Wigner's Problem and Alternative Commutation Relations for Quantum Mechanics

It is shown, that for quantum systems the vectorfield associated with the equations of motion may admit alternative Hamiltonian descriptions, both in the Schr\"odinger and Heisenberg pictures. We illustrate these ambiguities in terms of simple examples.Comment: Latex,14 pages,accepted by Int. Jour.Mod.Phy

Optimal Design for Vibration Mitigation of a Planar Parallel Mechanism for a Fast Automatic Machine

This work studies a planar parallel mechanism installed on a fast-operating automatic machine. In particular, the mechanism design is optimized to mitigate experimentally-observed vibrations. The latter are a frequent issue in mechanisms operating at high speeds, since they may lead to low-quality products and, ultimately, to permanent damage to the goods that are processed. In order to identify the vibration cause, several possible factors are explored, such as resonance phenomena, elastic deformations of the components, and joint deformations under operation loads. Then, two design optimization are performed, which result in a significant improvement in the vibrational behaviour, with oscillations being strongly reduced in comparison to the initial design

Workspace Computation of Planar Continuum Parallel Robots

Continuum parallel robots (CPRs) comprise several flexible beams connected in parallel to an end-effector. They combine the inherent compliance of continuum robots with the high payload capacity of parallel robots. Workspace characterization is a crucial point in the performance evaluation of CPRs. In this paper, we propose a methodology for the workspace evaluation of planar continuum parallel robots (PCPRs), with focus on the constant-orientation workspace. An explorative algorithm, based on the iterative solution of the inverse geometrico-static problem is proposed for the workspace computation of a generic PCPR. Thanks to an energy-based modelling strategy, and derivative approximation by finite differences, we are able to apply the Kantorovich theorem to certify the existence, uniqueness, and convergence of the solution of the inverse geometrico-static problem at each step of the procedure. Three case studies are shown to demonstrate the effectiveness of the proposed approach

Complex Economies have a Lateral Escape from the Poverty Trap

We analyze the decisive role played by the complexity of economic systems at the onset of the industrialization process of countries over the past 50 years. Our analysis of the input growth dynamics, considering a further dimension through a recently introduced measure of economic complexity, reveals that more differentiated and more complex economies face a lower barrier (in terms of GDP per capita) when starting the transition towards industrialization. As a consequence, we can extend the classical concept of a one-dimensional poverty trap, by introducing a two-dimensional poverty trap: a country will start the industrialization process if it is rich enough (as in neo-classical economic theories), complex enough (using this new dimension and laterally escaping from the poverty trap), or a linear combination of the two. This naturally leads to the proposal of a Complex Index of Relative Development (CIRD) which shows, when analyzed as a function of the growth due to input, a shape of an upside down parabola similar to that expected from the standard economic theories when considering only the GDP per capita dimension

Multi-scheme approach for efficient surface plasmon polariton generation in metallic conical tips on AFM-based cantilevers

We report on the possibility of realizing adiabatic surface plasmon polaritons compression on metallic conical tips built-in on AFM cantilevers by means of different approaches. The problem is faced considering the role of the source, when linear and radial polarizations are assumed, associated to different fabrication schemes. Nano-patterned devices properly combined with metallic conical tips can affect the adiabatic characteristic of the surface electric field. The results are analyzed in terms of tradeoff between fabrication difficulties and device performances. Suggestions on the best possible scheme are provided

Emergent Chiral Symmetry: Parity and Time Reversal Doubles

There are numerous examples of approximately degenerate states of opposite parity in molecular physics. Theory indicates that these doubles can occur in molecules that are reflection-asymmetric. Such parity doubles occur in nuclear physics as well, among nuclei with odd A $\sim$ 219-229. We have also suggested elsewhere that such doubles occur in particle physics for baryons made up of `cbu' and `cbd' quarks. In this article, we discuss the theoretical foundations of these doubles in detail, demonstrating their emergence as a surprisingly subtle consequence of the Born-Oppenheimer approximation, and emphasizing their bundle-theoretic and topological underpinnings. Starting with certain ``low energy'' effective theories in which classical symmetries like parity and time reversal are anomalously broken on quantization, we show how these symmetries can be restored by judicious inclusion of ``high-energy'' degrees of freedom. This mechanism of restoring the symmetry naturally leads to the aforementioned doublet structure. A novel by-product of this mechanism is the emergence of an approximate symmetry (corresponding to the approximate degeneracy of the doubles) at low energies which is not evident in the full Hamiltonian. We also discuss the implications of this mechanism for Skyrmion physics, monopoles, anomalies and quantum gravity.Comment: 32 pages, latex. minor changes in presentation and reference