Loss of purity by wave packet scattering at low energies

We study the quantum entanglement produced by a head-on collision between two gaussian wave packets in three-dimensional space. By deriving the two-particle wave function modified by s-wave scattering amplitudes, we obtain an approximate analytic expression of the purity of an individual particle. The loss of purity provides an indicator of the degree of entanglement. In the case the wave packets are narrow in momentum space, we show that the loss of purity is solely controlled by the ratio of the scattering cross section to the transverse area of the wave packets.Comment: 7 pages, 1 figur

S-wave quantum entanglement in a harmonic trap

We analyze the quantum entanglement between two interacting atoms trapped in a spherical harmonic potential. At ultra-cold temperature, ground state entanglement is generated by the dominated s-wave interaction. Based on a regularized pseudo-potential Hamiltonian, we examine the quantum entanglement by performing the Schmidt decomposition of low-energy eigenfunctions. We indicate how the atoms are paired and quantify the entanglement as a function of a modified s-wave scattering length inside the trap.Comment: 10 pages, 5 figures, to be apear in PR

Comment on "Position-dependent effective mass Dirac equations with PT- symmetric and non - PT- symmetric potentials" [J. Phys. A: Math. Gen. 39 (2006) 11877--11887]

Jia and Dutra (J. Phys. A: Math. Gen. 39 (2006) 11877) have considered the one-dimensional non-Hermitian complexified potentials with real spectra in the context of position-dependent mass in Dirac equation. In their second example, a smooth step shape mass distribution is considered and a non-Hermitian non - PT- symmetric Lorentz vector potential is obtained. They have mapped this problem into an exactly solvable Rosen-Morse Schrodinger model and claimed that the energy spectrum is real. The energy spectrum they have reported is pure imaginary or at best forms an empty set. Their claim on the reality of the energy spectrum is fragile, therefore.Comment: 3 pages, 1 figure. To appear in J. Phys.

Pass-back chain extension expands multimodular assembly line biosynthesis.

Modular nonribosomal peptide synthetase (NRPS) and polyketide synthase (PKS) enzymatic assembly lines are large and dynamic protein machines that generally effect a linear sequence of catalytic cycles. Here, we report the heterologous reconstitution and comprehensive characterization of two hybrid NRPS-PKS assembly lines that defy many standard rules of assembly line biosynthesis to generate a large combinatorial library of cyclic lipodepsipeptide protease inhibitors called thalassospiramides. We generate a series of precise domain-inactivating mutations in thalassospiramide assembly lines, and present evidence for an unprecedented biosynthetic model that invokes intermodule substrate activation and tailoring, module skipping and pass-back chain extension, whereby the ability to pass the growing chain back to a preceding module is flexible and substrate driven. Expanding bidirectional intermodule domain interactions could represent a viable mechanism for generating chemical diversity without increasing the size of biosynthetic assembly lines and challenges our understanding of the potential elasticity of multimodular megaenzymes