Related papers: Fourier-Matsubara series expansion for imaginary-t…
The discrete Fourier transform is approximated by summing over part of the terms with corresponding weights. The approximation reduces significantly the requirement for computer memory storage and enhances the numerical computation…
Femtoscopic interferometry is a powerful tool for probing the spatio-temporal evolution of emission sources in heavy-ion collisions. A major challenge in the field is formulating a self-consistent description of the source function,…
In the present article the author extends the Fourier transform to a more general class of functions; First to power-law functions with integer and half-integer exponents then to the widely used quantum statistics function (Fermi-Dirac and…
The Fourier extension method, also known as the Fourier continuation method, is a method for approximating non-periodic functions on an interval using truncated Fourier series with period larger than the interval on which the function is…
An expansion for quantum statistical mechanics is derived that gives classical statistical mechanics as the leading term. Each quantum correction comes from successively larger permutation loops, which arise from the factorization of the…
By combining conventional finite-temperature many-body perturbation theory with cluster expansions, we develop a systematic method to carry out high order arbitrary temperature perturbative calculations on the computer. The method is well…
We consider quantum corrections to classical real time correlation functions at finite temperature. We derive a semi-classical expansion in powers of $\hbar$ with coefficients including all orders in the coupling constant. We give explicit…
Experiments creating extreme states of matter almost invariably create non-equilibrium states. These are very interesting in their own right but need to be understood even if the ultimate goal is to probe high-pressure or high-temperature…
An exact series representation of the even frequency moments of the dynamic structure factor is derived. Truncations are proposed that allow to evaluate the explicitly unknown second, fourth and fifth frequency moments for the finite…
We study an extension to Fourier transforms of the old problem on absolute convergence of the re-expansion in the sine (cosine) Fourier series of an absolutely convergent cosine (sine) Fourier series. The results are obtained by revealing…
We rewrite the imaginary-time formalism of finite temperature field theory in a form that all graphs used in calculating physical processes do not have any loops. Any production of a particle from a heat bath which is itself not thermalized…
A generalization of the max-plus transformation, which is known as a method to derive cellular automata from integrable equations, is proposed for complex numbers. Operation rules for this transformation is also studied for general number…
A statistical method is derived for the calculation of thermodynamic properties of many-body systems at low temperatures. This method is based on the self-healing diffusion Monte Carlo method for complex functions [F. A. Reboredo J. Chem.…
In this note we consider the Fourier expansion of the Ferrers function P of the first kind. We determine its mode of convergence.
In this article, the concept of $\mu-$ monotonic property of interval-valued function in higher dimension is introduced. Expansion of interval-valued function in higher dimension is developed using this property. Generalized Hukuhara…
This is a discussion of miscellaneous summation, integration and transformation formulas obtained using Fourier analysis. The topics covered are: Series of the form $\sum_{n\in\mathbb{Z}} c_ne^{\pi i \gamma n^2}$; Fusion of integrals, and…
An abstract theory of Fourier series in locally convex topological vector spaces is developed. An analog of Fej\'{e}r's theorem is proved for these series. The theory is applied to distributional solutions of Cauchy-Riemann equations to…
We discuss the various definitions of time correlation functions and how to estimate them from experimental or simulation data. We start with the various definitions, both in real and in Fourier space, and explain how to extract from them a…
Some of the well-known effects regarding the vacuum are revisited under the formalism of the imaginary-time field theory. From these effects, they could imply the existence of one thermal vacuum in different circumstances. The…
The use of empirical characteristic functions for inference problems, including estimation in some special parametric settings and testing for goodness of fit, has a long history dating back to the 70s (see for example, Feuerverger and…