Recent relativistic coupled-cluster (RCC) calculations of electric dipole moments (EDMs) of diamagnetic atoms due to parity and time-reversal violating ($P,T$-odd) interactions, which are essential ingredients for probing new physics beyond the standard model of particle interactions, differ substantially from the previous theoretical results. It is therefore necessary to perform an independent test of the validity of these results. In view of this, the normal coupled-cluster method has been extended to the relativistic regime [relativistic normal coupled-cluster (RNCC) method] to calculate the EDMs of atoms by simultaneously incorporating the electrostatic and $P,T$-odd interactions in order to overcome the shortcomings of the ordinary RCC method. This new relativistic method has been applied to ${}^{199}\mathrm{Hg}$, which currently has a lower EDM limit than that of any other system. The results of our RNCC and self-consistent RCC calculations of the EDM of this atom are found to be close. The discrepancies between these two results on the one hand and those of previous calculations on the other are elucidated. Furthermore, the electric dipole polarizability of this atom, which has computational similarities with the EDM, is evaluated and it is in very good agreement with its measured value.

Lifetimes of the $6d{}^{2}D_{3/2}$ and $6d{}^{2}D_{5/2}$ states in Fr are determined from calculations of the radiative transition amplitudes of the allowed electric dipole $\left(E1\right)$ and the forbidden electric quadrupole $\left(E2\right)$ and magnetic dipole $\left(M1\right)$ channels which were performed using the second-order many-body perturbation theory and the coupled-cluster method at different levels of approximations in the relativistic framework. The values obtained for these two quantities are 540(10) and 1704(32) ns, respectively. These relatively long lifetimes and the large electric dipole parity-non-conserving amplitudes of $7s{}^{2}S_{1/2}\to 6d{}^{2}D_{3/2,5/2}$ transitions strongly favor Fr as a leading candidate for the measurement of parity nonconservation arising from the neutral-current weak interaction and the nuclear anapole moment. In another important application, these $6D$ states in Fr can be used efficiently for resonance ionization spectroscopic techniques to carry out precise measurements of the properties of the higher excited states due to the long lifetimes of these states.

Employing the relativistic coupled-cluster method, comparative studies of the parity nonconserving electric dipole amplitudes for the $7s{}^{2}S_{1/2}\to 6d{}^{2}D_{5/2}$ transitions in ${}^{210}\mathrm{Fr}$ and ${}^{211}\mathrm{Fr}$ isotopes have been carried out. It is found that these transition amplitudes, sensitive only to the nuclear spin-dependent effects, are enhanced substantially owing to the very large contributions from the electron core-polarization effects in Fr. This translates to a relatively large and, in principle, measurable induced light shift, which would be a signature of nuclear spin-dependent parity nonconservation that is dominated by the nuclear anapole moment in a heavy atom like Fr. A plausible scheme to measure this quantity using the Cyclotron and Radioisotope Center (CYRIC) facility at Tohoku University has been outlined.

We investigate the two-component quantum walk in one-dimensional lattice. We show that the inter-component interaction strength together with the hopping imbalance between the components exhibit distinct features in the quantum walk for different initial states. When the walkers are initially on the same site, both the slow and fast particles perform independent particle quantum walks when the interaction between them is weak. However, stronger inter-particle interactions result in quantum walks by the repulsively bound pair formed between the two particles. For different initial states when the walkers are on different sites initially, the quantum walk performed by the slow particle is almost independent of that of the fast particle, which exhibits reflected and transmitted components across the particle with large hopping strength for weak interactions. Beyond a critical value of the interaction strength, the wave function of the fast particle ceases to penetrate through the slow particle signalling a spatial phase separation. However, when the two particles are initially at the two opposite edges of the lattice, then the interaction facilitates the complete reflection of both of them from each other. We analyze the above mentioned features by examining various physical quantities such as the on-site density evolution, two-particle correlation functions and transmission coefficients.

In search of suitable molecular candidates for probing the electric dipole moment (EDM) of the electron ($d_e$), a property that arises due to parity and time-reversal violating (P,T-odd) interactions, we consider the triatomic mercury hydroxide (HgOH) molecule. The impetus for this proposal is based on previous works on two systems: the recently proposed ytterbium hydroxide (YbOH) experiment that demonstrates the advantages of polyatomics for such EDM searches, and the finding that mercury halides provide the highest enhancement due to $d_e$ compared to other diatomic molecules. We identify the ground state of HgOH as being in a bent geometry, and show that its intrinsic EDM sensitivity is comparable to the corresponding value for YbOH. Along with the theoretical results, we discuss plausible experimental schemes for an EDM measurement in HgOH. Furthermore, we provide pilot calculations of the EDM sensitivity for $d_e$ for HgCH${}_3$ and HgCF${}_3$, that are natural extensions of HgOH.