Ground and Low-Lying Collective States of Rotating Three-Boson System

The ground and low-lying collective states of a rotating system of N=3 bosons harmonically confined in quasi-two-dimension and interacting via repulsive finite-range Gaussian potential is studied in weakly to moderately interacting regime.The N-body Hamiltonian matrix is diagonalized in subspaces of quantized total angular momenta 0 ≤ L ≤ 4N to obtain the ground and low-lying eigenstates.Our numerical results show that breathing modes with N-body eigenenergy spacing of 2hω⊥,known to exist in strictly 2D system with zero-range(δ-function) interaction potential,may as well exist in quasi-2D system with finite-range Gaussian interaction potential.To gain an insight into the many-body states,the von Neumann entropy is calculated as a measure of quantum correlation and the conditional probability distribution is analyzed for the internal structure of the eigenstates.In the rapidly rotating regime the ground state in angular momentum subspaces L=(q/2)N(N-1) with q=2,4 is found to exhibit the anticorrelation structure suggesting that it may variationally be described by a Bose–Laughlin like state.We further observe that the first breathing mode exhibits features similar to the Bose–Laughlin state in having eigenenergy,von Neumann entropy and internal structure independent of interaction for the three-boson system considered here.On the contrary,for eigenstates lying between the Bose–Laughlin like ground state and the first breathing mode,values of eigenenergy,von Neumann entropy and internal structure are found to vary with interaction.     

Preparation and characterization of HypoGel-supported Pd nanocatalysts for Suzuki reaction under mild conditions

A new heterogeneous catalyst composed of Pd nanoparticles immobilized within a HypoGel resin has been prepared in the absence of any ligands using an extensive cross-linking method. This new-ly develop...