The rank of variants of nilpotent pseudovarieties

We investigate the rank of pseudovarieties defined by several of the variants of nilpotency conditions for semigroups in the sense of Mal'cev. For several of them, we provide finite bases of pseudoidentities. We also show that the Neumann-Taylor variant does not have finite rank.Comment: 41 page

Generating quantum discord between two distant Bose-Einstein condensates with Bell-like detection

We propose a technique that enables the creation of quantum discord between two distant nodes, each containing a cavity consist of the Bose-Einstein condensate, by applying a non-ideal Bell-like detection on the output modes of optical cavities. We find the covariance matrix of the system after the non-ideal Bell-like detection, showing explicitly that one enables manipulation of the quantum correlations, and particularly quantum discord, between remote Bose-Einstein condensates. We also find that the non-ideal Bell-like detection can create entanglement between distant Bose-Einstein condensates at the two remote site

Cooling of a Nanomechanical Resonator in the Presence of a Single Diatomic Molecule

We propose a theoretical scheme for coupling a nanomechanical resonator to a single diatomic molecule via microwave cavity mode of a driven LC resonator. We describe the diatomic molecule by a Morse potential and find the corresponding equations of motion of the hybrid system by using Fokker-Planck formalism. Analytical expressions for the effective frequency and the effective damping of the nanomechanical resonator are obtained. We analyze the ground state cooling of the nanomechanical resonator in presence of the diatomic molecule. The results confirm that presence of the molecule improves the cooling process of the mechanical resonator. Finally, the effect of molecule's parameters on the cooling mechanism is studied.Comment: 10 pages, 8 figure

Shear viscosity of the A_1-phase of superfluid 3He

The scattering processes between the quasiparticles in spin- up superfluid with the quasiparticles in spin-down normal fluid are added to the other relevant scattering processes in the Boltzmann collision terms. The Boltzmann equation has been solved exactly for temperatures just below T_c_1. The shear viscosity component of the A_1- phase drops as C_1(1-T/T_c_1)^(1/2). The numerical factor C_1 is in fairly good agreement with the experiments