Search results for "Mathematical physics"
showing 10 items of 2687 documents
Infinite sets of conservation laws for linear and nonlinear field equations
1984
The relation between an infinite set of conservation laws of a linear field equation and the enveloping algebra of the space-time symmetry group is established. It is shown that each symmetric element of the enveloping algebra of the space-time symmetry group of a linear field equation generates a one-parameter group of symmetries of the field equation. The cases of the Maxwell and Dirac equations are studied in detail. Then it is shown that (at least in the sense of a power series in the ‘coupling constant’) the conservation laws of the linear case can be deformed to conservation laws of a nonlinear field equation which is obtained from the linear one by adding a nonlinear term invariant u…
Asymptotic Analysis of a Slightly Rarefied Gas with Nonlocal Boundary Conditions
2011
In this paper nonlocal boundary conditions for the Navier–Stokes equations are derived, starting from the Boltzmann equation in the limit for the Knudsen number being vanishingly small. In the same spirit of (Lombardo et al. in J. Stat. Phys. 130:69–82, 2008) where a nonlocal Poisson scattering kernel was introduced, a gaussian scattering kernel which models nonlocal interactions between the gas molecules and the wall boundary is proposed. It is proved to satisfy the global mass conservation and a generalized reciprocity relation. The asymptotic expansion of the boundary-value problem for the Boltzmann equation, provides, in the continuum limit, the Navier–Stokes equations associated with a…
Affine Surfaces With a Huge Group of Automorphisms
2013
We describe a family of rational affine surfaces S with huge groups of automorphisms in the following sense: the normal subgroup Aut(S)alg of Aut(S) generated by all algebraic subgroups of Aut(S) is not generated by any countable family of such subgroups, and the quotient Aut(S)/Aut(S)alg cointains a free group over an uncountable set of generators.
On Fibrations Between Internal Groupoids and Their Normalizations
2018
We characterize fibrations and $$*$$ -fibrations in the 2-category of internal groupoids in terms of the comparison functor from certain pullbacks to the corresponding strong homotopy pullbacks. As an application, we deduce the internal version of the Brown exact sequence for $$*$$ -fibrations from the internal version of the Gabriel–Zisman exact sequence. We also analyse fibrations and $$*$$ -fibrations in the category of arrows and study when the normalization functor preserves and reflects them. This analysis allows us to give a characterization of protomodular categories using strong homotopy kernels and a generalization of the Snake Lemma.
Uncertainty quantification in electromagnetic observables of nuclei
2023
We present strategies to quantify theoretical uncertainties in modern ab-initio calculations of electromagnetic observables in light and medium-mass nuclei. We discuss how uncertainties build up from various sources, such as the approximations introduced by the few- or many-body solver and the truncation of the chiral effective field theory expansion. We review the recent progress encompassing a broad range of electromagnetic observables in stable and unstable nuclei.
Neutron-proton pairing correlations in a single l-shell model
2017
The long standing problem of neutron-proton pairing correlations is revisited by employing the Hartree-Fock-Bogoliubov formalism with neutron-proton mixing in both the particle-hole and particle-hole channels. We compare numerical calculations performed within this method with an exact pairing model based on the $SO(8)$ algebra. The neutron-proton mixing is included in our calculations by performing rotations in the isospin space using the isocranking technique.
Unitarized Chiral Perturbation Theory in a finite volume: scalar meson sector
2011
We develop a scheme for the extraction of the properties of the scalar mesons f0(600), f0(980), and a0(980) from lattice QCD data. This scheme is based on a two-channel chiral unitary approach with fully relativistic propagators in a finite volume. In order to discuss the feasibility of finding the mass and width of the scalar resonances, we analyze synthetic lattice data with a fixed error assigned, and show that the framework can be indeed used for an accurate determination of resonance pole positions in the multi-channel scattering.
Two-loop QED corrections to the Altarelli-Parisi splitting functions
2016
We compute the two-loop QED corrections to the Altarelli-Parisi (AP) splitting functions by using a deconstructive algorithmic Abelianization of the well-known NLO QCD corrections. We present explicit results for the full set of splitting kernels in a basis that includes the leptonic distribution functions that, starting from this order in the QED coupling, couple to the partonic densities. Finally, we perform a phenomenological analysis of the impact of these corrections in the splitting functions.
Critical point Higgs inflation in the Palatini formulation
2021
We study Higgs inflation in the Palatini formulation with the renormalisation group improved potential in the case when loop corrections generate a feature similar to an inflection point. Assuming that there is a threshold correction for the Higgs quartic coupling $\lambda$ and the top Yukawa coupling $y_t$, we scan the three-dimensional parameter space formed by the two jumps and the non-minimal coupling $\xi$. The spectral index $n_s$ can take any value in the observationally allowed range. The lower limit for the running is $\alpha_s>-3.5\times10^{-3}$, and $\alpha_s$ can be as large as the observational upper limit. Running of the running is small. The tensor-to-scalar ratio is $2.2\tim…
Quantum algorithms for search with wildcards and combinatorial group testing
2012
We consider two combinatorial problems. The first we call "search with wildcards": given an unknown n-bit string x, and the ability to check whether any subset of the bits of x is equal to a provided query string, the goal is to output x. We give a nearly optimal O(sqrt(n) log n) quantum query algorithm for search with wildcards, beating the classical lower bound of Omega(n) queries. Rather than using amplitude amplification or a quantum walk, our algorithm is ultimately based on the solution to a state discrimination problem. The second problem we consider is combinatorial group testing, which is the task of identifying a subset of at most k special items out of a set of n items, given the…