Related papers: Evaluating Sums over the Matsubara Frequencies
In this paper we will give a proof of a certain summation formula for Gamma functions utilizing Gegenbauer polynomials.
A method devised by the author is used to calculate analytical expressions for one loop integrals at finite temperature. A non-perturbative regularization of the integrals is performed, yielding expressions of non-polynomial nature. A…
We discuss a systematic way to dimensionally regularize divergent sums arising in field theories with an arbitrary number of physical compact dimensions or finite temperature. The method preserves the same symmetries of the action as the…
We give a short review on recent progress in the field of automated calculations in finite-temperature field theory, where integration-by-parts techniques have proven (almost) as useful as in the zero-temperature case. Furthermore, we…
We propose new quantum algorithms for estimating spectral sums of positive semi-definite (PSD) matrices. The spectral sum of an PSD matrix $A$, for a function $f$, is defined as $ \text{Tr}[f(A)] = \sum_j f(\lambda_j)$, where $\lambda_j$…
We describe a new and consistent perturbation theory for solid-state quantum computation with many qubits. The errors in the implementation of simple quantum logic operations caused by non-resonant transitions are estimated. We verify our…
It is shown how quantum field theory at finite temperature can be used to set up self-consistent and gauge invariant equations for cosmological perturbations sustained by an ultrarelativistic plasma. While in the collisionless case, the…
Hybrid automata are a natural framework for modeling and analyzing systems which exhibit a mixed discrete continuous behaviour. However, the standard operational semantics defined over such models implicitly assume perfect knowledge of the…
In various contexts in mathematical physics one needs to compute the logarithm of a positive unbounded operator. Examples include the von Neumann entropy of a density matrix and the flow of operators with the modular Hamiltonian in the…
Several problems in computer algebra can be efficiently solved by reducing them to calculations over finite fields. In this paper, we describe an algorithm for the reconstruction of multivariate polynomials and rational functions from their…
Measuring the vibronic spectrum probes dynamical processes in molecular systems. When interpreted via suitable theoretical tools, the experimental data provides comprehensive information about the system in question. For complex many-body…
Perturbation theory (PT) is often used to model statistical observables capturing the translation and rotation-invariant information in cosmological density fields. PT produces higher-order corrections by integration over linear statistics…
We illustrate the application of Quantum Computing techniques to the investigation of the thermodynamical properties of a simple system, made up of three quantum spins with frustrated pair interactions and affected by a hard sign problem…
We present a method to considerably improve the numerical performance for solving Eliashberg-type coupled equations on the imaginary axis. Instead of the standard practice of introducing a hard numerical cutoff for treating the infinite…
Time-domain radio astronomy utilizes a harmonic sum algorithm as part of the Fourier domain periodicity search, this type of search is used to discover single pulsars. The harmonic sum algorithm is also used as part of the Fourier domain…
We explore the behavior and establish new properties of the cumulative-sum process (CUSUM) and its running maximum. The study includes precise expressions for CUSUM's moment generating function and moments, fast recursive computing…
An algorithm, based on numerical description of the terms of many-body perturbation theory (Goldstone diagrams), is presented. The algorithm allows the use of the same piece of computer code to evaluate any particular diagram in any…
We have looked for evidence of large cross sections at large multiplicities in weakly coupled scalar field theory in three dimensions. We use spectral function sum rules to derive bounds on total cross sections where the sum can be expresed…
We formulate a general method for perturbative evaluations of statistics of smoothed cosmic fields, and provide useful formulas in application of the perturbation theory to various statistics. This formalism is an extensive generalization…
For a weakly coupled quantum field at high temperature the classical approximation offers a possibility to gain insight into nonperturbative real-time dynamics. I use this to present a nonperturbative approach to the computation of spectral…