Angular Momentum Operator and Fermion-Pair Creation for Non-Abelian Fields

We study the extended structure of non-Abelian dyons, the generalized electromagnetic field and the resulting residual angular momentum in the interior as well as exterior regions of the dyon, and it has been demonstrated that at the dyonic centre there exists no well-defined U(1) charge symmetry and the density of residual angular momentum becomes infinity. The mechanism of creation of a fermionic pair at the dyonic core involving the extremely high density of residual angular momentum has been developed, which leads to baryon-number nonconservation in the presence of non-Abelian dyons. The fermion-number–breaking amplitudes in the presence of a non-Abelian dyon have been analyzed and are not suppressed by exp(– const/e ²). Further, the relevant properties of left-handed fermions in a non-Abelian field has been summarized and the zeroth-order approximation is described. Within this approximation the density of the fermion-number–breaking condensate is found to be O(1), i.e. to be independent of the coupling constant and of the vacuum expectation value of the Higgs field.     

Vortex-antivortex wavefunction of a degenerate quantum gas

A mechanism of a pinning of the quantized matter wave vortices by optical vortices in a specially arranged optical dipole traps is discussed. The vortex-antivortex optical arrays of rectangular symmetry are shown to transfer angular orbital momentum and form the “antiferromagnet”-like matter waves. The separable Hamiltonian for matter waves in pancake trapping geometry is proposed and 3D-wavefunction is factorized in a product of wavefunctions of the 1D harmonic oscillator and 2D vortex-antivortex quantum state. The 2D wavefunction’s phase gradient field associated via Madelung transform with the field of classical velocities forms labyrinth-like structure. The macroscopic quantum state composed of periodically spaced counter-rotating BEC superfluid vortices has zero angular momentum and nonzero rotational energy.     

A frame bundle generalization of multisymplectic momentum mappings

We construct momentum mappings for covariant Hamiltonian field theories using a generalization of symplectic geometry to the bundle L_VY of vertically adapted linear frames over the bundle of field configurations Y. Field momentum observables are vector-valued momentum mappings generated from automorphisms of Y, using the (n + k)-symplectic geometry of L_VY. These momentum observables on L_VY generalize those in covariant multisymplectic geometry and produce conserved field quantities along flows. Three examples illustrate the utility of these momentum mappings: orthogonal symmetry of a Kaluza-Klein theory generates the conservation of field angular momentum, affine reparametrization symmetry in time-evolution mechanics produces a version of the parallel axis theorem of rotational dynamics, and time reparametrization symmetry in time-evolution mechanics gives us an improvement upon a parallel transport law.     

Variations on the Kepler problem

The elliptical orbits resulting from Newtonian gravitation are generated with a multifaceted symmetry, mainly resulting from their conservation of both angular momentum and a vector fixing their orientation in space—the Laplace or Runge-Lenz vector. From the ancient formalisms of celestial mechanics, I show a rather counterintuitive behavior of the classical hydrogen atom, whose orbits respond in a direction perpendicular to a weak externally-applied electric field. I then show how the same results can be obtained more easily and directly from the intrinsic symmetry of the Kepler problem. If the atom is subjected to an oscillating electric field, it enjoys symmetry in the time domain as well, which is manifest by quasi-energy states defined only modulo ħω. Using the Runge-Lenz vector in place of the radius vector leads to an exactly-solvable model Hamiltonian for an atom in an oscillating electric field—embodying one of the few meaningful exact solutions in quantum mechanics, and a member of an even more exclusive set of exact solutions having a time-dependent Hamiltonian. I further show that, as long as the atom suffers no change in principal quantum number, incident radiation will produce harmonic radiation with polarization perpendicular to the incident radiation. This unusual polarization results from the perpendicular response of the wavefunction, and is distinguished from most usual harmonic radiation resulting from a scalar nonlinear susceptibility. Finally, I speculate on how this radiation might be observed.     

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.     

Topology of zero riemann curvature flat space in supergravity

The equation of motion of the gravitino is investigated in a flat space reduced from the Kerr geometry by taking the massless limit of the gravitational source. We adopt the ansatz ψ_μ(x)=δ_μoψ(x), i.e., the Coulomb potential analogue to the Rarita-Schwinger Majorana field of the gravitino. A non-trivial exact classical solution of ψ(x) is obtained and it is interpreted as the source of the intrinsic topology of the background flat space. This flat space is spanned by two Minkowski sheets interconnected through a disk of radius a (the angular momentum parameter in the Kerr geometry).     

Gauge-invariant exact solution of a general separable potential model of a quantum system in a laser field

In this Letter we present the exact stationary solution in the length-gauge of the Schrödinger equation for interaction of a circularly polarized laser field with a quantum system possessing the continuous spectrum and any (finite) number of bound states of arbitrary angular momentum symmetry. This manifestly gauge-invariant solution complements the recently given velocity-gauge solution of the model. We also briefly consider the corresponding model with a quantum field in the number-state representation.     

Beams of electromagnetic radiation carrying angular momentum: The Riemann-Silberstein vector and the classical-quantum correspondence

All beams of electromagnetic radiation are made of photons. Therefore, it is important to find a precise relationship between the classical properties of the beam and the quantum characteristics of the photons that make a particular beam. It is shown that this relationship is best expressed in terms of the Riemann-Silberstein vector - a complex combination of the electric and magnetic field vectors - that plays the role of the photon wave function. The Whittaker representation of this vector in terms of a single complex function satisfying the wave equation greatly simplifies the analysis. Bessel beams, exact Laguerre-Gauss beams, and other related beams of electromagnetic radiation can be described in a unified fashion. The appropriate photon quantum numbers for these beams are identified. Special emphasis is put on the angular momentum of a single photon and its connection with the angular momentum of the beam.     

Asymmetry of neutrino emission from neutron beta decay in superdense matter and a strong magnetic field

The probability of neutron beta decay in the presence of degenerate magnetized matter consisting of electrons, protons, and neutrons is calculated by using exact solutions to the Dirac equation for charged particles in a uniform magnetic field. The asymmetry of the angular distribution of the momentum carried away by product antineutrinos is studied with allowance for the effect of a strong magnetic field. The values of basic parameters (magnetic-field strength, matter density, and matter temperature) that affect the reaction being considered are chosen in such a way as to render this investigation applicable to an analysis of the cooling of a neutron star.     

Sturm-Coulomb problem in a magnetic field and its implications for quantum chaos

The Sturm-Coulomb problem is an integrable one since its symmetry group is O(4). When we apply to it a magnetic field, this symmetry is broken and reduced to the O(2) group. The problem is then nonintegrable, but we can derive its matrix representation in a basis in which the Sturm-Coulomb problem alone is diagonal. We use this matrix representation to obtain the corresponding eigenvalues and their nearest neighbor spacing distribution. From the histogram of the latter, we discuss the presence or absence of quantum chaos as a function of the intensity H of the magnetic field and the angular momentum m in the direction of this field.     

A radiating Kerr-Newman solution

A non-static exact solution of Einstein’s equations corresponding to a field of flowing null radiation plus an electromagnetic field is presented. The geometry of the solution is described by the Kerr-Schild metric. The solution admits a shear-free, geodetic null congruence. It has the symmetry of the Kerr-Newman solution and when a certain parameter is put equal to zero the solution becomes static and reduces to the Kerr-Newman solution.     

Spectral properties of helical quantum wires

The spectrum of states of a helical quantum wire has been investigated theoretically. Eigenstates were found using an exact method based on alternating-direction implicit (ADI) evolution in imaginary time, for a wavefunction defined at discrete points in occupation number space and a nearest-neighbor interaction. A helical wire is a special case of a one-dimensional superlattice with an infinitesimal glide symmetry and associated glide-momentum quantum number. The continuous symmetry prevents the appearance of band gaps. Energy eigenstates have unquenched angular momentum--angular momentum increases with glide momentum. Band anharmonicity and angular momentum nonlinearity demonstrate effects of centrifugal acceleration.     

Wobbling geometry in a simple triaxial rotor

The spectroscopic properties and angular momentum geometry of the wobbling motion of a simple triaxial rotor are investigated within the triaxial rotor model. The obtained exact solutions of energy spectra and reduced quadrupole transition probabilities are compared to the approximate analytic solutions from the harmonic approximation formula and Holstein-Primakoff formula. It is found that the low lying wobbling bands can be well described by the analytic formulae. The evolution of the angular momentum geometry as well as the K-distribution with respect to the rotation and the wobbling phonon excitation are studied in detail. It is demonstrated that with the increase of the wobbling phonon number, the triaxial rotor changes its wobbling motions along the axis with the largest moment of inertia to the axis with the smallest moment of inertia. In this process, a specific evolutionary track that can be used to depict the motion of a triaxial rotating nucleus is proposed.     

Reversibility and irreversibility from an initial value formulation

From a time evolution equation for the single particle distribution function derived from the N-particle distribution function (A. Muriel, M. Dresden, Physica D 101 (1997) 297), an exact solution for the 3D Navier–Stokes equation – an old problem – has been found (A. Muriel, Results Phys. 1 (2011) 2). In this Letter, a second exact conclusion from the above-mentioned work is presented. We analyze the time symmetry properties of a formal, exact solution for the single-particle distribution function contracted from the many-body Liouville equation. This analysis must be done because group theoretic results on time reversal symmetry of the full Liouville equation (E.C.G. Sudarshan, N. Mukunda, Classical Mechanics: A Modern Perspective, Wiley, 1974). no longer applies automatically to the single particle distribution function contracted from the formal solution of the N-body Liouville equation. We find the following result: if the initial momentum distribution is even in the momentum, the single particle distribution is reversible. If there is any asymmetry in the initial momentum distribution, no matter how small, the system is irreversible.     

Angular momentum partition in heavy ion induced fission and the effects of shells on gamma-ray multiplicities

Gamma-ray multiplicities have been measured following fission of nuclei with a wide range of mass and angular momentum. The average multiplicity reflects the total angular momentum of the fragments, but the observed variation of multiplicity with fragment mass asymmetry is dominated by shell effects. The highest average multiplicity arises fission of the heaviest compound system, produced with the lowest angular moméntum. This behaviour is well described by spin enhancement through statistical excitation.     

Spontaneous T-symmetry breaking in a cosmological model of the Gödel type

The vacuum average of the 4-angular momentum of scalar field is computed in the Gödel type metric for the case of spontaneously broken gauge symmetry. It is shown that under the sign change (change of sign of the angular velocity), the vacuum average of the 4-angular momentum changes sign as well, which proves the presence of a spontaneous T-symmetry breakdown in the stationary Gödel model.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 14–16, September, 1989.In conclusion, the author thanks the participants of Professor D. D. Ivanenko's seminar for a discussion of this result.     

Limitations of the strong field approximation in ionization of the hydrogen atom by ultrashort pulses

We present a theoretical study of the ionization of hydrogen atoms as a result of the interaction with an ultrashort external electric field. Doubly-differential momentum distributions and angular momentum distributions of ejected electrons calculated in the framework of the Coulomb-Volkov and strong field approximations, as well as classical calculations are compared with the exact solution of the time dependent Schr ödinger equation. We show that in the impulsive limit, the Coulomb-Volkov distorted wave theory reproduces the exact solution. The validity of the strong field approximation is probed both classically and quantum mechanically. We found that classical mechanics describes the proper quantum momentum distributions of the ejected electrons right after a sudden momentum transfer, however pronounced the differences at latter stages that arise during the subsequent electron-nucleus interaction. Although the classical calculations reproduce the quantum momentum distributions, it fails to describe properly the angular momentum distributions, even in the limit of strong fields. The origin of this failure can be attributed to the difference between quantum and classical initial spatial distributions.     

The influence of substrate geometry on the emission properties of a liquid metal ion source

The effect of needle radius, cone angle and shaft diameter on the threshold voltage and angular intensity — total current relationships for a Ga liquid-metal ion source (LMIS) was investigated. The variation of threshold voltage with needle geometry could be described in terms of the Taylor theory of liquid cone formation by electrostatic fields. The beam energy spread was mainly a function of total source current and was not a sensitive function of emitter geometry. Source angular intensity at a constant total current increased linearly with threshold voltage when the latter was altered due to source geometry.     

The Aharonov-Bohm effect: Why it cannot be eliminated from quantum mechanics

The Aharonov-Bohm effect is a necessary and easily understood feature of conventional quantum mechanics. Attempts to remove it from the theory must involve a drastic change in our understanding of the quantization and conservation of angular momentum, or of the role of the classical equations of motion in quantum mechanics. The key point is that a charged particle is the source of an electric field which will penetrate a magnetic field from which the particle is excluded. The crossed fields contain angular momentum whose existence alters the motion of the particle because the total angular momentum is quantized.