We have studied the squeezing properties of arbitrary numbers of superpositions of various squeezed states such as squeezed vacuum state, photon-added coherent states, and two mode squeezed vacuum state. We have considered two superpositions: the first kind and the second kind. In the case of the first kind, the superpositions of squeezed states do not show both squeezing and higher-order squeezing of all orders. This is found to be true for any state which has quadrature squeezing and multi-mode squeezed states.

The dynamics of quantum systems play an essential role in quantum information processing and computing. We have studied the dynamics of superposition of wavepackets evolving under different nonlinear Hamiltonians corresponding to Kerr medium, Morse oscillator, and bosonic Josephson junction. We have shown that quantum systems' periodic, quasi-periodic, ergodic, and chaotic dynamics can change drastically if we change just the initial state to its superposition by keeping all other system parameters the same.

[Funded by SERB: Govt. of India: 2016-2019; Project Investigator - S. Jayanthi]

We investigate in detail the underlying spin-dynamics associated with time-dependent Hamiltonians by developing theoretical models in complex spin systems (1H-14N, 1H-35Cl etc.). In a recent work, published in Journal of Magnetic Resonance we employed matrix logarithm and Floquet theory to compute numerically the effective Hamiltonian associated to a time-dependent problem in solid state Nuclear Magnetic Resonance, Cross-Polarization under fast Magic Angle Spinning (MAS) and Double Cross Polarization under fast MAS.

In this work, a novel experiment using selective longitudinal Cross Polarization is proposed and demonstrated that enhances the sensitivity and resolution of homonuclear NOESY correlations by targeting selected 1H–15N spin pairs.The enhanced signal sensitivity (~ 2-5) as well as access to both 15N–1H and 1H–1H NOESY dimensions can greatly facilitate RNA assignments and secondary structure determinations, as demonstrated with the analysis of genome fragments derived from the SARS-CoV-2 virus.

Improvement of heteronuclear transfers through J-driven cross polarization (J-CP), which transfers polarization by spin-locking the coupled spins under Hartmann-Hahn conditions. J-CP provides certain immunity against chemical exchange and other T2-like relaxation effects, a behavior that is examined in depth by both Liouville-space numerical and analytical derivations describing the transfer efficiency.

Figure: Numerical vs analytical solutions for J-CP as a function of contact time.

A way to obtain artifact-free correlations between labile sites as well as between labile and non-labile sites – the extended Hadamard scheme, and its performance corroborated with a series of RNA-based measurements in SARS-CoV2 RNA Fragments.

The onset of turbulence is often related to the randomness of background movement, for instance, structural vibrations, magnetic fields, and other environmental disturbances. One way to model this is to consider randomly forced Navier-Stokes equations. The stochastic forcing that is added to the deterministic Navier-Stokes equation models the influence of the random environment on the fluid in fully developed turbulence.

The graph embedding is the process of representing the graph in a vector space using properties of the graphs. The existing graph embeddings rely mostly on a single property of graphs for data representation which is found to be inappropriate to capture all the characteristics of the data. Hence we designed graph embedding using multi-view approach, where each view is an embedding of the graph using a graph property. The input space of multi-view learning is then taken as the direct sum of the subspaces in which the graph embedding lie.

A problem in affine algebraic geometry asks the following.

Problem 1. Let R be a ring containing Q, A an A2-fibration over R and D : A → A a fixed point free R-LND. Does D have a slice?