Comparison of different forms for the "spin" and "orbital" components of the angular momentum of light

We compare three attempts that have been made to decompose the angular momentum of the electromagnetic field into components of an "orbital" and "spin" nature. All three expressions are different and it appears, on the basis of classical electrodynamics, that there is no preferred way of decomposing the angular momentum of the electromagnetic field into orbital and spin components, even in an inertial frame.Comment: Some clarifications. 7 pages pdf. Earlier version published in International Journal of Optics: http://www.hindawi.com/journals/ijo/aip/728350

Longitudinal and transverse components of a vector field

A unified account, from a pedagogical perspective, is given of the longitudinal and transverse projective delta functions proposed by Belinfante and of their relation to the Helmholtz theorem for the decomposition of a three-vector field into its longitudinal and transverse components. It is argued that the results are applicable to fields that are time-dependent as well as fields that are time-independent.Comment: 9 pages pdf format. Includes derivation and extension of the Frahm relation and volume integrals of projector

Interatomic forces, phonons, the Foreman-Lomer Theorem and the Blackman Sum Rule

Foreman and Lomer proposed in 1957 a method of estimating the harmonic forces between parallel planes of atoms of primitive cubic crystals by Fourier transforming the squared frequencies of phonons propagating along principal directions. A generalized form of this theorem is derived in this paper and it is shown that it is more appropriate to apply the method to certain combinations of the phonon dispersion relations rather than to individual dispersion relations themselves. Further, it is also shown how the method may be extended to the non-primitive hexagonal close packed and diamond lattices. Explicit, exact and general relations in terms of atomic force constants are found for deviations from the Blackman sum rule which itself is shown to be derived from the generalized Foreman-Lomer theorem.Comment: 13 pages pd

Derivation of the paraxial form of the angular momentum of the electromagnetic field from the general form

It is shown how the standard forms for the spin and orbital components of the angular momentum of a paraxial wave of electromagnetic radiation are obtained from the general expressions for the angular momentum that have been derived recently. This result will enable the general expressions for angular momentum to be applied with confidence to the many configurations of electromagnetic fields that are more complicated than plane or paraxial waves.Comment: typos corrected 6 page

Fuzzy based load and energy aware multipath routing for mobile ad hoc networks

Routing is a challenging task in Mobile Ad hoc Networks (MANET) due to their dynamic topology and lack of central administration. As a consequence of un-predictable topology changes of such networks, routing protocols employed need to accurately capture the delay, load, available bandwidth and residual node energy at various locations of the network for effective energy and load balancing. This paper presents a fuzzy logic based scheme that ensures delay, load and energy aware routing to avoid congestion and minimise end-to-end delay in MANETs. In the proposed approach, forwarding delay, average load, available bandwidth and residual battery energy at a mobile node are given as inputs to a fuzzy inference engine to determine the traffic distribution possibility from that node based on the given fuzzy rules. Based on the output from the fuzzy system, traffic is distributed over fail-safe multiple routes to reduce the load at a congested node. Through simulation results, we show that our approach reduces end-to-end delay, packet drop and average energy consumption and increases packet delivery ratio for constant bit rate (CBR) traffic when compared with the popular Ad hoc On-demand Multipath Distance Vector (AOMDV) routing protocol

From quantum circuits to adiabatic algorithms

This paper explores several aspects of the adiabatic quantum computation model. We first show a way that directly maps any arbitrary circuit in the standard quantum computing model to an adiabatic algorithm of the same depth. Specifically, we look for a smooth time-dependent Hamiltonian whose unique ground state slowly changes from the initial state of the circuit to its final state. Since this construction requires in general an n-local Hamiltonian, we will study whether approximation is possible using previous results on ground state entanglement and perturbation theory. Finally we will point out how the adiabatic model can be relaxed in various ways to allow for 2-local partially adiabatic algorithms as well as 2-local holonomic quantum algorithms.Comment: Version accepted by and to appear in Phys. Rev.