Definition 1. Given a vector |v〉 ∈ H, by a Schmidt decomposition across the (i, i + 1) cut we shall mean a decomposition |v〉 = ∑j=1 λj|aj〉|bj〉 with {|aj〉} (respectively {|bj〉} ) a family of orthonormal vectors of H[1,i] (respectively H[i+1,n]) and with λj ≥ λj+1 > 0 for all 1 ≤ j ≤ D. The vectors |aj〉 will be called the left Schmidt vectors across that cut, and the vectors |bj〉 the right Schmid...

Orientation states of two coupled polar molecules controlled by laser pulses are studied theoretically. By varying the period of a series of periodically applied laser pulse, transition from regular to chaotic behavior may occur. Schmidt decomposition is used to measure the degree of entanglement. It is found that the entanglement can be enhanced by increasing the strength of laser pulse. PACS:...

Entanglement is defined for each vector subspace of the tensor product of two finite-dimensional Hilbert spaces, by applying the notion of operator entanglement to the projection operator onto that subspace. The operator Schmidt decomposition of the projection operator defines a string of Schmidt coefficients for each subspace, and this string is assumed to characterize its entanglement, so tha...

The Lagrangian spectral relaxation ~LSR! model is extended to treat turbulent mixing of two passive scalars (fa and fb) with different molecular diffusivity coefficients ~i.e., differential-diffusion effects!. Because of the multiscale description employed in the LSR model, the scale dependence of differential-diffusion effects is described explicitly, including the generation of scalar decorre...