Related papers: Systematic Resummed Perturbation Theory
We analyze in full mathematical rigor the most general quartically perturbed invariant probability measure for a random tensor. Using a version of the Loop Vertex Expansion (which we call the mixed expansion) we show that the cumulants…
In this paper we consider a quantum open system and treat the master equation with some restricted dissipator which consists of a set of projection operators (projectors). The exact solution is given under the commutable approximation (in…
Linear systems under the influence of nonlinear and random linear perturbations, and with random initial and boundary conditions, are discussed. The notion of states of a system is substituted by the notion of the generating vectors for…
A theory of the propagation of acoustic waves in a porous medium filled with superfluid solution is developed. The elastic coefficients in the system of equations are expressed in terms of physically measurable quantities. The equations…
We take some first steps in providing a synthetic theory of distributions. In particular, we are interested in the use of distribution theory as foundation, not just as tool, in the study of the wave equation.
Results of perturbation theory in quantum field theory generally depend on the renormalization scheme that is in use. In particular, they depend on the scale. We try to make perturbation theory scheme invariant by re-expanding with respect…
We propose a computational method to obtain series expansions in powers of time for general dynamical systems described by a set of hierarchical rate equations. The method is generally applicable to problems in both equilibrium and…
We explore the properties of two-point cosmic propagators when Perturbation Theory (PT) loop corrections are consistently taken into account. We show in particular how the interpolation scheme proposed in arXiv:1112.3895 can be explicitly…
A new nonlinear equation governing asymptotic dynamics of ripples is derived by using a short wave perturbative expansion on a generalized version of the Green-Naghdi system. It admits peakon solutions with amplitude, velocity and width in…
The standard perturbation theory (SPT) approach to gravitational clustering is based on a fluid approximation of the underlying Vlasov-Poisson dynamics, taking only the zeroth and first cumulant of the phase-space distribution function into…
A closure theory is developed for inhomogeneous turbulent flow, which enables a systematic derivation of the turbulence constitutive relations without relying on any empirical parameters. Renormalized-perturbation approximation is performed…
With respect to earlier investigations, the theory of multi-component, concentric, copolar, axisymmetric, rigidly rotating polytropes is improved and extended, including subsystems with nonzero density on the boundary and subsystems with…
We study a novel geometric expansion for scattering amplitudes in the planar sector of N=4 super Yang-Mills theory, in the context of the Amplituhedron which reproduces the all-loop integrand as a canonical differential form on the positive…
In this paper we study an asymptotic expansion for the distribution of a random motion of a particle driven by a Markov process in diffusion approximation. We show that the singularly perturbed equation of a Markovian random motion can be…
Unitary transformations are an essential tool for the theoretical understanding of many systems by mapping them to simpler effective models. A systematically controlled variant to perform such a mapping is a perturbative continuous unitary…
We develop a systematic method to obtain the solution of the collisionless Boltzmann equation which describes the growth of large-scale structures as a perturbative series over the initial density perturbations. We give an explicit…
The nonlinear Vlasov equation contains the full nonlinear dynamics and collective effects of a given Hamiltonian system. The linearized approximation is not valid for a variety of interesting systems, nor is it simple to extend to higher…
The incompressible fluid dynamics is reformulated as dynamics of closed loops $C$ in coordinate space. This formulation allows to derive explicit functional equation for the generating functional $\Psi[C]$ in inertial range of spatial…
We give an expression for the solution to propagator-type Dyson-Schwinger equations with one primitive at 1 loop as an expansion over rooted connected chord diagrams. Along the way we give a refinement of a classical recurrence of rooted…
Shape derivative is an important analytical tool for studying scattering problems involving perturbations in scatterers. Many applications, including inverse scattering, optimal design, and uncertainty quantification, are based on shape…