Exact quantum dynamics of XXZ central spin problems

We obtain analytically close forms of benchmark quantum dynamics of the collapse and revival (CR), reduced density matrix, Von Neumann entropy, and fidelity for the XXZ central spin problem. These quantities characterize the quantum decoherence and entanglement of the system with few to many bath spins, and for a short to infinitely long time evolution. For the homogeneous central spin problem, the effective magnetic field $B$, coupling constant $A$ and longitudinal interaction $\Delta$ significantly influence the time scales of the quantum dynamics of the central spin and the bath, providing a tunable resource for quantum metrology. Under the resonance condition $B=\Delta=A$, the location of the $m$-th revival peak in time reaches a simple relation $t_{r} \simeq\frac{\pi N}{A} m$ for a large $N$. For $\Delta =0$, $N\to \infty$ and a small polarization in the initial spin coherent state, our analytical result for the CR recovers the known expression found in the Jaynes-Cummings model, thus building up an exact dynamical connection between the central spin problems and the light-matter interacting systems in quantum nonlinear optics. In addition, the CR dynamics is robust to a moderate inhomogeneity of the coupling amplitudes, while disappearing at strong inhomogeneity.Comment: added new result on inhomogeneous central spin problem and added new references and supplementary material, 6 pages + 15 pages; 4 figures + 14 figure

Universal Properties of Fermi Gases in One-dimension

In this Rapid Communication, we investigate the universal properties of a spin-polarized two-component Fermi gas in one dimension (1D) using Bethe ansatz. We discuss the quantum phases and phase transitions by obtaining exact results for the equation of state, the contact, the magnetic susceptibility and the contact susceptibility, giving a precise understanding of the 1D analogue of the Bose-Einstein condensation and Bardeen-Cooper-Schrieffer crossover in three dimension (3D) and the associated universal magnetic properties. In particular, we obtain the exact form of the magnetic susceptibility $\chi \sim {1}/{\sqrt{T}}\exp(-\Delta/T)$ at low temperatures, where $\Delta$ is the energy gap and $T$ is the temperature. Moreover, we establish exact upper and lower bounds for the relation between polarization $P$ and the contact $C$ for both repulsive and attractive Fermi gases. Our findings emphasize the role of the pair fluctuations in strongly interacting 1D fermion systems that can shed light on higher dimensions.Comment: 4 figures, the main pape

Multiple positive solutions for functional dynamic equations on time scales

AbstractIn this paper, we study the following functional dynamic equation on time scales: {[Φ(uΔ(t))]∇+a(t)f(u(t),u(μ(t)))=0,t∈(0,T)T,u(t)=φ(t),t∈[−r,0)T,u(0)−B0(uΔ(0))=0,uΔ(T)=0, where Φ:R→R is an increasing homeomorphism and a positive homomorphism and Φ(0)=0. By using the well-known Leggett–Williams fixed point theorem, existence criteria for multiple positive solutions are established. An example is also given to illustrate the main results

Positive Solutions for Third-Order p

We study the following third-order p-Laplacian functional dynamic equation on time scales: Φp(uΔ∇(t))∇+a(t)f(u(t),u(μ(t)))=0, t∈0,TT,  u(t)=φ(t),  t∈-r,0T,  uΔ(0)=uΔ∇(T)=0, and u(T)+B0(uΔ(η))=0. By applying the Five-Functional Fixed Point Theorem, the existence criteria of three positive solutions are established

N-Phenyl­anthranilic anhydride

The complete mol­ecule of the title compound, C26H20N2O3, is generated by crystallographic twofold symmetry, with the central O atom lying on the rotation axis. The conformation is stabilized by an intra­molecular N—H⋯O hydrogen bond. The dihedral angle between the inner and outer aromatic ring planes is 61.12 (5)°

Effects of triazolodiazepine on the production of interleukin-6 from murine spleen cells and rabbit synovial cells in vitro

Interleukin-6 (IL-6) is a multifunctional cytokine that regulates the immune response, acute phase anaphylactic reaction, and haematopoiesis. Lipopolysaccharide (6–24 μg/ml) significantly induced IL-6 release from murine spleen cells. In cultured rabbit synovial cells interleukin-1 (IL-1, 1–10 U/ml) induced IL-6 production in a concentration-dependent manner. Triazolodiazepine (Tri) is a hetrazepine platelet-activating factor antagonist. In this study we found that Tri (0.1–10 μmol/l) exerted strong inhibitory effects on LPS stimulated IL-6 production in murine spleen cells. Kinetic studies showed that the inhibition of IL-6 release was time-independent. In rabbit synovial cells Tri also reduced IL-6 release induced by IL-1 and tumour necrosis factor. Inhibition of cytokine production by Tri may partially explain its wide and strong anti-inflammatory effects