The extended Fourier transform for 2D spectral estimation.

We present a linear algebraic method, named the eXtended Fourier Transform (XFT), for spectral estimation from truncated time signals. The method is a hybrid of the discrete Fourier transform (DFT) and the regularized resolvent transform (RRT) (J. Chen et al., J. Magn. Reson. 147, 129-137 (2000)). Namely, it estimates the remainder of a finite DFT by RRT. The RRT estimation corresponds to solution of an ill-conditioned problem, which requires regularization. The regularization depends on a parameter, q, that essentially controls the resolution. By varying q from 0 to infinity one can "tune" the spectrum between a high-resolution spectral estimate and the finite DFT. The optimal value of q is chosen according to how well the data fits the form of a sum of complex sinusoids and, in particular, the signal-to-noise ratio. Both 1D and 2D XFT are presented with applications to experimental NMR signals.     

An optimal semiclassical bound on commutators of spectral projections with position and momentum operators

Letters in Mathematical Physics - We prove an optimal semiclassical bound on the trace norm of the following commutators $$[{varvec{1}}_{(-infty ,0]}(H_hbar ),x]$$ , $$[{varvec{1}}_{(-infty...     

The spectral decomposition for a class of linear transport operators

The spectral decomposition theorem is proved for linear transport operators with separable scattering kernels and energy-dependent collision frequency in both one- and three-dimensional geometries.     

On the spectral and conservation properties of nonlinear discretization operators

Following the study of Pirozzoli [1], the objective of the present work is to provide a detailed theoretical analysis of the spectral properties and the conservation properties of nonlinear finite difference discretizations. First, a Nonlinear Spectral Analysis (NSA) is proposed in order to study the statistical behavior of the modified wavenumber of a nonlinear finite difference operator, for a large set of synthetic scalar fields with prescribed energy spectrum and random phase. Second, the necessary conditions for local and global conservation of momentum and kinetic energy are derived and verified for nonlinear discretizations. Because the nonlinear mechanisms result in a violation of the energy conservation conditions, the NSA is used to quantify the energy imbalance. Third, the effect of aliasing errors due to the nonlinearity is analyzed. Finally, the theoretical observations are verified for two simple, thought relevant, numerical simulations.     

Wilson loops,geometric operators and fermions in 3d group field theory

Group field theories whose Feynman diagrams describe 3d gravity with a varying configuration of Wilson loop observables and 3d gravity with volume observables at each vertex are defined. The volume observables are created by the usual spin network grasping operators which require the introduction of vector fields on the group. We then use this to define group field theories that give a previously defined spin foam model for fermion fields coupled to gravity, and the simpler “quenched” approximation, by using tensor fields on the group. The group field theory naturally includes the sum over fermionic loops at each order of the perturbation theory.     

Formulation of the Fourier transform in the spectral domain technique

A way to formulate the transform in spectral domain technique is presented.     

Universality aspects of the 2d random-bond Ising and 3d Blume-Capel models

We report on large-scale Wang-Landau Monte Carlo simulations of the critical behavior of two spin models in two- (2d) and three-dimensions (3d), namely the 2d random-bond Ising model and the pure 3d Blume-Capel model at zero crystal-field coupling. The numerical data we obtain and the relevant finite-size scaling analysis provide clear answers regarding the universality aspects of both models. In particular, for the random-bond case of the 2d Ising model the theoretically predicted strong universality’s hypothesis is verified, whereas for the second-order regime of the Blume-Capel model, the expected d = 3 Ising universality is verified. Our study is facilitated by the combined use of the Wang-Landau algorithm and the critical energy subspace scheme, indicating that the proposed scheme is able to provide accurate results on the critical behavior of complex spin systems.     

Phase fluctuations and single-fermion spectral density in 2d systems with attraction

The effect of static fluctuations in the phase of the order parameter on the normal and superconducting properties of a 2D system with attractive four-fermion interaction is studied. Analytic expressions for the fermion Green’s function, its spectral density, and the density of states are derived in the approximation where the coupling between the spin and charge degrees of freedom is neglected. The resulting single-particle Green’s function clearly demonstrates a non-Fermi-liquid behavior. The results show that as the temperature increases through the 2D critical temperature, the widths of the quasiparticle peaks broaden significantly.     

The measuring of spectral emissivity of object using chaotic optimal algorithm

There exist a considerable variety of factors affecting the spectral emissivity of an object. The authors have designed an improved combined neural network emissivity model, which can identify the continuous spectral emissivity and true temperature of any object only based on the measured brightness temperature data. In order to improve the accuracy of approximate calculations, the local minimum problem in the algorithm must be solved.Therefore, the authors design an optimal algorithm, i.e. a hybrid chaotic optimal algorithm, in which the chaos is used to roughly seek for the parameters involved in the model, and then a second seek for them is performed using the steepest descent. The modelling of emissivity settles the problems in assumptive models in multi-spectral theory.     

Transition probabilities of lines with origin in the 3d′(5/2)2, 3d′(5/2)3 and 3d′(3/2)1 levels of Ne(I).

Relative transition probabilities for twenty near-i.r. electric dipole lines and for three forbidden lines of Ne(I) with origin in the 3d′(5/2)₂, 3d′(5/2)₃ and 3d′(3/2)₁ levels have been measured. The calculated lifetime in jK coupling of the 3d′(5/2)₂ and 3d′(5/2)₃ levels was used to put on an absolute scale the transition probabilities of fourteen lines. The values of the present work are compared with theoretical calculations obtained by use of the Coulomb approximation and the intermediate-coupling scheme.     

The electronic and magnetic properties of the 3d transition metal intercalates of TiS2

The introduction of 3d transition metals (M) into the van der Waals gaps between the weakly coupled layers of transition metal dichalcogenides TX₂ (T:transition metal, X:chalcogen) produces an interesting family of intercalation compounds, M _x TX₂, the physical properties of which are different from those of the host TX₂ matrix because of ‘host-guest’ interactions. In this article we shall review the salient features of the M _x TiS₂ family with the simple 1T-CdI₂ type layered structure, which have been extensively studied by structural, transport, specific heat and lattice dynamic, magnetic and photoemission spectroscopic measurements. In contrast with the previously reported series of intercalation complexes of the Group V transition metal dichalcogenides, a characteristic of the M _x TiS₂ materials is strong hybridisation between the guest atom M 3d orbitals and the host Ti 3d and S 3p orbitals, leading to changes in the Fermi energy E _F of the conduction band, the density of states at E _F and various types of magnetic orderings. These properties are understood in terms of an itinerant electron or band picture for the intercalant, rather than a rigid band or localised model.     

Formalism of symmetrization operators in the theory of self-broadening of spectral lines

The operators that symmetrize many-particle states in accordance with the quantum statistics of particles are introduced to construct the theory of self-broadening of spectral lines. In this case, the self-broadening problem becomes formally similar to the problem of broadening by a foreign gas. Comparison is made with papers of other authors.     

Schur-decomposition for 3D matrix equations and its application in solving radiative discrete ordinates equations discretized by Chebyshev collocation spectral method

The Schur-decomposition for three-dimensional matrix equations is developed and used to directly solve the radiative discrete ordinates equations which are discretized by Chebyshev collocation spectral method. Three methods, say, the spectral methods based on 2D and 3D matrix equation solvers individually, and the standard discrete ordinates method, are presented. The numerical results show the good accuracy of spectral method based on direct solvers. The CPU time cost comparisons against the resolutions between these three methods are made using MATLAB and FORTRAN 95 computer languages separately. The results show that the CPU time cost of Chebyshev collocation spectral method with 3D Schur-decomposition solver is the least, and almost only one thirtieth to one fiftieth CPU time is needed when using the spectral method with 3D Schur-decomposition solver compared with the standard discrete ordinates method.