相关论文: A Real Space Renormalization Group Approach to Fie…
We introduce the general formulation of a renormalization method suitable to study the critical properties of non-equilibrium systems with steady-states: the Dynamically Driven Renormalization Group. We renormalize the time evolution…
For For a given PDE system, or an exterior differential system possessing a Lie group of internal symmetries the orbit reduction procedure is introduced. It is proved that the solutions of the reduced exterior differential system are in…
We demonstrate our simple strategy for renormalization with QED at one-loop level, basing on an elaboration of the effective field theory philosophy. No artificial regularization or deformation of the original theory is introduced here and…
The quantum evolution equations for the field expectation value are analytically solved to cubic order in the field amplitude and to one-loop level in the lambda phi-fourth model. We adapt and use the renormalization group (RG) method for…
We give a pedagogical introduction into the functional renormalization group treatment of disordered systems. After a review of its phenomenology, we show why in the context of disordered systems a functional renormalization group treatment…
We propose a novel scheme for the exact renormalisation group motivated by the desire of reducing the complexity of practical computations. The key idea is to specify renormalisation conditions for all inessential couplings, leaving us with…
We introduce an approach for approximate real-time evolution of quantum systems using Tensor Renormalization Group (TRG) methods originally developed for imaginary time. We use Higher- Order TRG (HOTRG) to generate a coarse-grained time…
We derive the renormalization group equations for a generic nonrenormalizable theory. We show that the equations allow one to derive the structure of the leading divergences at any loop order in terms of one-loop diagrams only. In chiral…
This paper deals with model-order reduction of parametric partial differential equations (PPDE). More specifically, we consider the problem of finding a good approximation subspace of the solution manifold of the PPDE when only partial…
We present an exact dimensional reduction for high-dimensional dynamical systems composed of $N$ identical dynamical units governed by quasi-linear ordinary differential equations (ODEs) of order $M$. In these systems, each unit follows a…
Partial Integral Equations (PIEs) have been used to represent both systems with delay and systems of Partial Differential Equations (PDEs) in one or two spatial dimensions. In this paper, we show that these results can be combined to obtain…
The necessity of renormalization arises from the infinite integrals which are caused by the discrepancy between the orders of differential and integral operators in the four dimensional QFTs. Therefore in view of the fact that finiteness…
The renormalization group method is a successive integration over the fluctuations which are ordered according to their length scale, a parameter in the external space. A different procedure is described, where the fluctuations are treated…
We discuss various compatibility criteria for overdetermined systems of PDEs generalizing the approach to formal integrability via brackets of differential operators. Then we give sufficient conditions that guarantee that a PDE possessing a…
We give a systematic description of a canonical renormalisation procedure of stochastic PDEs containing nonlinearities involving generalised functions. This theory is based on the construction of a new class of regularity structures which…
The Polchinski version of the exact renormalization group equation is discussed and its applications in scalar and fermionic theories are reviewed. Relation between this approach and the standard renormalization group is studied, in…
We present and analyze a novel sparse polynomial technique for the simultaneous approximation of parameterized partial differential equations (PDEs) with deterministic and stochastic inputs. Our approach treats the numerical solution as a…
Developing efficient numerical algorithms for the solution of high dimensional random Partial Differential Equations (PDEs) has been a challenging task due to the well-known curse of dimensionality. We present a new solution framework for…
Effective Field Theory calculations used in countless phenomenological analyses employ dimensional regularization, and at intermediate stages of computations, the operator bases extend beyond the four-dimensional ones. The extra pieces --…
We are interested in the numerical solution of coupled nonlinear partial differential equations (PDEs) in two and three dimensions. Under certain assumptions on the domain, we take advantage of the Kronecker structure arising in standard…