Higher-order solutions to non-Markovian quantum dynamics via hierarchical functional derivative

Solving realistic quantum systems coupled to an environment is a challenging task. Here we develop a hierarchical functional derivative (HFD) approach for efficiently solving the non-Markovian quantum trajectories of an open quantum system embedded in a bosonic bath. An explicit expression for arbitrary order HFD equation is derived systematically. Moreover, it is found that for an analytically solvable model, this hierarchical equation naturally terminates at a given order and thus becomes exactly solvable. This HFD approach provides a systematic method to study the non-Markovian quantum dynamics of an open system coupled to a bosonic environment.Comment: 5 pages, 2 figure

Dynamical invariants in non-Markovian quantum state diffusion equation

We find dynamical invariants for open quantum systems described by the non-Markovian quantum state diffusion (QSD) equation. In stark contrast to closed systems where the dynamical invariant can be identical to the system density operator, these dynamical invariants no longer share the equation of motion for the density operator. Moreover, the invariants obtained with from bi-orthonormal basis can be used to render an exact solution to the QSD equation and the corresponding non-Markovian dynamics without using master equations or numerical simulations. Significantly we show that we can apply these dynamic invariants to reverse-engineering a Hamiltonian that is capable of driving the system to the target state, providing a novel way to design control strategy for open quantum systems.Comment: 6 pages, 2 figure

Diaqua­bis(N,N′-dibenzyl­ethane-1,2-diamine-κ2 N,N′)nickel(II) dichloride N,N-dimethyl­formamide solvate

The asymmetric unit of the title complex, [Ni(C16H20N2)2(H2O)2]Cl2·C3H7NO, consists of two NiII atoms, each lying on an inversion center, two Cl anions, two N,N′-dibenzyl­ethane-1,2-diamine ligands, two coordinated water mol­ecules and one N,N-dimethyl­formamide solvent mol­ecule. Each NiII atom is six-coordinated in a distorted octa­hedral coordination geometry, with the equatorial plane formed by four N atoms and the axial positions occupied by two water mol­ecules. The complex mol­ecules are linked into a chain along [001] by N—H⋯Cl, N—H⋯O and O—H⋯Cl hydrogen bonds. The C atoms and H atoms of the solvent mol­ecule are disordered over two sites in a ratio of 0.52 (2):0.48 (2)

Tetra­kis(μ-naphthalene-1-acetato-1:2κ2 O:O′)bis­(naphthalene-1-acetato)-1κ2 O,O′;2κ2 O,O′-bis­(1,10-phenanthroline)-1κ2 N,N′;2κ2 N,N′-europium(III)samarium(III)

In the title compound, [EuSm(C12H9O2)6(C12H8N2)2], the metal site is statistically occupied (50:50) by Eu and Sm atoms, forming a centrosymmetric complex. The metal site is nine-coordinate, in a distorted monocapped square-anti­prismatic coordination geometry. Mol­ecules are linked into three chains by C—H⋯π interactions and C—H⋯O hydrogen bonds. The combination of these chains generates a three-dimensional framework structure. One of the bridging naphthalene-1-ace­tate ligands was found to be disordered over two sites; the site occupancies for the naphthylmethyl group refined to 0.628 (14) and 0.372 (14)

Poly[(N,N-dimethyl­formamide-κO)tris­(μ-naphthalene-1-acetato)terbium(III)]

In title compound, [Tb(C12H9O2)3(C3H7NO)]n, the Tb atom is nine-coordinated by nine O atoms from three naphthalene-1-acetate and one N,N-dimethyl­formamide ligands. The Tb atoms are linked by three bridging naphthalene-1-acetate ligands into a chain parallel to the b axis. Further stabilization of the structure is accomplished by non-classical C—H⋯O hydrogen bonds and C—H⋯π interactions

N-Benzyl-2-propynamide

Pale-yellow crystals of the title compound, C10H9NO, have been obtained by the reaction of benzyl­amine and methyl propiolate. Weak inter­molecular hydrogen bonding is observed between acetyl­enic H and carbonyl O atoms. The crystal packing is stabilized by these C—H⋯O and by N—H⋯O inter­molecular hydrogen-bonding inter­actions

Optical and Gamma-Ray Variability Behaviors of 3C 454.3 from 2006 to 2011

We present our photometric monitoring of a flat spectrum radio quasar (FSRQ) 3C 454.3 at Yunnan observatories from 2006 to 2011. We find that the optical color of 3C 454.3 shows obvious redder-when-brighter trend, which reaches a saturation stage when the source is brighter than 15.15 mag at V band. We perform a simulation with multiple values of disk luminosity and spectral index to reproduce the magnitude-color diagram. The results show that the contamination caused by the disk radiation alone is difficult to produce the observed color variability. The variability properties during the outburst in December 2009 are also compared with $\gamma$-ray data derived from Fermi $\gamma$-ray space telescope. The flux variation of these two bands follow a linear relation with $F_{\gamma} \propto F_R^{1.14\pm0.07}$, which provides an observational evidence for external Compton process in 3C 454.3. Meanwhile, this flux correlation indicates that electron injection is the main mechanism for variability origin. We also explore the variation of the flux ratio $F_{\gamma}/F_R$ and the detailed structures in the lightcurves, and discuss some possible origins for the detailed variability behaviors.Comment: accepted for publication in The Astrophysical Journal, 5 figures, 2 table