Related papers: Finite volume corrections of non-diagonal form fac…
Boundary form factor axioms are derived for the matrix elements of local boundary operators in integrable 1+1 dimensional boundary quantum field theories using the analyticity properties of correlators via the boundary reduction formula.…
In present work, a relativistic relation that connects the difference of interacting and non-interacting integrated two-particle correlation functions in finite volume to infinite volume scattering phase shift through an integral is…
The finite-volume nature of lattice QCD entails a variety of effects that must be handled in the process of performing chiral extrapolations. Since the pion cloud that surrounds hadrons becomes distorted in a finite volume, hadronic…
We consider an interface problem often arising in transport problems: a coupled system of partial differential equations with one (elliptic) transport equation on a bounded domain and one equation (in this case the Laplace problem) on the…
The mass shifts for two-fermion bound and scattering P-wave states subject to the long-range interactions due to QED in the non-relativistic regime are derived. Introducing a short range force coupling the spinless fermions to one unit of…
In this paper we study the convergence of a finite volume approximation of a convective diffusive elliptic problem with Neumann boundary conditions and L 1 data. To deal with the non-coercive character of the equation and the low regularity…
Multi-soliton form factors in sine-Gordon theory from the bootstrap are compared to finite volume matrix elements computed using the truncated conformal space approach. We find convincing agreement, and resolve most of the issues raised in…
Quantum cosmology implies corrections to the classical equations of motion which may lead to significant departures from the classical trajectory, especially at high curvature near the big-bang singularity. Corrections could in principle be…
Electromagnetic effects are increasingly being accounted for in lattice quantum chromodynamics computations. Because of their long-range nature, they lead to large finite-size effects over which it is important to gain analytical control.…
The analytic structure of the partition function in finite-volume systems is investigated at complex chemical potentials in a minimal mean-field effective model of QCD with finite-size effects incorporated. We discuss the temperature…
We explore variational approach to the finite-volume $N$-body problem. The general formalism for N non-relativistic spinless particles interacting with periodic pair-wise potentials yields N-body secular equations. The solutions depend on…
In this paper we propose a nonconforming finite element method for the solution of the ill-posed elliptic Cauchy problem. We prove error estimates using continuous dependence estimates in the $L^2$-norm. The effect of perturbations in data…
We propose a finite volume stochastic collocation method for the random Euler system. We rigorously prove the convergence of random finite volume solutions under the assumption that the discrete differential quotients remain bounded in…
The finite-volume spectrum of an integrable massive perturbation of a rational conformal field theory interpolates between massive multi-particle states in infinite volume (IR limit) and conformal states, which are approached at zero volume…
Lattice QCD has become a crucial tool for studying hadron-hadron interactions from first principles. However, significant challenges arise when extracting infinite-volume scattering parameters from finite-volume energy levels using the…
We propose formulas for the L\"uscher type finite size energy correction of multiparticle states on the interval and evaluate them for the simplest case in the AdS/CFT setting. By this we determine the leading wrapping correction to the…
Finite-volume modifications of the two-flavor chiral phase diagram are investigated within an effective quark-meson model in various mean-field approximations. The role of vacuum fluctuations and boundary conditions, their influence on…
A uniform bounded variation estimate for finite volume approximations of the nonlinear scalar conservation law $\partial_t \alpha + \mathrm{div}(\boldsymbol{u}f(\alpha)) = 0$ in two and three spatial dimensions with an initial data of…
Scattering observables can be computed in lattice field theory by measuring the volume dependence of energy levels of two particle states. The dominant volume dependence, proportional to inverse powers of the volume, is determined by the…
A general framework for goal-oriented a posteriori error estimation for finite volume methods is presented. The framework does not rely on recasting finite volume methods as special cases of finite element methods, but instead directly…