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

Hole-trapping by Ni, Kondo effect and electronic phase diagram in non-superconducting Ni-substituted La2-xSrxCu1-yNiyO4

In order to investigate the electronic state in the normal state of high-Tc cuprates in a wide range of temperature and hole-concentration, specific-heat, electrical-resistivity, magnetization and muon-spin-relaxation (muSR) measurements have been performed in non-superconducting Ni-substituted La2-xSrxCu1-yNiyO4 where the superconductivity is suppressed through the partial substitution of Ni for Cu without disturbing the Cu-spin correlation in the CuO2 plane so much. In the underdoped regime, it has been found that there exist both weakly localized holes around Ni and itinerant holes at high temperatures. With decreasing temperature, all holes tend to be localized, followed by the occurrence of variable-range hopping conduction at low temperatures. Finally, in the ground state, it has been found that each Ni2+ ion traps a hole strongly and that a magnetically ordered state appears. In the overdoped regime, on the other hand, it has been found that a Kondo-like state is formed around each Ni2+ spin at low temperatures. In conclusion, the ground state of non-superconducting La2-xSrxCu1-yNiyO4 changes upon hole doping from a magnetically ordered state with the strong hole-trapping by Ni2+ to a metallic state with Kondo-like behavior due to Ni2+ spins, and the quantum phase transition is crossover-like due to the phase separation into short-range magnetically ordered and metallic regions.Comment: 9 pages, 8 figures, accepted for publication in Phys. Rev.

Quantum gauge boson propagators in the light front

Gauge fields in the light front are traditionally addressed via the employment of an algebraic condition $n\cdot A=0$ in the Lagrangian density, where $A_{\mu}$ is the gauge field (Abelian or non-Abelian) and $n^\mu$ is the external, light-like, constant vector which defines the gauge proper. However, this condition though necessary is not sufficient to fix the gauge completely; there still remains a residual gauge freedom that must be addressed appropriately. To do this, we need to define the condition $(n\cdot A)(\partial \cdot A)=0$ with $n\cdot A=0=\partial \cdot A$. The implementation of this condition in the theory gives rise to a gauge boson propagator (in momentum space) leading to conspicuous non-local singularities of the type $(k\cdot n)^{-\alpha}$ where $\alpha=1,2$. These singularities must be conveniently treated, and by convenient we mean not only matemathically well-defined but physically sound and meaningfull as well. In calculating such a propagator for one and two noncovariant gauge bosons those singularities demand from the outset the use of a prescription such as the Mandelstam-Leibbrandt (ML) one. We show that the implementation of the ML prescription does not remove certain pathologies associated with zero modes. However we present a causal, singularity-softening prescription and show how to keep causality from being broken without the zero mode nuisance and letting only the propagation of physical degrees of freedom.Comment: 10 page

A small and light weight heat exchanger for on-board helium refrigerator

A small and light weight heat exchanger used for small helium refrigerator has been developed by Sumitomo Heavy Industries, Ltd. This heat exchanger is a laminated metal heat exchanger which consists of perforated aluminum metal plates and glassfiber reinforced plastic separators. The size is from 100 mm to 28 mm in diameter and about 300 mm in length. The weight is from 2.5 kg to 0.6 kg. Also it can be used between room temperature and liquid helium temperature. The thermal efficiency obtained has been more than 96%. The heat exchanger has been practically used for on-board helium refrigerator in Japanese National Railways' superconducting magnetic levitated trains

On the perfect lattice actions of abelian-projected SU(2) QCD

We study the perfect lattice actions of abelian-projected SU(2) gluodynamics. Using the BKT and duality transformations on the lattice, an effective string model is derived from the direction-dependent quadratic monopole action, obtained numerically from SU(2) gluodynamics in maximally abelian gauge. The string tension and the restoration of continuum rotational invariance are investigated using strong coupling expansion of lattice string model analytically. We also found that the block spin transformation can be performed analytically for the quadratic monopole action.Comment: 3 pages, Latex, 1 figures; talk presented at LATTICE9

Dynamical mean field theory of correlated gap formation in Pu monochalcogenides

The correlated Kondo insulator state of the plutonium monochalcogenides is investigated using the dynamical mean field theory (DMFT) and the local density approximation +U (LDA+U). The DMFT-dynamical fluctuations lead to a correlated insulator state at elevated temperature, in sharp contrast to the static LDA+U approach that fails to reproduce both the insulating behavior and anomalous lattice constant. The DMFT conversely predicts the experimentally observed anomalous increase of the gap with pressure and explains the lattice constant very well.Comment: 4 pages, 4 figure

The light-cone gauge without prescriptions

Feynman integrals in the physical light-cone gauge are harder to solve than their covariant counterparts. The difficulty is associated with the presence of unphysical singularities due to the inherent residual gauge freedom in the intermediate boson propagators constrained within this gauge choice. In order to circumvent these non-physical singularities, the headlong approach has always been to call for mathematical devices --- prescriptions --- some successful ones and others not so much so. A more elegant approach is to consider the propagator from its physical point of view, that is, an object obeying basic principles such as causality. Once this fact is realized and carefully taken into account, the crutch of prescriptions can be avoided altogether. An alternative third approach, which for practical computations could dispense with prescriptions as well as prescinding the necessity of careful stepwise watching out of causality would be of great advantage. And this third option is realizable within the context of negative dimensions, or as it has been coined, negative dimensional integration method, NDIM for short.Comment: 9 pages, PTPTeX (included

Feynman integrals with tensorial structure in the negative dimensional integration scheme

Negative dimensional integration method (NDIM) is revealing itself as a very useful technique for computing Feynman integrals, massless and/or massive, covariant and non-covariant alike. Up to now, however, the illustrative calculations done using such method are mostly covariant scalar integrals, without numerator factors. Here we show how those integrals with tensorial structures can also be handled with easiness and in a straightforward manner. However, contrary to the absence of significant features in the usual approach, here the NDIM also allows us to come across surprising unsuspected bonuses. In this line, we present two alternative ways of working out the integrals and illustrate them by taking the easiest Feynman integrals in this category that emerges in the computation of a standard one-loop self-energy diagram. One of the novel and as yet unsuspected bonus is that there are degeneracies in the way one can express the final result for the referred Feynman integral.Comment: 9 pages, revtex, no figure