Related papers: Numerical Stochastic Perturbation Theory in the Sc…
The SU(3) beta function is computed from Wilson loops to 20th order numerical stochastic perturbation theory. An attempt is made to include massless fermions, whose contribution is known analytically to 4th order. The question whether the…
Strong - weak coupling duality in string theory allows us to compute physical quantities both at the weak coupling end and at the strong coupling end. Furthermore perturbative string theory can be used to compute corrections to the leading…
For the first time, the general nonlinear Schr\"odinger equation is investigated, in which the chromatic dispersion and potential are specified by two arbitrary functions. The equation in question is a natural generalization of a wide class…
Previous results on fermion chirality-flipping four-point functions are extended to $SU(N)$ gauge theories. The problem is purely non-perturbative, and it is approached by truncating the Schwinger-Dyson hierarchy. The large-$N$ limit also…
The SU(3) gauge theory with fermions in the sextet representation is one of several theories of interest for technicolor models. We have carried out a Schrodinger functional (SF) calculation for the lattice theory with two flavors of Wilson…
We present a perturbative approach within the scope of Kohn-Sham density functional theory (DFT). The method is based on the exact exchange-only optimized effective potential method, and correlation is included via perturbation expansion…
We consider the inverse problems of for the fractional Schr\"odinger equation by using monotonicity formulas. We provide if-and-only-if monotonicity relations between positive bounded potentials and their associated nonlocal…
We consider the Cauchy problem for the defocusing stochastic nonlinear Schr\"odinger equations (SNLS) with an additive noise in the mass-critical and energy-critical settings. By adapting the probabilistic perturbation argument employed in…
We study the scattering for the energy-subcritical stochastic nonlinear Schr\"odinger equation (SNLS) with additive noise. In particular, we examine the long-time behavior of solutions associated with the noise…
This article is concerned with the numerical solution of subspace optimization problems, consisting of minimizing a smooth functional over the set of orthogonal projectors of fixed rank. Such problems are encountered in particular in…
Density Functional Theory (DFT) is widely used for atomistic simulations. However, its reach stays limited due to several limitations such as lack of accurate exchange-correlation functional, requirement of costly O(N 3) diagonalization…
Stochastic partial differential equations (SPDEs) are the basic tool for modeling systems where noise is important. In this paper we set up a functional integral formalism and demonstrate how to extract all the one-loop physics for an…
We analyze perturbative aspects of gauged matrix models, including those where classically the gauge symmetry is partially broken. Ghost fields play a crucial role in the Feynman rules for these vacua. We use this formalism to elucidate the…
A new general approach is introduced for definining an optimum zero-order Hamiltonian for Rayleigh-Schr\"odinger perturbation theory. Instead of taking the operator directly from a model problem, it is constructed to be a best fit to the…
We present an evaluation of the running coupling constant and the quark mass renormalization factor for $N_f=2+1$ QCD. The Schr\"odinger functional scheme is used as the intermediate scheme to carry out non-perturbative running from the low…
The time dependent complex Schr\"odinger equation with cubic nonlinearity is solved by constructing differential quadrature algorithm based on sinc functions. Reduction to a coupled system of real equations enables to approach the space…
We present a new method for the solution of the Schrodinger equation applicable to problems of non-perturbative nature. The method works by identifying three different scales in the problem, which then are treated independently: An…
We give a pedagogical introduction of the stochastic variational method by considering the quantization of a non-inertial particle system. We show that the effects of fictitious forces are represented in the forms of vector fields which…
We study a stochastic Nonlinear Schroedinger Equation (NLSE), with additive white Gaussian noise, by means of the Nonlinear Fourier Transform (NFT). In particular, we focus on the propagation of discrete eigenvalues along a focusing fiber.…
The Schwinger model is perhaps the simplest non-trivial exactly-solvable QFT. In this note we examine the perturbative structure of the theory on the sphere and show that its quantum corrections match those predicted by the expansion of the…