On the theory of beta-radioactivity III : The influence of electric and magnetic fields on polarized electron beams

The influence of electric and magnetic fields on the spin orientation (polarization) of electrons in a beam is calculated according to the Pauli spin theory and the Dirac theory. For the cases, where the field is perpendicular or parallel to a polarized electron beam, the following results are found. Transverse electric field. In the non-relativistic approximation the spin orientation remains constant in space, even if the beam is deflected; the relativistic formula gives for the ratio of the rotation of the spin orientation and the angle of deflection of the beam: Ekin/E (ratio of kinetic energy and total energy, i.e., including the rest mass). Transverse magnetic field. The spin orientation does not change in relation to the direction of propagation. Longitudinal electric field. Though the beam is accelerated (or retarded) the spin orientation remains constant in space. Longitudinal magnetic field. The spin orientation rotates about the direction of propagation. It is shown that longitudinal polarization of electron beams (spins parallel or antiparallel to the direction of propagation) can be observed by means of an electric deflection of the beam and a scattering experiment in succession

On the theory of beta-radioactivity IV : The polarization of beta-rays emitted by aligned nuclei in allowed transitions

The consequences of alignment of nuclei, which show allowed ß-transitions, are investigated. A general formula is derived for the transition probability of an allowed β-transition, in which the direction of emission of electron and neutrino, the polarization of the electron and the orientation of the nuclear spin are taken into account. The calculations have been made for a Hamiltonian for the β-interaction, which is an arbitrary "mixture" of the five invariants of the Dirac theory. The influence of the nuclear charge has, however, been neglected. From this formula the following results are immediately obtained: The angular distribution of the β-radiation remains spherically symmetric if the nuclei are aligned, so that the alignment cannot be detected in this way. The emitted β-radiation is polarized and the degree of polarization follows from the general formula. If we take the special case that the interaction Hamiltonian is of the tensor or the axial vector type and if the β-rays are emitted perpendicular to the direction of the nuclear spin of completely aligned nuclei with nuclear spin ji, the degree of polarization is given by: a) 1/Eif ji = jf + 1, b) 1/E(ji + 1), if ji = jf,c)ji/E(ji + 1), if ji = ji - 1. (E is the relativistic energy of the electrons, E ≈ 1 for small kinetic energies; jf gives the spin of the final nucleus)

A general theorem on the transition probabilities of a quantum mechanical system with spatial degeneracy

In the general case of a quantum mechanical system with a Hamiltonian that is invariant for rotations spatial degeneracy will exist. So the initial state must be characterized except by the energy also by e.g. the magnetic quantum number. Both for emission of light and electrons plus neutrinos (ß-radioactivity) of a quantum mechanical system the following theorem is important: the total transition probability from an initial level with some definite magnetic quantum number mi to every possible final level belonging to one energy does not depend on mi. A simple proof is given for this theorem that embraces the case of forbidden transitions, which case is not covered by the usual proof. In the proof a Gibbs ensemble of quantum mechanical systems is used; the necessary and sufficient conditions for the rotational invariance of such an ensemble are give

Non-equilibrium thermodynamics and liquid helium II

The thermodynamics of irreversible processes, based on the O n s a g e r reciprocal relations, is applied to a system consisting of a mixture of two substances, of which one can go over into the other. The mixture is enclosed in two communicating reservoirs at different temperatures T and T + ΔT. The situations, in which systems arrive, when one, two or more differences between the values of state parameters in the two reservoirs are kept fixed, are called “stationary states of first, second etc. order”. For the stationary state of the first order with fixed ?T the corresponding pressure difference ?P is calculated. This gives the thermomolecular pressure effect ΔP/ΔT = —Q*/v T = (h — U*)/v T, where h and v. are the mean specific enthalpy and volume. This equation shows the connection with the mechano-caloric effect Q*, since application of the O n s a g e r relations shows that Q* is the “heat of transfer” i.e. the heat supplied per unit of time from the surroundings to the reservoir at temperature T, when one unit of mass is transferred from one reservoir to the other in the stationary state of the second order with fixed ΔP and ΔT = 0 (uniform temperature). Similarly U* is the “energy of transfer”. The influence of ΔT on the relative separation (thermal effusion) and the “chemical affinity” of the two components is also calculated. The heat conduction can be split into an “abnormal” part due to the coupling of diffusion and chemical reaction between the components and a “normal” part also present when no reaction takes place. The results can be applied to liquid helium II, considered in the two-fluid theory as a mixture of “normal” (1) and “superfluid” (2) atoms, capable of the “chemical reaction” 1 ⇔ 2. When it is supposed that chemical equilibrium is immediately established and that only superfluid atoms can pass through a sufficiently narrow capillary, the above mentioned equation leads . to G o r t e r's formula v ΔP/ΔT = χ1 ∂s/∂χ1, where χ1 is the fraction of normal atoms and s the mean specific entropy of the mixture. Under the same circumstances only the “normal” part of the heat conduction subsists

Correspondence in Quasiperiodic and Chaotic Maps: Quantization via the von Neumann Equation

A generalized approach to the quantization of a large class of maps on a torus, i.e. quantization via the von Neumann Equation, is described and a number of issues related to the quantization of model systems are discussed. The approach yields well behaved mixed quantum states for tori for which the corresponding Schrodinger equation has no solutions, as well as an extended spectrum for tori where the Schrodinger equation can be solved. Quantum-classical correspondence is demonstrated for the class of mappings considered, with the Wigner-Weyl density $\rho(p,q,t)$ going to the correct classical limit. An application to the cat map yields, in a direct manner, nonchaotic quantum dynamics, plus the exact chaotic classical propagator in the correspondence limit.Comment: 36 pages, RevTex preprint forma

Pervasive and standalone computing: The perceptual effects of variable multimedia quality.

The introduction of multimedia on pervasive and mobile communication devices raises a number of perceptual quality issues, however, limited work has been done examining the 3-way interaction between use of equipment, quality of perception and quality of service. Our work measures levels of informational transfer (objective) and user satisfaction (subjective)when users are presented with multimedia video clips at three different frame rates, using four different display devices, simulating variation in participant mobility. Our results will show that variation in frame-rate does not impact a user’s level of information assimilation, however, does impact a users’ perception of multimedia video ‘quality’. Additionally, increased visual immersion can be used to increase transfer of video information, but can negatively affect the users’ perception of ‘quality’. Finally, we illustrate the significant affect of clip-content on the transfer of video, audio and textual information, placing into doubt the use of purely objective quality definitions when considering multimedia presentations