Parametric arbitrage-free models for implied smile dynamics

Based on the theory of Tangent Levy model [1] developed by R. Carmona and S. Nadtochiy, this thesis gives a paramatrized realization of dynamic implied smile.\ud \ud After specifying a Dirac style Levy measure, we give argument about the consistency issue of our model with the Tangent Levy Model. A corresponding no arbitrage drift condition is derived for the parameters. Numerical setup under our model for option pricing and parameter estimation for calibration is given. Implementation results are illustrated in detail and in the end we provide with simulation results of one day ahead implied smile

Towards microscopic studies of survival probabilities of compound superheavy nuclei

The microscopic approach of fission rates and neutron emission rates in compound nuclei have been applied to $^{258}$No and $^{286}$Cn. The microscopic framework is based on the finite-temperature Skyrme-Hartree-Fock+BCS calculations, in which the fission barriers and mass parameters are self-consistently temperature dependent. The fission rates from low to high temperatures can be obtained based on the imaginary free energy method. The neutron emission rates are obtained with neutron gases at surfaces. Finally the survival probabilities of superheavy nuclei can be calculated microscopically. The microscopic approach has been compared with the widely used statistical models. Generally, there are still large uncertainties in descriptions of fission rates.Comment: 9 pages,7 figures, accepted for Physica Scripta Special Issu

Microscopic description of neutron emission rates in compound nuclei

The neutron emission rates in thermal excited nuclei are conventionally described by statistical models with a phenomenological level density parameter that depends on excitation energies, deformations and mass regions. In the microscopic view of hot nuclei, the neutron emission rates can be determined by the external neutron gas densities without any free parameters. Therefore the microscopic description of thermal neutron emissions is desirable that can impact several understandings such as survival probabilities of superheavy compound nuclei and neutron emissivity in reactors. To describe the neutron emission rates microscopically, the external thermal neutron gases are self-consistently obtained based on the Finite-Temperature Hartree-Fock-Bogoliubov (FT-HFB) approach. The results are compared with the statistical model to explore the connections between the FT-HFB approach and the statistical model. The Skyrme FT-HFB equation is solved by HFB-AX in deformed coordinate spaces. Based on the FT-HFB approach, the thermal properties and external neutron gas are properly described with the self-consistent gas substraction procedure. Then neutron emission rates can be obtained based on the densities of external neutron gases. The thermal statistical properties of $^{238}$U and $^{258}$U are studied in detail in terms of excitation energies. The thermal neutron emission rates in $^{238, 258}$U and superheavy compound nuclei $_{112}^{278}$Cn and $_{114}^{292}$Fl are calculated, which agree well with the statistical model by adopting an excitation-energy-dependent level density parameter. The coordinate-space FT-HFB approach can provide reliable microscopic descriptions of neutron emission rates in hot nuclei, as well as microscopic constraints on the excitation energy dependence of level density parameters for statistical models.Comment: 6 pages, 5 figures, revised and accepted for PR

Scalar CFTs and Their Large N Limits

We study scalar conformal field theories whose large $N$ spectrum is fixed by the operator dimensions of either Ising model or Lee-Yang edge singularity. Using numerical bootstrap to study CFTs with $S_N\otimes Z_2$ symmetry, we find a series of kinks whose locations approach $(\Delta^{\text{Ising}}_{\sigma},\Delta^{\text{Ising}}_{\epsilon})$ at $N\rightarrow \infty$. Setting $N=4$, we study the cubic anisotropic fixed point with three spin components. As byproducts of our numerical bootstrap work, we discover another series of kinks whose identification with previous known CFTs remains a mystery. We also show that "minimal models" of $\mathcal{W}_3$ algebra saturate the numerical bootstrap bounds of CFTs with $S_3$ symmetry.Comment: 29 pages, 5 figure

Extension and parameterization of high-order density dependence in Skyrme forces

The three-body force is indispensable in nuclear energy density functionals which leads to a density dependent two-body term in the Hartree-Fock approach. Usually a single factional power of density dependency has been adopted. We consider the possibility of an additional higher-order density dependence in extended Skyrme forces. As a result, new extended Skyrme parametertizations based on the SLy4 force are obtained and the improvements in descriptions of global nuclei have been demonstrated. The higher-order term can also substantially affect nuclear properties in the high density region in general ways.Comment: 6 pages, 5 figure