions of the Dirac Equation for Mie-Type Potential Including a Coulomb-like Tensor Potential

We solve the Dirac equation for Mie-type potential including a Coulomb-like tensor potential under spin and pseudospin symmetry limits with arbitrary spin–orbit coupling quantum number κ. The Nikiforov–Uvarov method is used to obtain analytical solutions of the Dirac equation. Since it is only the wave functions which are obtained in a closed exact form; as for the eigenvalues, only the eigenvalue equations have been given and they have been solved numerically. It is also shown that the degeneracy between spin doublets and pseudospin doublets is removed by tensor interaction.     

Time-independent point-spread function for NMR microscopy.

The resolution of NMR microscopy is analyzed in terms of the point-spread function, PSF(r), and the equivalent k space modulation transfer function, MTF(k). The analysis is developed for NMR spin warp and projection reconstruction imaging experiments; however, the framework provided is quite general. Incoherent spin motion is analyzed to predict what limits, if any, on spatial resolution are imposed by diffusion. Previous estimates of diffusion limits at 1-5 microns were developed for specific imaging techniques, typically using a mean displacement argument. Although qualitatively correct, the quantitative predictions represent practical rather than fundamental limits. It is shown that diffusion-dependent "blurring" can be made arbitrarily small and that the practical limits are less stringent than previously thought. A major point illustrated by the PSF-MTF formulation is that the irreversible loss of coherence by randomly diffusing spins occurs faster than the physical displacement, thereby reducing their effect considerably on the frequency or phase of the net detected signal. The irreversible loss of signal due to diffusive motion will contribute to and possibly dominate the signal-to-noise limit of resolution. The resolution as measured by the width of the PSF and MTF for diffusion is shown to be independent of the signal acquisition time, and their functional forms allow selection of microscopic imaging parameters. An example of a three-dimensional spin-warp image of a green algae cell is shown with resolution of approximately 16 microns x 13 microns x 10 microns.     

Dirac Equation for Scalar,Vector and Tensor Generalized Cornell Interaction

We consider spin and pseudospin symmetry limits of Dirac equation in the presence of scalar, vector and tensor generalized Cornell interaction and report the solutions via the quasi-exact analytical ansatz approach.     

Gravitational radiation in asymptotic de Sitter space

A solution of the gravitational field equations is found by using an axially symmetric metric which is asymptotically a de Sitter space metric. We use the general approach of Bondi, van der Burg, and Metzner as applied to the asymptotic flat-space case and search for the necessary conditions for gravitational radiation in asymptotic de Sitter space. We find that the character of the gravitational radiation, if it exists at all, is considerably different from that obtained in the case of asymptotic flat space.     

Evolution of the spin Hall effect in Pt nanowires: size and temperature effects

We have studied the evolution of the spin Hall effect (SHE) in the regime where the material size responsible for the spin accumulation is either smaller or larger than the spin diffusion length. Lateral spin valve structures with Pt insertions were successfully used to measure the spin absorption efficiency as well as the spin accumulation in Pt induced through the spin Hall effect. Under a constant applied current the results show a decrease of the spin accumulation signal is more pronounced as the Pt thickness exceeds the spin diffusion length. This implies that the spin accumulation originates from bulk scattering inside the Pt wire and the spin diffusion length limits the SHE. We have also analyzed the temperature variation of the spin Hall conductivity to identify the dominant scattering mechanism.     

Semi-Classical Dynamics in Quantum Spin Systems

We consider two limiting regimes, the large-spin and the mean-field limit, for the dynamical evolution of quantum spin systems. We prove that, in these limits, the time evolution of a class of quantum spin systems is determined by a corresponding Hamiltonian dynamics of classical spins. This result can be viewed as a Egorov-type theorem. We extend our results to the thermodynamic limit of lattice spin systems and continuum domains of infinite size, and we study the time evolution of coherent spin states in these limiting regimes.     

Goldfish Geodesics and Hamiltonian Reduction of Matrix Dynamics

We describe the Hamiltonian reduction of a time-dependent real-symmetric N×N matrix system to free vector dynamics, and also provide a geodesic interpretation of Ruijsenaars–Schneider systems. The simplest of the latter, the goldfish equation, is found to represent a flat-space geodesic in curvilinear coordinates.      

The effect of Schwarzschild field on spin 1/2 particles compared to the effect of a uniformly accelerating frame

The Dirac Hamiltonian is calculated in the Schwarzschild space and compared to the analogous one in a uniformly accelerating Minkowski frame yielding a test of the equivalence principle. Comparing these Hamiltonians, we see that the flat-space energy-mass terms and their redshifted forms are the same in the two cases, but the coefficient of the spin-orbit coupling term is different and an additional term appears in the gravitational case.     

Continuous weak measurement and nonlinear dynamics in a cold spin ensemble

A weak continuous quantum measurement of an atomic spin ensemble can be implemented via Faraday rotation of an off-resonance probe beam, and may be used to create and probe nonclassical spin states and dynamics. We show that the probe light shift leads to nonlinearity in the spin dynamics and limits the useful Faraday measurement window. Removing the nonlinearity allows a nonperturbing measurement on the much longer time scale set by decoherence. The nonlinear spin Hamiltonian is of interest for studies of quantum chaos and real-time quantum state estimation.     

Some comments on the Sherrington-Kirkpatrick model of spin glasses

In this paper the high-temperature phase of general mean-field spin glass models, including the Sherrington-Kirkpatrick (SK) model, is analyzed. The free energy in zero magnetic field is calculated explicitly for the SK model, and uniform bounds on quenched susceptibilities are established. It is also shown that, at high temperatures, mean-field spin glasses are limits of short-range spin glasses, as the range of the interactions tends to infinity.     

Intrinsic localized modes of a classical discrete anisotropic Heisenberg ferromagnetic spin chain

We report several exact intrinsic localized mode solutions of the classical spin evolution equation of a one-dimensional anisotropic Heisenberg ferromagnetic spin chain in terms of Jacobian elliptic functions. These include one, two and three spin excitations. All these solutions have smooth anticontinuum limits. Their linear stability and semiclassical quantization are also discussed briefly.     

A self-consistent approach to quantum field theory for extended particles

A notion of quantum space-time is introduced, physically defined as the totality of all flows of quantum test particles in free fall. In quantum space-time the classical notion of deterministic inertial frames is replaced by that of stochastic frames marked by extended particles. The same particles are used both as markers of quantum space-time points as well as natural clocks, each species of quantum test particle thus providing a standard for space-time measurements. In the considered flat-space case, the fluctuations in coordinate values with respect to stochastic frames are described by coordinate probability amplitudes related to irreducible stochastic phase space representations of the Poincaré group. Lagrangian field theory on quantum space-time is formulated. The ensuing equations of motion for interacting fields contain no singularities in their nonlinear terms, and therefore can be handled by methods borrowed from classical nonlinear analysis.Supported in part by an NSERC grant.     

Solutions to the Dirac equation for symmetric and asymmetric trigonometric Rosen-Morse potential using SUSYQM

In this paper, we calculate the energy spectra and the corresponding wavefunction for the symmetric and asymmetric trigonometric Rosen-Morse potential of the Dirac equation within the framework of spin and pseudospin symmetry limits including the tensor interaction using the supersymmetric quantum mechanics (SUSYQM) formalism. We have also reported some numerical results and figures to show the effect of tensor interaction.     

Semiclassical limits for the QCD Dirac operator

We identify three semiclassical parameters in the QCD Dirac operator. Mutual coupling of the different types of degrees of freedom (translational, colour and spin) depends on how the semiclassical limit is taken. We discuss various semiclassical limits and their potential to describe spectrum and spectral statistics of the QCD Dirac operator close to zero virtuality.