We examine the effects of strain and cation substitution on the superconducting phase of polar semiconductors near a ferroelectric quantum phase transition with a model that combines a strong coupling theory of superconductors with a standard microscopic framework for displacive polar modes coupled to strain degrees of freedom. Our calculations reveal that the superconducting transition temperature Tc is enhanced by proximity to the ferroelectric instability from the disordered side, while it is generally suppressed in the ordered phase due to its increase in dielectric stiffness and a reduction of critical fluctuations from dipolar induced anisotropies. The condensation of the pairing phonon excitations generates a kink in Tc at a charge density that is generally lower than that of the quantum critical point (QCP) and where both superconducting and ferroelectric orders set in. We apply our model to SrTiO3 and find that the antiadiabatic limit places the kink nearly at its QCP. As the QCP is pushed to higher charge densities with either tuning parameter, we find that the dome narrows and sharpens. Our model is in qualitative and fair quantitative agreement with the recent observation of overlapping ferroelectric-like and superconducting instabilities in ndoped Sr1−xCaxTiO3 and strain tuning of Tc in n-doped SrTiO3. We compare our results to previous models invoking order-disorder lattice dynamics to describe the pairing excitations.

Relaxor ferroelectrics are complex oxide materials which are rather unique to study the effects of compositional disorder on phase transitions. Here, we study the effects of quenched cubic random electric fields on the lattice instabilities that lead to a ferroelectric transition and show that, within a microscopic model and a statistical mechanical solution, even weak compositional disorder can prohibit the development of long-range order and that a random field state with anisotropic and power-law correlations of polarization emerges from the combined effect of their characteristic dipole forces and their inherent charge disorder. We compare and reproduce several key experimental observations in the well-studied relaxor PbMg 1/3 Nb 2/3 O 3 -PbTiO 3 .

In this contribution, we calculate the light deflection, perihelion shift, time delay and gravitational redshift using an approximate metric that contains the Kerr metric and an approximation of the Erez-Rosen spacetime. The results were obtained directly using (Mathematica 2018 Wolfram Research, Inc., Version 11.3, Champaign). The results agree with the ones presented in the literature, but they are extended until second order terms of mass, angular momentum and mass quadrupole. The inclusion of the mass quadrupole is done by means of the metric; no expansion of the gravitational potential as in the parameterized post-Newtonian is required.

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