Search results for "propagator"
showing 10 items of 173 documents
Non-autonomous rough semilinear PDEs and the multiplicative Sewing Lemma
2021
We investigate existence, uniqueness and regularity for local solutions of rough parabolic equations with subcritical noise of the form $du_t- L_tu_tdt= N(u_t)dt + \sum_{i = 1}^dF_i(u_t)d\mathbf X^i_t$ where $(L_t)_{t\in[0,T]}$ is a time-dependent family of unbounded operators acting on some scale of Banach spaces, while $\mathbf X\equiv(X,\mathbb X)$ is a two-step (non-necessarily geometric) rough path of H\"older regularity $\gamma >1/3.$ Besides dealing with non-autonomous evolution equations, our results also allow for unbounded operations in the noise term (up to some critical loss of regularity depending on that of the rough path $\mathbf X$). As a technical tool, we introduce a versi…
One-loop integrals with XLOOPS-GiNaC
2001
We present a new algorithm for the reduction of one-loop tensor Feynman integrals within the framework of the XLOOPS project, covering both mathematical and programming aspects. The new algorithm supplies a clean way to reduce the one-loop one-, two- and three-point Feynman integrals with arbitrary tensor rank and powers of the propagators to a basis of simple integrals. We also present a new method of coding XLOOPS in C++ using the GiNaC library.
Including theΔ(1232)resonance in baryon chiral perturbation theory
2005
Baryon chiral perturbation theory with explicit $\ensuremath{\Delta}(1232)$ degrees of freedom is considered. The most general interactions of pions, nucleons, and \ensuremath{\Delta} consistent with all underlying symmetries as well as with the constraint structure of higher-spin fields are constructed. By use of the extended on-mass-shell renormalization scheme, a manifestly Lorentz-invariant effective-field theory with a systematic power counting is obtained. As applications, we discuss the mass of the nucleon, the pion-nucleon \ensuremath{\sigma} term, and the pole of the \ensuremath{\Delta} propagator.
Impulsive control of the bilinear Schrödinger equation: propagators and attainable sets
2019
International audience; We consider a linear Schrödinger equation with an unbounded bilinear control term. The control term is the derivative of function with bounded variations (impulsive control). Well-posedness results and regularity of the associated propagators follow from classical theory from Kato. As a byproduct, one obtains a topological obstruction to exact controllability of the system in the spirit of the results of Ball, Marsden and Slemrod.
Numerical propagator method solutions for the linear parabolic initial boundary-value problems
2007
On the base of our numerical propagator method a new finite volume difference scheme is proposed for solution of linear initial-boundary value problems. Stability of the scheme is investigated taking into account the obtained analytical solution of the initial-boundary value problems. It is shown that stability restrictions for the propagator scheme become weaker in comparison to traditional semi-implicit difference schemes. There are some regions of coefficients, for which the elaborated propagator difference scheme becomes absolutely stable. It is proven that the scheme is unconditionally monotonic. Analytical solutions, which are consistent with solubility conditions of the problem are f…
Prediction of water's isotropic nuclear shieldings and indirect nuclear spin–spin coupling constants (SSCCs) using correlation‐consistent and polariz…
2009
Density functional theory (DFT) was used to estimate water's isotropic nuclear shieldings and indirect nuclear spin-spin coupling constants (SSCCs) in the Kohn-Sham (KS) complete basis set (CBS) limit. Correlation-consistent cc-pVxZ and cc-pCVxZ (x = D, T, Q, 5, and 6), and their modified versions (ccJ-pVxZ, unc-ccJ-pVxZ, and aug-cc-pVTZ-J) and polarization-consistent pc-n and pcJ-n (n = 0, 1, 2, 3, and 4) basis sets were used, and the results fitted with a simple mathematical formula. The performance of over 20 studied density functionals was assessed from comparison with the experiment. The agreement between the CBS DFT-predicted isotropic shieldings, spin-spin values, and the experimenta…
Coherent Pions From Neutrino Scattering Off Nuclei
2010
We describe a model for pion production off nucleons and coherent pions from nuclei induced by neutrinos in the 1 GeV energy regime. Besides the dominant Delta pole contribution, it takes into account the effect of background terms required by chiral symmetry. Moreover, the model uses a reduced nucleon-to-Delta resonance axial coupling, which leads to coherent pion production cross sections around a factor two smaller than most of the previous theoretical estimates. Nuclear effects like medium corrections on the Delta propagator and final pion distortion are included.
φ meson mass and decay width in nuclear matter
2002
The $\phi$ meson spectrum, which in vacuum is dominated by its coupling to the $\bar{K} K$ system, is modified in nuclear matter. Following a model based on chiral SU(3) dynamics we calculate the $\phi$ meson selfenergy in nuclear matter considering the $K$ and $\bar{K}$ in-medium properties. For the latter we use the results of previous calculations which account for $S-$ and $P-$wave kaon-nucleon interactions based on the lowest order meson-baryon chiral effective Lagrangian, and this leads to a dressing of the kaon propagators in the medium. In addition, a set of vertex corrections is evaluated to fulfill gauge invariance, which involves contact couplings of the $\phi$ meson to $S-$wave …
On new efficient algorithms for PIMC and PIMD
2002
Abstract The properties of various algorithms, estimators, and high-temperature density matrix (HTDM) decompositions relevant for path integral simulations are discussed. It is shown that Fourier accelerated path integral molecular dynamics (PIMD) completely eliminates slowing down with increasing Trotter number P . A new primitive estimator of the kinetic energy for use in PIMD simulations is found to behave less pathologically than the original virial estimator. In particular, its variance does not increase significantly with P . Two non-primitive HTDM decompositions are compared as well: one decomposition used in the Takahashi Imada algorithm and another one based on an effective propaga…
A new formulation of the loop-tree duality at higher loops
2019
We present a new formulation of the loop-tree duality theorem for higher loop diagrams valid both for massless and massive cases. $l$-loop integrals are expressed as weighted sum of trees obtained from cutting $l$ internal propagators of the loop graph. In addition, the uncut propagators gain a modified $i \delta$-prescription, named dual-propagators. In this new framework one can go beyond graphs and calculate the integrand of loop amplitudes as a weighted sum of tree graphs, which form a tree-like object. These objects can be computed efficiently via recurrence relations.