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71.
Trond Digernes David Weisbart 《P-Adic Numbers, Ultrametric Analysis, and Applications》2009,1(2):136-144
We consider quantum systems that have as their configuration spaces finite dimensional vector spaces over local fields. The
quantum Hilbert space is taken to be a space with complex coefficients and we include in our model particles with internal
symmetry. The Hamiltonian operator is a pseudo-differential operator that is initially only formally defined. For a wide class
of potentials we prove that this Hamiltonian is well-defined as an unbounded self-adjoint operator. The free part of the operator
gives rise to ameasure on the Skorokhod space of paths,D[0,∞), and with respect to this measure there is a path integral representation for the semigroup associated to the Hamiltonian.
We prove this Feynman-Kac formula in the local field setting as a consequence of the Hille-Yosida theory of semi-groups.
The text was submitted by the authors in English. 相似文献
72.
Hartree-Fock and DFT (B3LYP) nonrelativistic (scalar relativistic pseudopotentials for the metallic cation) and relativistic (molecular four-component approach coupled to an all-electron basis set) calculations are performed on a series of six nd10 (n+1)s0 [M(H2O)]p+ complexes to investigate their geometry, either planar C2v or nonplanar C(s). These complexes are, formally, entities originating from the complexation of a water molecule to a metallic cation: in the present study, no internal reorganization has been found, which ensures that the complexes can be regarded as a water molecule interacting with a metallic cation. For [Au(H2O)]+ and [Hg(H2O)]2+, it is observed that both electronic correlation and relativistic effects are required to recover the C(s) structures predicted by the four-component relativistic all-electron DFT calculations. However, including the zero-point energy corrections makes these shallow C(s) minima vanish and the systems become floppy. In all other systems, namely [Cu(H2O)]+, [Zn(H2O)]2+, [Ag(H2O)]+, and [Cd(H2O)]2+, all calculations predict a C2v geometry arising from especially flat potential energy surfaces related to the out-of-plane wagging vibration mode. In all cases, our computations point to the quasi-perfect transferability of the atomic pseudopotentials considered toward the molecular species investigated. A rationalization of the shape of the wagging potential energy surfaces (i.e., single well vs. double well) is proposed based on the Constrained Space Orbital Variation decompositions of the complexation energies. Any way of stabilizing the lowest unoccupied orbital of the metallic cation is expected to favor charge-transfer (from the highest occupied orbital(s) of the water ligand), covalence, and, consequently, C(s) structures. The CSOV complexation energy decompositions unambiguously reveal that such stabilizations are achieved by means of relativistic effects for [Au(H2O)]+, and, to a lesser extent, for [Hg(H2O)]2+. Such analyses allow to numerically quantify the rule of thumb known for Au+ which, once again, appears as a better archetype of a relativistic cation than Hg2+. This observation is reinforced due to the especially high contribution of the nonadditive correlation/relativity terms to the total complexation energy of [Au(H2O)]+. 相似文献
73.
A. Reitan 《Nuclear Physics B》1974,68(2):387-396
We have re-examined the reaction in the framework of the Glauber model in order to take excangess terms properly into account. Satisfactory agreement with the experiments can only be obtained if one introduces configuration mixing in the nuclear states. 相似文献
74.
76.
One of the central problems of scientific computation is the efficient numerical solution of the system of n equations in n unknowns F (x) = 0 where F: Rn → Rn is sufficiently smooth. While Newton's method is usually used for solving such systems, third order methods will in general use fewer iterations than a second order method to reach the same accuracy. However, the number of arithmetic operations per iteration is higher for third order methods than second order methods. In this note we will consider the case where F = ∇f, where f is three times continuously differentiable. We will show that for a large class of sparse problems the ratio of the number of arithmetic operations of a third order method and Newton's method is constant per iteration. It is shown that when the structure of the tensor is induced by a general sparse structured Hessian matrix which gives no fill-ins when we use a direct method to solve a system of linear equations. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
77.
We show that for any liquid or solid with strong correlation between its NVT virial and potential-energy equilibrium fluctuations, the temperature is a product of a function of excess entropy per particle and a function of density, T = f(s)h(ρ). This implies that (1) the system's isomorphs (curves in the phase diagram of invariant structure and dynamics) are described by h(ρ)/T = Const., (2) the density-scaling exponent is a function of density only, and (3) a Gru?neisen-type equation of state applies for the configurational degrees of freedom. For strongly correlating atomic systems one has h(ρ) = ∑(n)C(n)ρ(n/3) in which the only non-zero terms are those appearing in the pair potential expanded as ν(r) = ∑(n)ν(n)r(-n). Molecular dynamics simulations of Lennard-Jones type systems confirm the theory. 相似文献
78.
Synthesis of juniperonic acid [(all-Z)-5,11,14,17-eicosatetraenoic acid], has been achieved in eight steps and in 19% overall yield starting from eicosapentaenoic acid. 相似文献
79.
The first synthesis of (all-Z)-1-[(2-phenylethyl)amino]-octadeca-6,9,12,15-tetraen-3-one has been achieved in nine steps and in 13% overall yield using eicosapentaenoic acid as the starting material. 相似文献
80.
Schröder-Turk GE Varslot T de Campo L Kapfer SC Mickel W 《Langmuir : the ACS journal of surfaces and colloids》2011,27(17):10475-10483
We report that a specific realization of Schwarz's triply periodic hexagonal minimal surface is isotropic with respect to the Doi-Ohta interface tensor and simultaneously has minimal packing and stretching frustration similar to those of the commonly found cubic bicontinuous mesophases. This hexagonal surface, of symmetry P6(3)/mmc with a lattice ratio of c/a = 0.832, is therefore a likely candidate geometry for self-assembled lipid/surfactant or copolymer mesophases. Furthermore, both the peak position ratios in its powder diffraction pattern and the elastic moduli closely resemble those of the cubic bicontinuous phases. We therefore argue that a genuine possibility of experimental misidentification exists. 相似文献