Search results for "Linear Algebra."
showing 10 items of 552 documents
The Tensor Networks Anthology: Simulation techniques for many-body quantum lattice systems
2019
We present a compendium of numerical simulation techniques, based on tensor network methods, aiming to address problems of many-body quantum mechanics on a classical computer. The core setting of this anthology are lattice problems in low spatial dimension at finite size, a physical scenario where tensor network methods, both Density Matrix Renormalization Group and beyond, have long proven to be winning strategies. Here we explore in detail the numerical frameworks and methods employed to deal with low-dimension physical setups, from a computational physics perspective. We focus on symmetries and closed-system simulations in arbitrary boundary conditions, while discussing the numerical dat…
An algebraic approach to the study of multipartite entanglement
2012
A simple algebraic approach to the study of multipartite entanglement for pure states is introduced together with a class of suitable functionals able to detect entanglement. On this basis, some known results are reproduced. Indeed, by investigating the properties of the introduced functionals, it is shown that a subset of such class is strictly connected to the purity. Moreover, a direct and basic solution to the problem of the simultaneous maximization of three appropriate functionals for three-qubit states is provided, confirming that the simultaneous maximization of the entanglement for all possible bipartitions is compatible only with the structure of GHZ-states.
The Equilibrium Structure of Benzene
2000
The re structure of benzene is revised on the basis of high-level quantum chemical calculations at the CCSD(T)/cc-pVQZ level as well a reanalysis of the experimental rotational constants using computed vibrational corrections. A least-squares fit to empirically determined Be constants yields re(CC) = 1.3914 ± 0.0010 A and re(CH) = 1.0802 ± 0.0020 A; the latter distance is significantly shorter than the best previous estimate based on experimental data. Comparison of computed rg and rz distances with experiment as well as considerations of bond lengthening due to anharmonicity are consistent with the estimated re distance, indicating that the recommended structural parameters are very accura…
2p x-ray absorption spectroscopy of 3d transition metal systems
2021
Abstract This review provides an overview of the different methods and computer codes that are used to interpret 2p x-ray absorption spectra of 3d transition metal ions. We first introduce the basic parameters and give an overview of the methods used. We start with the semi-empirical multiplet codes and compare the different codes that are available. A special chapter is devoted to the user friendly interfaces that have been written on the basis of these codes. Next we discuss the first principle codes based on band structure, including a chapter on Density Functional theory based approaches. We also give an overview of the first-principle multiplet codes that start from a cluster calculati…
Lattice quantum hadrodynamics on a CRAY Y-MP
1992
Quantum corrections to the mean-field equation of state for nuclear matter are estimated in a lattice simulation of quantum hadrodynamics on a CRAY Y-MP. In contrast with lattice quantum chromodynamics, where coordinate space methods are the standard, the calculations are carried out in momentum space and on nonhypercubic (irregular) lattices. The quantum corrections to the known, mean-field equation of state were found to be considerable. The time frame of the project and the large computational needs of the program required the use of powerful supercomputers, like the CRAY Y-MP, which are capable of performing at a very high computing speed by using both vector and parallel hardware, the …
Multiple polylogarithms with algebraic arguments and the two-loop EW-QCD Drell-Yan master integrals
2020
We consider Feynman integrals with algebraic leading singularities and total differentials in $\epsilon\,\mathrm{d}\ln$ form. We show for the first time that it is possible to evaluate integrals with singularities involving unrationalizable roots in terms of conventional multiple polylogarithms, by either parametric integration or matching the symbol. As our main application, we evaluate the two-loop master integrals relevant to the $\alpha \alpha_s$ corrections to Drell-Yan lepton pair production at hadron colliders. We optimize our functional basis to allow for fast and stable numerical evaluations in the physical region of phase space.
Impact of the pion mass on nonpower expansion for QCD observables
2005
A new set of functions, which form a basis of the massive nonpower expansion for physical observables, is presented in the framework of the analytic approach to QCD at the four-loop level. The effects due to the $\pi$ meson mass are taken into account by employing the dispersion relation for the Adler function. The nonvanishing pion mass substantially modifies the functional expansion at low energies. Specifically, the spacelike functions are affected by the mass of the $\pi$ meson in the infrared domain below few GeV, whereas the timelike functions acquire characteristic plateaulike behavior below the two-pion threshold. At the same time, all the appealing features of the massless nonpower…
First Look at Two-Loop Five-Gluon Scattering in QCD.
2018
We compute the leading colour contributions to five-gluon scattering at two loops in massless QCD. The integrands of all independent helicity amplitudes are evaluated using d-dimensional generalised unitarity cuts and finite field reconstruction techniques. Numerical evaluation of the integral basis is performed with sector decomposition methods to obtain the first benchmark results for all helicity configurations of a 2 to 3 scattering process in QCD.
Linear optical implementation of nonlocal product states and their indistinguishability
2001
In a recent paper Bennett et al.[Phys. Rev.A 59, 1070 (1999)] have shown the existence of a basis of product states of a bipartite system with manifest non-local properties. In particular these states cannot be completely discriminated by means of bilocal measurements. In this paper we propose an optical realization of these states and we will show that they cannot be completely discriminate by means of a global measurement using only optical linear elements, conditional transformation and auxiliary photons.
Applications of Quantum Mechanics
2013
Quantum mechanics provides the basis for most fields of modern physics and there are many well advanced methods of practical solution of specific and topical problems