Effective Field calculations of the Energy Spectrum of the PT\mathcal{PT}% -Symmetric (−x4-x^{4}) Potential

In this work, we show that the traditional effective field approach can be applied to the $\mathcal{PT}$-symmetric wrong sign ($-x^{4}$) quartic potential. The importance of this work lies in the possibility of its extension to the more important $\mathcal{PT}$-symmetric quantum field theory while the other approaches which use complex contours are not willing to be applicable. We calculated the effective potential of the massless $-x^{4}$ theory as well as the full spectrum of the theory. Although the calculations are carried out up to first order in the coupling, the predicted spectrum is very close to the exact one taken from other works. The most important result of this work is that the effective potential obtained, which is equivalent to the Gaussian effective potential, is bounded from below while the classical potential is bounded from above. This explains the stability of the vacuum of the theory. The obtained quasi-particle Hamiltonian is non-Hermitian but $\mathcal{PT}$-symmetric and we showed that the calculation of the metric operator can go perturbatively. In fact, the calculation of the metric operator can be done even for higher dimensions (quantum field theory) which, up till now, can not be calculated in the other approaches either perturbatively or in a closed form due to the possible appearance of field radicals. Moreover, we argued that the effective theory is perturbative for the whole range of the coupling constant and the perturbation series is expected to converge rapidly (the effective coupling $g_{eff}={1/6}$).Comment: 14 pages, 5 figure

Non-Empirically Tuned Range-Separated DFT Accurately Predicts Both Fundamental and Excitation Gaps in DNA and RNA Nucleobases

Using a non-empirically tuned range-separated DFT approach, we study both the quasiparticle properties (HOMO-LUMO fundamental gaps) and excitation energies of DNA and RNA nucleobases (adenine, thymine, cytosine, guanine, and uracil). Our calculations demonstrate that a physically-motivated, first-principles tuned DFT approach accurately reproduces results from both experimental benchmarks and more computationally intensive techniques such as many-body GW theory. Furthermore, in the same set of nucleobases, we show that the non-empirical range-separated procedure also leads to significantly improved results for excitation energies compared to conventional DFT methods. The present results emphasize the importance of a non-empirically tuned range-separation approach for accurately predicting both fundamental and excitation gaps in DNA and RNA nucleobases.Comment: Accepted by the Journal of Chemical Theory and Computatio

Calculating two- and three-body decays with FeynArts and FormCalc

The Feynman diagram generator FeynArts and the computer algebra program FormCalc allow for an automatic computation of 2->2 and 2->3 scattering processes in High Energy Physics. We have extended this package by four new kinematical routines and adapted one existing routine in order to accomodate also two- and three-body decays of massive particles. This makes it possible to compute automatically two- and three-body particle decay widths and decay energy distributions as well as resonant particle production within the Standard Model and the Minimal Supersymmetric Standard Model at the tree- and loop-level. The use of the program is illustrated with three standard examples: h->b\bar{b}, \mu->e\bar{\nu}_e\nu_\mu, and Z->\nu_e\bar{\nu}_e.Comment: 8 pages, 1 figur

The spatial structure of networks

We study networks that connect points in geographic space, such as transportation networks and the Internet. We find that there are strong signatures in these networks of topography and use patterns, giving the networks shapes that are quite distinct from one another and from non-geographic networks. We offer an explanation of these differences in terms of the costs and benefits of transportation and communication, and give a simple model based on the Monte Carlo optimization of these costs and benefits that reproduces well the qualitative features of the networks studied.Comment: 5 pages, 3 figure

Optimal design of spatial distribution networks

We consider the problem of constructing public facilities, such as hospitals, airports, or malls, in a country with a non-uniform population density, such that the average distance from a person's home to the nearest facility is minimized. Approximate analytic arguments suggest that the optimal distribution of facilities should have a density that increases with population density, but does so slower than linearly, as the two-thirds power. This result is confirmed numerically for the particular case of the United States with recent population data using two independent methods, one a straightforward regression analysis, the other based on density dependent map projections. We also consider strategies for linking the facilities to form a spatial network, such as a network of flights between airports, so that the combined cost of maintenance of and travel on the network is minimized. We show specific examples of such optimal networks for the case of the United States.Comment: 6 pages, 5 figure