Thermal Entanglement between Alternate Qubits of a Four-qubit Heisenberg XX Chain in a Magnetic Field

The concurrence of two alternate qubits in a four-qubit Heisenberg XX chain is investigated when a uniform magnetic field B is included. It is found that there is no thermal entanglement between alternate qubits if B is close to zero. Magnetic field can induce entanglement in a certain range both for the antiferromagnetic and ferromagnetic cases. Near zero temperature, the entanglement undergoes two sudden changes with increasing value of the magnetic field B. This is due to the changes in the ground state. This novel property may be used as quantum entanglement switch. The anisotropy in the system can also induce the entanglement between two alternate qubits.Comment: 10 pages, 3 figure

Some recent developments in quantization of fractal measures

We give an overview on the quantization problem for fractal measures, including some related results and methods which have been developed in the last decades. Based on the work of Graf and Luschgy, we propose a three-step procedure to estimate the quantization errors. We survey some recent progress, which makes use of this procedure, including the quantization for self-affine measures, Markov-type measures on graph-directed fractals, and product measures on multiscale Moran sets. Several open problems are mentioned.Comment: 13 page

Reconstruction with velocities

Reconstruction is becoming a crucial procedure of galaxy clustering analysis for future spectroscopic redshift surveys to obtain subper cent level measurement of the baryon acoustic oscillation scale. Most reconstruction algorithms rely on an estimation of the displacement field from the observed galaxy distribution. However, the displacement reconstruction degrades near the survey boundary due to incomplete data and the boundary effects extend to ∼100 Mpc/h within the interior of the survey volume. We study the possibility of using radial velocities measured from the cosmic microwave background observation through the kinematic Sunyaev-Zeldovich effect to improve performance near the boundary. We find that the boundary effect can be reduced to ∼30 − 40 Mpc/h with the velocity information from Simons Observatory. This is especially helpful for dense low redshift surveys where the volume is relatively small and a large fraction of total volume is affected by the boundary

Gravitational Lensing Statistics as a Probe of Dark Energy

By using the comoving distance, we derive an analytic expression for the optical depth of gravitational lensing, which depends on the redshift to the source and the cosmological model characterized by the cosmic mass density parameter $\Omega_m$, the dark energy density parameter $\Omega_x$ and its equation of state $\omega_x = p_x/\rho_x$. It is shown that, the larger the dark energy density is and the more negative its pressure is, the higher the gravitational lensing probability is. This fact can provide an independent constraint for dark energy.Comment: 9 pages, 2 figure

Pump induced Autler-Townes effect and A-T mixing in a four level atoms

It is shown by theoretical simulation that tuning of the pump power can induce mixing and crossing of Autler-Townes(A-T)components of closely spaced transitions in atoms. Pump radiation also leads to small shifts of the central hole of A-T doublet. Off-resonance pumping gives an asymmetry in the A-T components and by controlling pump frequency detuning it is also possible to mix the A-T components.Comment: 10 Pages, 3 figur