Descripción: Short-time decay of the Loschmidt echo was discussed. It is used to measure the sensitivity to perturbations of quantum evolutions. It was found that the characteristic time of the regime is well described by the inverse of the width of the local density of states.

Descripción: We have employed the Douglas-Kroll-Hess approximation to derive the perturbative Hamiltonians involved in the calculation of NMR spin-spin couplings in molecules containing heavy elements. We have applied this two-component quasirelativistic approach using finite perturbation theory in combination with a generalized Kohn-Sham code that includes the spin-orbit interaction self-consistently and works with Hartree-Fock and both pure and hybrid density functionals. We present numerical results for one-bond spin-spin couplings in the series of tetrahydrides C H4, Si H4, Ge H4, and Sn H4. Our two-component Hartree-Fock results are in good agreement with four-component Dirac-Hartree-Fock calculations, although a density-functional treatment better reproduces the available experimental data. © 2005 American Institute of Physics.

Descripción: The evolution of the energy distribution was studied for a stadium with moving balls. A one period driving cycle was considered, which was characterized by an amplitude A and a wall velocity V. The spreading mechanism was dominated by transitions between neighboring levels for an extremely slow wall velocity V, while for larger velocities, the spreading mechanism had both perturbative and nonperturbative features.

Descripción: A scheme for resolving average optical rotatory power of a molecule into atomic contributions, applied to hydrogen peroxide, is presented. The scheme is based on the acceleration gauge for the electric dipole, and the torque formalism. Calculations are carried out to test the reliability of the partition method. The force and torque gauges provide different numerical values for atomic contributions.

Descripción: Recent experimental and theoretical methods allowed the efficient investigation of highly excited rovibrational states of molecular systems. At these levels of excitation the correspondence principle holds, and then classical mechanics can provide intuitive views of the involved processes. In this respect, we have recently shown that for completely hyperbolic systems, homoclinic motions, which are known to organize the classical chaotic region in Hamiltonian systems, imprint a clear signature in the corresponding highly excited quantum spectra. In this Communication we show that this result also holds in mixed systems, by considering an application to the floppy LiNCLiCN molecular system. © 2005 American Institute of Physics.

Descripción: We applied a methodology capable of resolving the optical rotatory power into atomic contributions. The individual atomic contributions to the optical rotatory power and molecular chirality of the methylhydroperoxide are obtained via a canonical transformation of the Hamiltonian by which the electric dipolar moment operator is transformed to the acceleration gauge formalism and the magnetic dipolar moment operator to the torque formalism. The gross atomic isotropic contributions have been evaluated for the carbon, the nonequivalent oxygen, and the nonequivalent hydrogen atoms of methylhydroperoxide, employing a very large Gaussian basis set which is close to the Hartree-Fock limit. © 2008 American Institute of Physics.

Descripción: A two-component theory for shielding calculations starting from a four-component Rayleigh-Schrodinger perturbation theory (RSPT) formalism is presented. Thus, a set of operators entering the RSPT expressions in terms of the Schrodinger molecular spectrum are derived by expanding such four-component expression as a power series in c-1. All formal expressions are retained, without neglecting any terms in the intermediate steps of the derivation.

Descripción: The Traveling Deliveryman Problem is a generalization of the Minimum Cost Hamiltonian Path Problem where the starting vertex of the path, i.e. a depot vertex, is fixed in advance and the cost associated with a Hamiltonian path equals the sum of the costs for the layers of paths (along the Hamiltonian path) going from the depot vertex to each of the remaining vertices. In this paper, we propose a new Integer Programming formulation for the problem and computationally evaluate the strength of its Linear Programming relaxation. Computational results are also presented for a cutting plane algorithm that uses a number of valid inequalities associated with the proposed formulation. Some of these inequalities are shown to be facet defining for the convex hull of feasible solutions to that formulation. These inequalities proved very effective when used to reinforce Linear Programming relaxation bounds, at the nodes of a Branch and Bound enumeration tree. © 2008 Elsevier B.V. All rights reserved.