Fine-grained domain counting and percolation analysis in two-dimensional lattice systems with linked lists.

We present a fine-grained approach to identify clusters and perform percolation analysis in a two-dimensional (2D) lattice system. In our approach, we develop an algorithm based on the linked-list data structure whereby the members of a cluster are nodes of a path. This path is mapped to a linked-list. This approach facilitates unique cluster labeling in a lattice with a single scan. We use the algorithm to determine the critical exponent in the quench dynamics from the Mott insulator to the superfluid phase of bosons in 2D square optical lattices. The results obtained are consistent with the Kibble-Zurek mechanism. We also employ the algorithm to compute the correlation length using definitions based on percolation theory and use it to identify the quantum critical point of the Bose Glass to superfluid transition in the disordered 2D square optical lattices. In addition, we compute the critical exponent ν which quantify the divergence of the correlation length ξ across the phase transition and the fractal dimension of the hulls of the superfluid clusters.

Probing CP violation with the electric dipole moment of atomic mercury.

The electric dipole moment of atomic 199Hg induced by the nuclear Schiff moment and the tensor-pseudotensor electron-nucleus interactions are calculated. For this, we develop and employ a novel method based on the relativistic coupled-cluster theory. The results of our theoretical calculations, combined with the latest experimental result of the 199Hg electric dipole moment, provide new bounds on the T reversal or CP violation parameters thetaQCD, the tensor-pseudotensor coupling constant CT, and (tilde d(u)-tilde d(d)). This is the most accurate calculation of these parameters to date. We highlight 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.

Strength functions, entropies, and duality in weakly to strongly interacting fermionic systems.

We revisit statistical wave function properties of finite systems of interacting fermions in the light of strength functions and their participation ratio and information entropy. For weakly interacting fermions in a mean-field with random two-body interactions of increasing strength lambda, the strength functions F(k) (E) are well known to change, in the regime where level fluctuations follow Wigner's surmise, from Breit-Wigner to Gaussian form. We propose an ansatz for the function describing this transition which we use to investigate the participation ratio xi(2) and the information entropy S(info) during this crossover, thereby extending the known behavior valid in the Gaussian domain into much of the Breit-Wigner domain. Our method also allows us to derive the scaling law lambda(d) approximately 1/sqrt[m] ( m is number of fermions) for the duality point lambda= lambda(d), where F(k) (E), xi(2), and S(info) in both the weak ( lambda=0 ) and strong mixing ( lambda= infinity ) basis coincide. As an application, the ansatz function for strength functions is used in describing the Breit-Wigner to Gaussian transition seen in neutral atoms CeI to SmI with valence electrons changing from 4 to 8.