Finding Exponential Product Formulas of Higher Orders

In the present article, we review a continual effort on generalization of the Trotter formula to higher-order exponential product formulas. The exponential product formula is a good and useful approximant, particularly because it conserves important symmetries of the system dynamics. We focuse on two algorithms of constructing higher-order exponential product formulas. The first is the fractal decomposition, where we construct higher-order formulas recursively. The second is to make use of the quantum analysis, where we compute higher-order correction terms directly. As interludes, we also have described the decomposition of symplectic integrators, the approximation of time-ordered exponentials, and the perturbational composition.Comment: 22 pages, 9 figures. To be published in the conference proceedings ''Quantum Annealing and Other Optimization Methods," eds. B.K.Chakrabarti and A.Das (Springer, Heidelberg

Recent trends and theoretical background in sintering of silicon carbide ceramics

This article gives an outline of sintering techniques of silicon carbide and refers to recent developments. These techniques are also applicable to other oxides with a high melting point and particularly high sinterability, namely MgO and BeO

Absorption Probability of De Sitter Horizon for Massless Fields with Spin

The evaluation of the absorption coefficients are important for particle emission caused by Hawking radiation. In the case of cosmological particle emission from the event horizon in De Sitter space, it is known that the scalar wave functions are solved in terms of Legendre functions. For fields with higher spin, the solution has been examined with low frequency approximation. We shows that the radial equations of the fields with spin $0,1/2,1$ and $2$ can be solved analytically in terms of the hypergeometric functions. We calculate the absorption probability using asymptotic expansion for high frequency limit. It turns out that the absorption coefficients are universal to all bosonic fields; They depend only on the angular momentum and not spin. In the case of spin $1/2$ fermions, we can also find non-vanishing absorption probability in contrast to the previously known result.Comment: 7 pages, Late

QCD Phase Transition at Finite Temperature in the Dual Ginzburg-Landau Theory

We study the pure-gauge QCD phase transition at finite temperatures in the dual Ginzburg-Landau theory, an effective theory of QCD based on the dual Higgs mechanism. We formulate the effective potential at various temperatures by introducing the quadratic source term, which is a new useful method to obtain the effective potential in the negative-curvature region. Thermal effects reduce the QCD-monopole condensate and bring a first-order deconfinement phase transition. We find a large reduction of the self-interaction among QCD-monopoles and the glueball masses near the critical temperature by considering the temperature dependence of the self-interaction. We also calculate the string tension at finite temperatures.Comment: 13 pages, uses PHYZZX ( 5 figures - available on request from [email protected]

Fast and stable method for simulating quantum electron dynamics

A fast and stable method is formulated to compute the time evolution of a wavefunction by numerically solving the time-dependent Schr{\"o}dinger equation. This method is a real space/real time evolution method implemented by several computational techniques such as Suzuki's exponential product, Cayley's form, the finite differential method and an operator named adhesive operator. This method conserves the norm of the wavefunction, manages periodic conditions and adaptive mesh refinement technique, and is suitable for vector- and parallel-type supercomputers. Applying this method to some simple electron dynamics, we confirmed the efficiency and accuracy of the method for simulating fast time-dependent quantum phenomena.Comment: 10 pages, 35 eps figure

Field-induced magnetic ordering in the Haldane system PbNi2V2O8

The Haldane system PbNi2V2O8 was investigated by the temperature dependent magnetization M(T) measurements at fields higher than H_c, with H_c the critical fields necessary to close the Haldane gap. It is revealed that M(T) for H > H_c exhibits a cusp-like minimum at T_{min}, below which M(T) increases with decreasing T having a convex curve. These features have been observed for both $H \parallel c$ and $H \perp c$, with c-axis being parallel to the chain. These data indicate the occurrence of field-induced magnetic ordering around T_{min}. Phase boundaries for $H \parallel c$ and $H \perp c$ do not cross each other, consistent with the theoretical calculation for negative single-ion anisotropy D.Comment: 3 figures, submitted to Phys. Rev.