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,

Scheduling of material through a steel plant

This paper addresses the optimal scheduling of material in a steel plant. The genetic algorithm is adapted to handle various constraints in the processing mills

Sudden change in dynamics of genuine multipartite entanglement of cavity-reservoir qubits

We study the dynamics of genuine multipartite entanglement for a system of four qubits. Using a computable entanglement monotone for multipartite systems, we investigate the as yet unexplored aspects of a cavity-reservoir system of qubits. For one specific initial state, we observe a sudden transition in the dynamics of genuine entanglement for the four qubits. This sudden change occurs only during a time window where neither cavity-cavity qubits nor reservoir-reservoir qubits are entangled. We show that this sudden change in dynamics of this specific state is extremely sensitive to white noise.Comment: 18 pages, 11 figure

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