Diagnostic evaluation of the mean meridional circulation-II

Summary We evaluate the mean meridional circulation for the Northern and Southern Hemispheres, working with the dry-static-energy and mass conservation equations. We derive an equation for the mass streamfunction on lines at constant dry static energy and we numerically integrate this equation using the annual mean data related to the period 1963 through 1973, as published by Oort in 1983. In both Hemispheres we find a rather intense Ferrel cell and a weaker Hadley cell; we do not find any polar cell. Cells strengths are accurately computed in the upper part of the troposphere; we are less confident on their numerical values in the lower part of the troposphere, for the presence of boundary layer. Comparisons with previous calculations are discussed.     

Free particle in q-deformed configuration space

The SO _q (N)-invariant Schrödinger equation for the free particle is formulated in polar coordinates as a partial differential equation in noncommutative geometry. For each value of the total angular momentum, a Hilbert space of radial functions is constructed as the space of normalizable functions respective to the q-integral. The spectrum of the Hamiltonian is found to be discrete.     

Raising and Lowering Operators for Orbital Angular Momentum Quantum Numbers

Two vector operators aimed at shifting orbital angular momentum quantum number l successfully constructed based on the primary form proposed by Prof. X.L. Ka in 2001. The lowering operators can give the lowest angular momentum quantum numbers l for a given magnetic quantum number m in spherical harmonics |lm〉; and the state with minimum angular momentum quantum number in whole set of the spherical harmonics turns out to be |0,0〉. How to use the raising and lowering operators as acting on the state |0,0〉. to generate whole set of spherical harmonics is illustrated.     

Angular momentum mixing in a non-spherical color superconductor

We study the angular momentum mixing effects in the color superconductor with non-spherical pairing. We first clarify the concept of the angular momentum mixing with a toy model for non-relativistic and spinless fermions. Then we derive the gap equation for the polar phase of dense QCD by minimizing the CJT free energy. The solution of the gap equation consists of all angular momentum partial waves of odd parity. The corresponding free energy is found to be lower than that reported in the literature with p-wave only.     

Spin-Dependent Bohm Trajectories for Pauli and Dirac Eigenstates of Hydrogen

The de Broglie-Bohm causal theory of quantum mechanics is applied to the hydrogen atom in the fully spin-dependent and relativistic framework of the Dirac equation, and in the nonrelativistic but spin-dependent framework of the Pauli equation. Eigenstates are chosen which are simultaneous eigenstates of the energy H, total angular momentum M, and z component of the total angular momentum M _z. We find the trajectories of the electron, and show that in these eigenstates, motion is circular about the z-axis, with constant angular velocity. We compute the rates of revolution for the ground (n=1) state and the n=2 states, and show that there is agreement in the relevant cases between the Dirac and Pauli results, and with earlier results on the Schrödinger equation.     

Neutron Stars in Teleparallel Gravity

In this paper, we deal with neutron stars, which are described by a perfect fluid model, in the context of the teleparallel equivalent of general relativity. We use numerical computations (based on the RNS code) to find the relation between the angular momentum of the field and the angular momentum of the source. One such relation was established for each stable star resulting from the numerical computation with an equation of state, the central energy density, and the ratio between the polar and equatorial radii as input, the central energy density and the ratio between polar and equatorial radii. We also find a regime in which the relation between gravitational angular momentum and moment of inertia (as well as the angular velocity of the fluid) is linear. We give the spatial distribution of the gravitational energy and show that it depends linearly on the squared angular velocity of the source.     

Torque equations for spin and orbital angular momenta of radiation fields and Faraday effect

The spin angular momentum S of light has never been linked to the Faraday rotation of light traveling in an optically active medium possessing a rotational invariance of a crystal, because there was no helicity term associated with the phase shift in the previous torque equation for S. In order to relate the change in S with time to the Faraday rotation, therefore, we derived an exact torque equation for S. As a result, a magnetic helicity term appeared in a new torque equation for S, so that one-half of the phase shift derived from the helicity term was equivalent to the Faraday rotation angle. However, the orbital angular momentum L had no relation to the Faraday rotation. It was thus clarified that the change in S with time is related to the Faraday rotation angle of light traveling in an optically active medium, owing to the appearance of the helicity term without a rotational invariance around the optical axis. It was also demonstrated theoretically that the Faraday rotation is accompanied by a torque acting on the crystal so that the total angular momentum of light and matter is conserved.     

Quantum theory of single events: Localized De Broglie wavelets,Schrödinger waves,and classical trajectories

For an arbitrary potential V with classical trajectoriesx=g(t), we construct localized oscillating three-dimensional wave lumps (x, t,g) representing a single quantum particle. The crest of the envelope of the ripple follows the classical orbitg(t), slightly modified due to the potential V, and (x, t,g) satisfies the Schrödinger equation. The field energy, momentum, and angular momentum calculated as integrals over all space are equal to the particle energy, momentum, and angular momentum. The relation to coherent states and to Schrödinger waves is also discussed.     

On long-time limit behavior of the solution of atom's master equation

We study long-time limit behavior of the solution of atom's master equation, for the first time we derive that the probability of the atom being in the α-th (α =j+1-j_z, j is the angular momentum quantum number, j_z is the z-component of angular momentum) state is {(1-K/G)/[1-(K/G)^2j+1]}(K/G)^α-1 as t→+∞, which coincides with the fact that when K/G > 1, the larger the α is, the larger probability of the atom being in the α-th state (the lower excited state). We also consider the case for some possible generalizations of the atomic master equation.     

A class of exact solutions to the force-free,axisymetric, stationary magnetosphere of a Kerr black hole

We analyze the constraint equation giving allowed solutions describing fields and currents in a force-free magnetosphere around a rotating black hole. Utilizing the divergence properties of the energy and angular-momentum fluxes, for physically allowed solutions with nonzero energy and angular momentum extraction, we conclude that poloidal surfaces are independent of the radial coordinate for large values of r. Imposing this requirement and the Znajek regularity condition, we explicitly derive all possible exact solutions admitted by the constraint equation for r independent poloidal surfaces which are given in terms of the electromagnetic angular velocity function , where a is the angular momentum per unit mass of the black hole. Further, we show that for the class of solutions we have developed there is no electromagnetic extraction of energy. G. M. acknowledges funding through a Troy University sabbatical. The work of C. D. D. is supported by the Office of Naval Research. This research was also supported through NASA GLAST Science Investigation No. DPR-S-1563-Y.     

Quantum Monodromy in the Spectrum of Schrödinger Equation with a Decatic Potential

In this study the spectral problem of the two-dimensional Schrödinger equation with the cylindrically symmetrical decatic potential is carried out. The concept of quantum monodromy is introduced to give insight into the energy levels of system with this potential. It is shown that quantum monodromy occurs at = 0 in the distribution of eigenstates around a critical point on the spectrum at E = 0 with zero angular momentum, such that there can be no smoothly valid assignment of quantum number. Cases with the three-well and four-well potentials are presented to give rise to the double degeneracies with respect to energy except for the angular momentum m = 0.     

Parametrization of the Kerr Solution

From the Kerr solution of Ernst equation under Ehlers and unitary transformations, we build a parametrized Kerr solution depending on three parameters, namely the mass, the angular momentum of the source and an adimensional parameter m ₁. Varying m ₁ produces a topological deformation of the ergosphere.     

Hawking Radiation of Charged Particles from a Rotating Black String

Using Damour-Ruffini method, Hawking radiation of rotating black strings is studied. Under the condition that the total energy, total angular momentum and total charge are conservative, the transition probability from initial state (energy M+ω, charge Q+e and angular momentum J+m) to final state (energy M, charge Q and angular momentum J) for black strings is derived considering the reaction of radiation particles to spacetime. That is, the probability that black strings radiate particles with energy ω, charge e and angular momentum m is obtained. The real spectrum is not a strictly pure thermal spectrum. Our result is consistent with Parikh and Wilczek’s result. It satisfies the unitary principle of quantum mechanics. However, in our result there are not only the term that denotes effect of energy and charge of radiation particles but also the term that denotes effect of radiation particles angular momentum on rotating black strings angular momentum. We provide a new way for investigating radiation of black strings.     

Simple numerical method of computing the probabilities of angular momentum Jν occurring among possible vectors J Resulting from n angular momentum jμ summation (μ=1?n)

Arelatively simple numerical method of summing angular momentum vectors with maintaining space quantization rules of each summed angular momentum has been presented. The method enables the calculation of the values of probability (p j _μ) of finding a definite angular momentum J _μ among all vectors J being the results of quantum summation of n angular momentum vectors j _μ(μ=1-n. It may be used, e.g., in the calculations of angular momentum of many-particle states. The significance of the paper is connected with the possibility of taking into account, in a simple way, the angular momentum conservation principle for a system which consists of an arbitrary number of excitons. From Yadernaya Fizika, Vol. 67, No. 11, 2004, pp. 2123–2128. Original English Text Copyright ? 2004 by Kaczmarczyk. This article was submitted by the author in English.     

Angular momentum analysis of a composite particle scattering problem and its cross channel analog

We investigate the solutions, by a determinental method, for a partial wave Bethe-Salpeter equation describing composite particle scattering and for its cross channel analog. We compare the behavior at s = ?∞ of the leading angular momentum singularity from the Bethe-Salpeter equation with that of the leading Regge singularity of the cross channel equation. We mention the effect of the general properties of the kernel of the Bethe-Salpeter equation on the angular momentum structure of the solution.     

Angular Momentum and Positive Mass Theorem

Total angular momentum for asymptotically flat manifolds is defined. Positive mass theorem for initial (spin) data set (M, g _ij , p _ij ) with nonsymmetric p _ij is proved. As an application, we establish positive mass theorems involving total linear momentum and total angular momentum. This gives an answer to a problem of S. T. Yau in his Problem Section [Ya2] and a partial answer to his recent conjecture on the relationship among total energy, total linear momentum, total angular momentum and entropy of black hole. Received: 26 October 1998 / Accepted: 10 March 1999     

Complex Parameters in Quantum Mechanics

The Schrödinger equation for stationary states in a central potential is studied in an arbitrary number of spatial dimensions, say q. After transformation into an equivalent equation, where the coefficient of the first derivative vanishes, it is shown that in such equation the coefficient of r ^–2 is an even function of a parameter, say , depending on a linear combination of q and of the angular momentum quantum number, say l. Thus, the case of complex values of , which is useful in scattering theory, involves, in general, both a complex value of the parameter originally viewed as the spatial dimension and complex values of the angular momentum quantum number. The paper ends with a proof of the Levinson theorem in an arbitrary number of spatial dimensions, when the potential includes a non-local term which might be useful to understand the interaction between two nucleons.     

Angular distribution of dileptons in hadronic collisions

The polar and azimuthal angular distributions of the lepton pair produced in hadron-hadron collisions are studied. For large Q_T these are calculated from lowest-order QCD diagrams. For low Q_T we present simple expressions which take into account the effect of primordial quark transverse momentum on the angular distributions.     

On some integrable cases of the two-dimensional motion of a charged particle in an electromagnetic field

Two cases of the two-dimensional motion of a charged particle in an electromagnetic field have been integrated. In these cases, the Hamiltonian commutes with the angular momentum. Variables are separable in polar coordinates. The vector potential and potential energy have been taken from my recent work regarding two cases of the two-dimensional Schrödinger equation, which belong to quasi-exactly solvable problems. In these cases, semiclassical and exact wavefunctions have been compared in classically forbidden regions.     

Solvation of large dipoles

A model system consisting of one strongly polar molecule dissolved in a pool of 499 moderately polar particles is studied in a molecular dynamics experiment. A pair potential of Stockmayer type is used. The structure of the solution has been analysed in terms of g(R), f(R), h _Δ(R), h _D(R), g(R, x), and Voronoi polyhedra. Solvent-solvent spatial correlations are presented and compared to solute-solvent properties already discussed in part I. Voronoi polyhedra analysis is also used to define structural relaxation around solute or solvent particles unambiguously. The dynamics of the system is described by means of angular momentum, orientational, and velocity autocorrelation functions. The solute's influence on the dynamics of the solvent is analysed by a polyhedral decomposition of time correlation functions.