Noncommutativity due to spin

Using the Berezin-Marinov pseudoclassical formulation of spin particle we propose a classical model of spin noncommutativity. In the nonrelativistic case, the Poisson brackets between the coordinates are proportional to the spin angular momentum. The quantization of the model leads to the noncommutativity with mixed spacial and spin degrees of freedom. A modified Pauli equation, describing a spin half particle in an external e.m. field is obtained. We show that nonlocality caused by the spin noncommutativity depends on the spin of the particle; for spin zero, nonlocality does not appear, for spin half, $\Delta x\Delta y\geq\theta^{2}/2$, etc. In the relativistic case the noncommutative Dirac equation was derived. For that we introduce a new star product. The advantage of our model is that in spite of the presence of noncommutativity and nonlocality, it is Lorentz invariant. Also, in the quasiclassical approximation it gives noncommutativity with a nilpotent parameter.Comment: 11 pages, references adda

Note on improvement precision of recursive function simulation in floating point standard

An improvement on precision of recursive function simulation in IEEE floating point standard is presented. It is shown that the average of rounding towards negative infinite and rounding towards positive infinite yields a better result than the usual standard rounding to the nearest in the simulation of recursive functions. In general, the method improves one digit of precision and it has also been useful to avoid divergence from a correct stationary regime in the logistic map. Numerical studies are presented to illustrate the method.Comment: DINCON 2017 - Conferencia Brasileira de Dinamica, Controle e Aplicacoes - Sao Jose do Rio Preto - Brazil. 8 page

Alternative structures and bi-Hamiltonian systems on a Hilbert space

We discuss transformations generated by dynamical quantum systems which are bi-unitary, i.e. unitary with respect to a pair of Hermitian structures on an infinite-dimensional complex Hilbert space. We introduce the notion of Hermitian structures in generic relative position. We provide few necessary and sufficient conditions for two Hermitian structures to be in generic relative position to better illustrate the relevance of this notion. The group of bi-unitary transformations is considered in both the generic and non-generic case. Finally, we generalize the analysis to real Hilbert spaces and extend to infinite dimensions results already available in the framework of finite-dimensional linear bi-Hamiltonian systems.Comment: 11 page

Controlled dephasing of a quantum dot in the Kondo regime

Kondo correlation in a spin polarized quantum dot (QD) results from the dynamical formation of a spin singlet between the dot's net spin and a Kondo cloud of electrons in the leads, leading to enhanced coherent transport through the QD. We demonstrate here significant dephasing of such transport by coupling the QD and its leads to potential fluctuations in a near by 'potential detector'. The qualitative dephasing is similar to that of a QD in the Coulomb Blockade regime in spite of the fact that the mechanism of transport is quite different. A much stronger than expected suppression of coherent transport is measured, suggesting that dephasing is induced mostly in the 'Kondo cloud' of electrons within the leads and not in the QD.Comment: to be published in PR

An Investigation into the Effect of the Shell on SALM Processed Parts

Shell Assisted Layer Manufacturing (SALM) is a novel process for rapid prototyping/ tooling/ manufacture (RP/RT/RM) which is presently undergoing feasibility studies. SALM is based on layered manufacturing technology (LMT). Initially it develops the shell (boundaries) of a selected layer using a technique similar to fused deposition modelling (FDM). The developed shell is filled with a UV curable resin and is exposed to UV radiation for curing. This procedure is repeated until the complete part is built. This paper compares and contrasts properties of parts made using two options available with the SALM technique: building the part using a soluble shell (FDM support structure material, finally dissolved to recover the part); or using a polymer material such as ABS that is bonded with the resin whilst making the part.Mechanical Engineerin