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We discuss how methods developed in the context of perturbation theory can be applied to the computation of lattice correlation functions, in particular in the non perturbative regime. The techniques we consider are integration-by-parts…
We establish bounds on the decay of time-dependent multipoint correlation functionals of one-dimensional quasi-free fermions in terms of the decay properties of their two-point function. At a technical level, this is done with the help of…
We present a general formalism based on scattering theory to calculate quantum correlation functions involving several time-dependent current operators. A key ingredient is the causality of the scattering matrix, which allows one to deal…
We introduce difference operators on the space of symmetric functions which are a natural generalization of the $(q,t)$-Macdonald operators. In the $t\to\infty$ limit, they satisfy the $A_{N-1}$ quantum $Q$-system. We identify the elements…
The analytic structure of elementary correlation functions of a quantum field is relevant for the calculation of masses of bound states and their time-like properties in general. In quantum chromodynamics, the calculation of correlation…
We derive conditions under which alternating renewal processes can be used to construct correlated Poisson processes. The pairwise correlation function is also derived, showing that the resulting correlations can be negative. The technique…
The Macdonald operator is known to coincide with a certain element of the quantum toroidal $\mathfrak{gl}(1)$ algebra in the Fock representation of levels $(1,0)$. A generalization of this operator to higher levels $(r,0)$ can be built…
In this paper we provide an alternative method to compute correlation functions in the in-in formalism, with a modified set of Feynman rules to compute loop corrections. The diagrammatic expansion is based on an iterative solution of the…
Schur's transforms of a polynomial are used to count its roots in the unit disk. These are generalized them by introducing the sequence of symmetric sub-resultants of two polynomials. Although they do have a determinantal definition, we…
In this work we apply a local quantum field theory approach in order to analyse the connection between real-time observables and Euclidean thermal correlation functions. In particular, using data generated from the functional…
We study correlations of hydrodynamic fluctuations in shear flow analytically and also by dissipative particle dynamics~(DPD) simulations. The hydrodynamic equations are linearized around the macroscopic velocity field and then solved by a…
We emphasize the importance of choosing an appropriate correlation function to reduce numerical errors in calculating the linear-response function as a Fourier transformation of a time-dependent correlation function. As an example we take…
Rosengren and Schlosser introduced notions of ${\it R}_N$-theta functions for the seven types of irreducible reduced affine root systems, ${\it R}_N={\it A}_{N-1}$, ${\it B}_{N}$, ${\it B}^{\vee}_N$, ${\it C}_{N}$, ${\it C}^{\vee}_N$, ${\it…
We compare two definitions of connected correlation functions in fluctuating geometries. We show results of the MC simulations for 4D dynamical triangulation in the elongated phase and compare them with the exact calculations of correlation…
This article presents a reformulation of the Theory of Functional Connections: a general methodology for functional interpolation that can embed a set of user-specified linear constraints. The reformulation presented in this paper exploits…
We apply symmetric function theory to study random processes formed by singular values of products of truncations of Haar distributed symplectic and orthogonal matrices. These product matrix processes are degenerations of Macdonald…
It is well known that martingale difference sequences are very useful in applications and theory. On the other hand, the operator fractional Brownian motion as an extension of the well-known fractional Brownian motion also plays important…
Explicit expressions for pion correlators are derived in position-space, employing Chiral Perturbation Theory (ChPT). Resonance exchange contributions are included to test the range of applicability of the leading-order ChPT expressions.…
In this paper we develop a technique of computation of correlation functions in theories with action being cubic or higher degree form in terms of discriminants of corresponding tensors. These are analogues of formula $\int \exp…
X-ray photon correlation spectroscopy was used to measure the diffusive dynamics of colloidal particles in a shear flow. The results presented here show how the intensity autocorrelation functions measure both the diffusive dynamics of the…