Research Progress on Ni-Based Antiperovskite Compounds

The superconductivity in antiperovskite compound MgCNi3 was discovered in 2001 following the discovery of the superconducting MgB2. In spite of its lower superconducting transition temperature (8 K) than MgB2 (39 K), MgCNi3 has attracted considerable attention due to its high content of magnetic element Ni and the cubic structure analogous to the perovskite cuprates. After years of extensive investigations both theoretically and experimentally, however, it is still not clear whether the mechanism for superconductivity is conventional or not. The central issue is if and how the ferromagnetic spin fluctuations contribute to the cooper paring. Recently, the experimental results on the single crystals firstly reported in 2007 trend to indicate a conventional s-wave mechanism. Meanwhile many compounds neighboring to MgCNi3 were synthesized and the physical properties were investigated, which enriches the physics of the Ni-based antiperovskite compounds and help understand the superconductivity in MgCNi3. In this paper, we summarize the research progress in these two aspects. Moreover, a universal phase diagram of these compounds is presented, which suggests a phonon-mediated mechanism for the superconductivity, as well as a clue for searching new superconductors with the antiperovskite structure. Finally, a few possible scopes for future research are proposed

Geometric vs. Dynamical Gates in Quantum Computing Implementations Using Zeeman and Heisenberg Hamiltonians

Quantum computing in terms of geometric phases, i.e. Berry or Aharonov-Anandan phases, is fault-tolerant to a certain degree. We examine its implementation based on Zeeman coupling with a rotating field and isotropic Heisenberg interaction, which describe NMR and can also be realized in quantum dots and cold atoms. Using a novel physical representation of the qubit basis states, we construct $\pi/8$ and Hadamard gates based on Berry and Aharonov-Anandan phases. For two interacting qubits in a rotating field, we find that it is always impossible to construct a two-qubit gate based on Berry phases, or based on Aharonov-Anandan phases when the gyromagnetic ratios of the two qubits are equal. In implementing a universal set of quantum gates, one may combine geometric $\pi/8$ and Hadamard gates and dynamical $\sqrt{\rm SWAP}$ gate.Comment: published version, 5 page

Geometric, Variational Integrators for Computer Animation

We present a general-purpose numerical scheme for time integration of Lagrangian dynamical systems—an important computational tool at the core of most physics-based animation techniques. Several features make this particular time integrator highly desirable for computer animation: it numerically preserves important invariants, such as linear and angular momenta; the symplectic nature of the integrator also guarantees a correct energy behavior, even when dissipation and external forces are added; holonomic constraints can also be enforced quite simply; finally, our simple methodology allows for the design of high-order accurate schemes if needed. Two key properties set the method apart from earlier approaches. First, the nonlinear equations that must be solved during an update step are replaced by a minimization of a novel functional, speeding up time stepping by more than a factor of two in practice. Second, the formulation introduces additional variables that provide key flexibility in the implementation of the method. These properties are achieved using a discrete form of a general variational principle called the Pontryagin-Hamilton principle, expressing time integration in a geometric manner. We demonstrate the applicability of our integrators to the simulation of non-linear elasticity with implementation details

Discrete Lie Advection of Differential Forms

In this paper, we present a numerical technique for performing Lie advection of arbitrary differential forms. Leveraging advances in high-resolution finite volume methods for scalar hyperbolic conservation laws, we first discretize the interior product (also called contraction) through integrals over Eulerian approximations of extrusions. This, along with Cartan's homotopy formula and a discrete exterior derivative, can then be used to derive a discrete Lie derivative. The usefulness of this operator is demonstrated through the numerical advection of scalar fields and 1-forms on regular grids.Comment: Accepted version; to be published in J. FoC