On the origin of kinematic distribution of the sub-parsec young stars in the Galactic center

Within a half-parsec from the Galactic center (GC), there is a population of coeval young stars which appear to reside in a coherent disk. Surrounding this dynamically-cool stellar system, there is a population of stars with a similar age and much larger eccentricities and inclinations relative to the disk. We propose a hypothesis for the origin of this dynamical dichotomy. Without specifying any specific mechanism, we consider the possibility that both stellar populations were formed within a disk some 6 Myr ago. But this orderly structure was dynamically perturbed outside-in by an intruding object with a mass ~10^4 Msun, which may be an intermediate-mass black hole (IMBH) or a dark stellar cluster hosting an IMBH. We suggest that the perturber migrated inward to ~0.15-0.3pc from the GC under the action of dynamical friction. Along the way, it captured many stars in the outer disk region into its mean-motion resonance, forced them to migrate with it, closely encountered with them, and induced the growth of their eccentricity and inclination. But stars in the inner regions of the disk retain their initial coplanar structure. We predict that some of the inclined and eccentric stars surrounding the disk may have similar Galactocentric semimajor axis. Future precision determination of their kinematic distribution of these stars will not only provide a test for this hypothesis but also evidences for the presence of an IMBH or a dark cluster at the immediate proximity of the massive black hole at the GC. (abridged)Comment: 14 pages, including 13 figures, typo corrected, reference added, ApJ in pres

Accurate numerical solution to the finite-size Dicke model

By using extended bosonic coherent states, a new technique to solve the Dicke model exactly is proposed in the numerical sense. The accessible system size is two orders of magnitude higher than that reported in literature. Finite-size scaling for several observables, such as the ground-state energy, Berry phase, and concurrence are analyzed. The existing discrepancy for the scaling exponent of the concurrence is reconciled.Comment: 4 pages, 5 figures. Phys. Rev. A (in press, a Rapid Communication

Path integral Monte Carlo study of the interacting quantum double-well model: Quantum phase transition and phase diagram

The discrete time path integral Monte Carlo (PIMC) with a one-particle density matrix approximation is applied to study the quantum phase transition in the coupled double-well chain. To improve the convergence properties, the exact action for a single particle in a double well potential is used to construct the many-particle action. The algorithm is applied to the interacting quantum double-well chain for which the zero-temperature phase diagram is determined. The quantum phase transition is studied via finite-size scaling and the critical exponents are shown to be compatible with the classical two-dimensional (2D) Ising universality class -- not only in the order-disorder limit (deep potential wells) but also in the displacive regime (shallow potential wells).Comment: 17 pages, 7 figures; Accepted for publication in Phys. Rev.

Multipartite Entanglement Measures and Quantum Criticality from Matrix and Tensor Product States

We compute the multipartite entanglement measures such as the global entanglement of various one- and two-dimensional quantum systems to probe the quantum criticality based on the matrix and tensor product states (MPSs/TPSs). We use infinite time-evolving block decimation (iTEBD) method to find the ground states numerically in the form of MPSs/TPSs, and then evaluate their entanglement measures by the method of tensor renormalization group (TRG). We find these entanglement measures can characterize the quantum phase transitions by their derivative discontinuity right at the critical points in all models considered here. We also comment on the scaling behaviors of the entanglement measures by the ideas of quantum state renormalization group transformations.Comment: 22 pages, 11 figure

Perturbation theorems for Hele-Shaw flows and their applications

In this work, we give a perturbation theorem for strong polynomial solutions to the zero surface tension Hele-Shaw equation driven by injection or suction, so called the Polubarinova-Galin equation. This theorem enables us to explore properties of solutions with initial functions close to but are not polynomial. Applications of this theorem are given in the suction or injection case. In the former case, we show that if the initial domain is close to a disk, most of fluid will be sucked before the strong solution blows up. In the later case, we obtain precise large-time rescaling behaviors for large data to Hele-Shaw flows in terms of invariant Richardson complex moments. This rescaling behavior result generalizes a recent result regarding large-time rescaling behavior for small data in terms of moments. As a byproduct of a theorem in this paper, a short proof of existence and uniqueness of strong solutions to the Polubarinova-Galin equation is given.Comment: 25 page