Complex free energy landscapes in biaxial nematics and role of repulsive interactions : A Wang - Landau study

General quadratic Hamiltonian models, describing interaction between crystal molecules (typically with $D_{2h}$ symmetry) take into account couplings between their uniaxial and biaxial tensors. While the attractive contributions arising from interactions between similar tensors of the participating molecules provide for eventual condensation of the respective orders at suitably low temperatures, the role of cross-coupling between unlike tensors is not fully appreciated. Our recent study with an advanced Monte Carlo technique (entropic sampling) showed clearly the increasing relevance of this cross term in determining the phase diagram, contravening in some regions of model parameter space, the predictions of mean field theory and standard Monte Carlo simulation results. In this context, we investigated the phase diagrams and the nature of the phases therein, on two trajectories in the parameter space: one is a line in the interior region of biaxial stability believed to be representative of the real systems, and the second is the extensively investigated parabolic path resulting from the London dispersion approximation. In both the cases, we find the destabilizing effect of increased cross-coupling interactions, which invariably result in the formation of local biaxial organizations inhomogeneously distributed. This manifests as a small, but unmistakable, contribution of biaxial order in the uniaxial phase.The free energy profiles computed in the present study as a function of the two dominant order parameters indicate complex landscapes, reflecting the difficulties in the ready realization of the biaxial phase in the laboratory.Comment: 23 pages, 12 figure

Relativistic and correlation effects in atoms

This review article deals with some case studies of relativistic and correlation effects in atomic systems. After a brief introduction to relativistic many-electron theory, a number of applications ranging from correlation energy to parity non-conservation in atoms are considered. There is a special emphasis on relativistic coupled-cluster theory as most of the results presented here are based on it.Comment: Review article, 4 eps figures, latex 2

Probing CP violation with the electric dipole moment of atomic mercury

The electric dipole moment of atomic $^{199}$Hg induced by the nuclear Schiff moment and tensor-pseudotensor electron-nucleus interactions has been calculated. For this, we have developed and employed a novel method based on the relativistic coupled-cluster theory. The results of our theoretical calculations combined with the latest experimental result of $^{199}$Hg electric dipole moment, provide new bounds on the T reversal or CP violation parameters $\theta_{\rm QCD}$, the tensor-pseudotensor coupling constant $C_T$ and $(\widetilde{d}_u - \widetilde{d}_d)$. This is the most accurate calculation of these parameters to date. We highlight the the crucial role of electron correlation effects in their interplay with the P,T violating interactions. Our results demonstrate substantial changes in the results of earlier calculations of these parameters which can be attributed to the more accurate inclusion of important correlation effects in the present work.Comment: 4 pages and 1 figur