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We present further mathematical results on a function appearing in the conformal blocks of four-point correlation functions with arbitrary quasi-primary operators. The $H$-function was introduced in a previous article and it has several…
We review various theoretical methods that have been used in recent years to calculate dynamical correlation functions of many-body systems. Time-dependent correlation functions and their associated frequency spectral densities are the…
The coherence properties of phase fluctuating Bose-Einstein condensates are studied both theoretically and experimentally. We derive a general expression for the N-particle correlation function of a condensed Bose gas in a highly elongated…
We make use of a simple pair correlated wave function approach to obtain results for the ground-state densities and momentum distribution of a one-dimensional three-body bosonic system with different interactions in a harmonic trap. For…
In the setting of polynomial jump-diffusion dynamics, we provide an explicit formula for computing correlators, namely, cross-moments of the process at different time points along its path. The formula appears as a linear combination of…
The double-direction orthogonalization algorithm is applied to construct sequences of polynomials, which are orthogonal over the interval [0,1]with the weighting function 1. Functional and recurrent relations are derived for the sequences…
The correlation function of the trajectory exactly at the Feigenbaum point of the logistic map is investigated and checked by numerical experiments. Taking advantage of recent closed analytical results on the symbol-to-symbol correlation…
We analyze fast interaction cycles in bipartite quantum systems, showing that the statistics in one of the parties (the detector) can be used to determine the two-point correlator of the observable which mediates the coupling in the other…
Recent advances are being discussed on the calculation, within the conformal field theory approach, of the correlation functions for local operators in the theory of 2D gravity coupled to the minimal models of matter.
The calculation of dynamic response functions is expected to be an early application benefiting from rapidly developing quantum hardware resources. The ability to calculate real-time quantities of strongly-correlated quantum systems is one…
Derivation of the procedures that can be applied in evaluating two-time correlation function in terms of coherent-state propagator and corresponding Q-function is presented. On the basis that the involved functions are generally exponential…
We consider multiple orthogonal polynomials corresponding to two Macdonald functions (modified Bessel functions of the second kind), with emphasis on the polynomials on the diagonal of the Hermite-Pad\'e table. We give some properties of…
We derive compact multiple integral formulas for several physical spin correlation functions in the semi-infinite XXZ chain with a longitudinal boundary magnetic field. Our formulas follow from several effective re-summations of the…
One of the most important problems in any conformal field theory is the calculation of three-point functions of primary operators. In this paper we provide explicit examples of correlators with two scalar operators in $\,{\cal N}=4$…
We consider the Rosenzweig-Porter model of random matrix which interpolates between Poisson and gaussian unitary statistics and compute exactly the two-point correlation function. Asymptotic formulas for this function are given near the…
We show point processes generated in different ways and having different structure, presenting very similar power-law two--point correlation functions at small scales and quite different shapes at large scales.
Quantum statistical correlations and momentum distributions are calculated for a spherically symmetric, three-dimensionally expanding finite fireballs, for non-relativistic expansions applying plane-wave approximation. The new concepts of…
We investigate the functional form of the order-parameter (two-point) correlation function in quantum critical phenomena. Contrary to the common lore, when there is no particle-hole symmetry we find that the equal-time correlation function…
Subsequently to the author's preceding paper, we give full proofs of some explicit formulas about factorizations of $K$-$k$-Schur functions associated with any multiple $k$-rectangles.
A correlation function of the classical orthogonal polynomials is defined and determined. The correlation function obeys a second order difference equation in two variables. The correlation function for the Gegenbauer, Chebyshev and…