Search results for "integral"
showing 10 items of 902 documents
Complete sets of logarithmic vector fields for integration-by-parts identities of Feynman integrals
2018
Integration-by-parts identities between loop integrals arise from the vanishing integration of total derivatives in dimensional regularization. Generic choices of total derivatives in the Baikov or parametric representations lead to identities which involve dimension shifts. These dimension shifts can be avoided by imposing a certain constraint on the total derivatives. The solutions of this constraint turn out to be a specific type of syzygies which correspond to logarithmic vector fields along the Gram determinant formed of the independent external and loop momenta. We present an explicit generating set of solutions in Baikov representation, valid for any number of loops and external mome…
Gibbs-ensemble path-integral Monte Carlo simulations of a mixed quantum-classical fluid
1995
We study a model fluid with classical translational degrees of freedom and internal quantum states in two spatial dimensions. The path-integral Monte Carlo and the Gibbs-ensemble Monte Carlo techniques are combined to investigate the liquid-gas coexistence region in this mixed quantum-classical system. A comparison with the phase diagram obtained in the canonical ensemble is also presented.
Green functions for nearest- and next-nearest-neighbor hopping on the Bethe lattice
2005
We calculate the local Green function for a quantum-mechanical particle with hopping between nearest and next-nearest neighbors on the Bethe lattice, where the on-site energies may alternate on sublattices. For infinite connectivity the renormalized perturbation expansion is carried out by counting all non-self-intersecting paths, leading to an implicit equation for the local Green function. By integrating out branches of the Bethe lattice the same equation is obtained from a path integral approach for the partition function. This also provides the local Green function for finite connectivity. Finally, a recently developed topological approach is extended to derive an operator identity whic…
Quantized Fields and Their Interpretation
2013
This chapter deals with the quantum theory of systems with an infinite number of degrees of freedom and provides elements of quantum field theory.
3D imaging and visualization: An overview of recent advances
2013
This paper presents an overview of our published work on physical principles, applications, and advances in integral imaging and digital holography. Various approaches for image capture, image reconstruction, and 3D display methods are overviewed. Applications including 3D underwater imaging, 3D imaging in photon-starved environments, 3D tracking of occluded objects, 3D optical microscopy, and 3D polarimetric imaging are reviewed.
Modelling uncertainties in phase-space boundary integral models of ray propagation
2020
Abstract A recently proposed phase-space boundary integral model for the stochastic propagation of ray densities is presented and, for the first time, explicit connections between this model and parametric uncertainties arising in the underlying physical model are derived. In particular, an asymptotic analysis for a weak noise perturbation of the propagation speed is used to derive expressions for the probability distribution of the phase-space boundary coordinates after transport along uncertain, and in general curved, ray trajectories. Furthermore, models are presented for incorporating geometric uncertainties in terms of both the location of an edge within a polygonal domain, as well as …
Relaxation of periodic and nonstandard growth integrals by means of two-scale convergence
2019
An integral representation result is obtained for the variational limit of the family functionals $\int_{\Omega}f\left(\frac{x}{\varepsilon}, Du\right)dx$, as $\varepsilon \to 0$, when the integrand $f = f (x,v)$ is a Carath\'eodory function, periodic in $x$, convex in $v$ and with nonstandard growth.
Magnetic field analysis and leakage inductance calculation in current transformers by means of 3-D integral methods
1996
This paper presents 3D integral approach to power current transformer magnetic field and inductance calculations. A minimization of the kernel norm has been carried out for the integral equation governing the field. The software package TRACAL3, based on the integral methods for field and inductance calculations, has been developed and implemented for personal computers. The application of the 3D mathematical models has been made for the leakage field in a current transformer. The results of calculations were compared with measurement data. The comparison yields good agreement.
Efficient Pole Expansion of the Generalized Impedance Matrix Representation for Planar Waveguide Junctions
2006
This paper proposes a novel pole expansion of the generalized impedance matrix representation for planar waveguide junctions. Proceeding in this way, we have obtained a very efficient algorithm for the accurate wide-band modelling of such junctions, since the most expensive computations are performed outside the frequency loop. For verification purposes, several practical examples are shown in order to prove the numerical efficiency and accuracy provided by this new technique.
Ab Initio Computation of the Longitudinal Response Function in Ca40
2021
We present a consistent ab initio computation of the longitudinal response function ${R}_{L}$ in $^{40}\mathrm{Ca}$ using the coupled-cluster and Lorentz integral transform methods starting from chiral nucleon-nucleon and three-nucleon interactions. We validate our approach by comparing our results for ${R}_{L}$ in $^{4}\mathrm{He}$ and the Coulomb sum rule in $^{40}\mathrm{Ca}$ against experimental data and other calculations. For ${R}_{L}$ in $^{40}\mathrm{Ca}$ we obtain a very good agreement with experiment in the quasielastic peak up to intermediate momentum transfers, and we find that final state interactions are essential for an accurate description of the data. This work presents a m…