Related papers: Auxiliary Field Loop expansion for the Effective A…
This work is devoted to deriving the Onsager-Machlup action functional for stochastic partial differential equations with (non-Gaussian) Levy process as well as Gaussian Brownian motion. This is achieved by applying the Girsanov…
The recently derived Fourier--Matsubara expansion of imaginary--time correlation functions comprises an exact result of linear response theory for finite-temperature quantum many-body systems. In its density--density version, the expansion…
We present stochastic variants of the exponential time differencing schemes for stiff stochastic differential equations. We derive three explicit schemes that offer better stability compared to Euler-Maruyama and Milstein's method, and…
This paper develops a new framework, called modular regression, to utilize auxiliary information -- such as variables other than the original features or additional data sets -- in the training process of linear models. At a high level, our…
Singular potentials (the inverse-square potential, for example) arise in many situations and their quantum treatment leads to well-known ambiguities in choosing boundary conditions for the wave-function at the position of the potential's…
We apply the open systems concept and the influence functional formalism introduced in Paper I to establish a stochastic theory of relativistic moving spinless particles in a quantum scalar field. The stochastic regime resting between the…
In this paper, we study two-loop contribution to the effective action of a two-dimensional sigma model. We derive a new formula, which can be applicable to a regularization of general type. As examples, we obtain known results for…
We rewrite the Martin-Siggia-Rose (MSR) formalism for the statistical dynamics of classical fields in a covariant second order form appropriate for the statistical dynamics of relativistic field theory. This second order formalism is…
Constructing discrete models of stochastic partial differential equations is very delicate. Stochastic centre manifold theory provides novel support for coarse grained, macroscale, spatial discretisations of nonlinear stochastic partial…
We consider spatially extended conductance based neuronal models with noise described by a stochastic reaction diffusion equation with additive noise coupled to a control variable with multiplicative noise but no diffusion. We only assume a…
We propose new approach for treatment of local and non-local interactions in correlated electronic systems, which uses self-energy and the two-particle irreducible vertices, obtained from (extended) dynamical mean-field theory, as an input…
This article proposes for stochastic partial differential equations (SPDEs) driven by additive noise, a novel approach for the approximate parameterizations of the ``small'' scales by the ``large'' ones, along with the derivaton of the…
Dynamical systems theory provides powerful methods to extract effective macroscopic dynamics from complex systems with slow modes and fast modes. Here we derive and theoretically support a macroscopic, spatially discrete, model for a class…
In this work we consider a relativistic drift-kinetic model for runaway electrons along with a Fokker-Planck operator for small-angle Coulomb collisions, a radiation damping operator, and a secondary knock-on (Boltzmann) collision source.…
We present a theory for the construction of renormalized kinetic equations to describe the dynamics of classical systems of particles in or out of equilibrium. A closed, self-consistent set of evolution equations is derived for the…
In this paper we consider the problem of deriving approximate autonomous dynamics for a number of variables of a dynamical system, which are weakly coupled to the remaining variables. In a previous paper we have used the Ruelle response…
We study the construction of the so-called intrinsic action for PDEs equipped with compatible presymplectic structures. In particular, we explicitly demonstrate that the intrinsic action for the standard Einstein-Hilbert gravity is the…
We establish the existence of weak martingale solutions to a class of second order parabolic stochastic partial differential equations. The equations are driven by multiplicative jump type noise, with a non-Lipschitz multiplicative…
Starting from many quark interactions, we construct a nonlinear sigma-omega model at finite temperature and density. The mesons are introduced as auxiliary fields. Effective quark-meson couplings are strongly related to effective meson…
We extend the Post-Minkowskian (PM) effective field theory (EFT) approach to incorporate conservative and dissipative radiation-reaction effects in a unified framework. This is achieved by implementing the Schwinger-Keldysh "in-in"…