Supersymmetry and the Atiyah-Singer Index Theorem I: Peierls Brackets, Green's Functions, and a Supersymmetric Proof of the Index Theorem

The Peierls bracket quantization scheme is applied to the supersymmetric system corresponding to the twisted spin index theorem. A detailed study of the quantum system is presented, and the Feynman propagator is exactly computed. The Green's function methods provide a direct derivation of the index formula. Note: This is essentially a new SUSY proof of the index theorem.Comment: 47 page

Can Compactifications Solve the Cosmological Constant Problem?

Recently, there have been claims in the literature that the cosmological constant problem can be dynamically solved by specific compactifications of gravity from higher-dimensional toy models. These models have the novel feature that in the four-dimensional theory, the cosmological constant $\Lambda$ is much smaller than the Planck density and in fact accumulates at $\Lambda=0$. Here we show that while these are very interesting models, they do not properly address the real cosmological constant problem. As we explain, the real problem is not simply to obtain $\Lambda$ that is small in Planck units in a toy model, but to explain why $\Lambda$ is much smaller than other mass scales (and combinations of scales) in the theory. Instead, in these toy models, all other particle mass scales have been either removed or sent to zero, thus ignoring the real problem. To this end, we provide a general argument that the included moduli masses are generically of order Hubble, so sending them to zero trivially sends the cosmological constant to zero. We also show that the fundamental Planck mass is being sent to zero, and so the central problem is trivially avoided by removing high energy physics altogether. On the other hand, by including various large mass scales from particle physics with a high fundamental Planck mass, one is faced with a real problem, whose only known solution involves accidental cancellations in a landscape.Comment: 7 pages in double column format. V2: Updated references. Published in JCA

Water flow risks and stakeholder impacts on the choice of a dam site

This study evaluates three alternative locations for building a fresh water dam in the Yeşilirmak Valley of North Cyprus. Each of the three sites has different investment costs, water storage capabilities and socio‐political repercussions. These kinds of trade‐offs have in recent years characterised much of the worldwide debate surrounding the construction of electricity and irrigation dams. Another issue raised in this paper is the appropriate treatment of the risk and variability associated with the availability of water to fill the dam through time. This paper demonstrates how an integrated financial‐economic‐stakeholder analysis can provide the inputs needed by decision‐makers in such situations to make rational political and economic choices.Resource /Energy Economics and Policy,

Plasmonic nanogaps for broadband and large spontaneous emission rate enhancement

We present the optical properties of a plasmonic nanogap formed between a silver metallic nanoparticle and an extended silver film that shows a strong enhancement in the spontaneous emission rate over the whole visible range. In particular, we use three-dimensional finite difference time domain calculations to study the spontaneous emission rate and the quantum efficiency of an emitting material placed within the gap region as a function of the geometrical parameters of the plasmonic nanogap. Our calculations reveal that the enhancements in the total decay rate can be divided into two regions as a function of wavelength; region I spans the wavelength range from 350 nm to 500 nm and peaks at approximately at 400 nm. Region II covers the spectral range between 500 nm and 1000 nm. The enhancements in total decay rate in region I are mainly dominated by Ohmic losses by the metal, while the enhancements in total decay rate in region II are mainly dominated by radiative decay rate enhancements. Furthermore, our calculations show over 100 times enhancement in the spontaneous emission rate in region II. We combine this with quantum efficiency enhancements of almost 30 times from materials with low intrinsic quantum efficiencies and only a small reduction in efficiency from those with high intrinsic quantum efficiencies. All results appear easily achievable using realistic geometrical parameters and simple synthesis techniques. These results are attributed to the strong field confinements in the nanogap region. The structures are of high interest for both the fundamental understanding of light mater interactions under extreme electromagnetic field confinements and also potential applications in quantum optics and Raman spectroscopy

Ultra-short of pico and femtosecond soliton laser pulse using microring resonator for cancer cells treatment

A system of microring resonators (MRRs) incorporating with an add/drop filter system is presented in which ultra-short single and multi temporal and spatial optical soliton pulses can be simulated and used to thermalbased killing of abnormal cells, tumor and cancer, applicable in nanomedical treatments. This proposed system uses chaotic signals generated by a bright soliton pulse within a nonlinear MRRs system. Interaction between gold nanoparticles and ultra-short femtosecond and picosecond laser pulses holds great interest in laser nanomedicine. By using the appropriate soliton input power and MRRs parameters, required spatial and temporal signals are generated spreading over the spectrum. Results obtained show that smallest single temporal and spatial soliton pulse with FWHM = 712 fs and FWHM = 17.5 pm could be generated respectively. The add/drop filter system is used to generate high capacity ultra-short soliton pulses in the range of nanometer/second and picometer/second

A novel approach for ANFIS modelling based on Grey system theory for thermal error compensation

The fast and accurate modelling of thermal errors in machining is an important aspect for the implementation of thermal error compensation. This paper presents a novel modelling approach for thermal error compensation on CNC machine tools. The method combines the Adaptive Neuro Fuzzy Inference System (ANFIS) and Grey system theory to predict thermal errors in machining. Instead of following a traditional approach, which utilises original data patterns to construct the ANFIS model, this paper proposes to exploit Accumulation Generation Operation (AGO) to simplify the modelling procedures. AGO, a basis of the Grey system theory, is used to uncover a development tendency so that the features and laws of integration hidden in the chaotic raw data can be sufficiently revealed. AGO properties make it easier for the proposed model to design and predict. According to the simulation results, the proposed model demonstrates stronger prediction power than standard ANFIS model only with minimum number of training samples