Related papers: Evaluating Sums over the Matsubara Frequencies
We consider the problem of an harmonic oscillator coupled to a scalar field in the framework of recently introduced dressed coordinates. We compute all the probabilities associated with the decay process of an excited level of the…
The study of the competition or coexistence of different ground states in many-body systems is an exciting and actual topic of research, both experimentally and theoretically. Quantum fluctuations of a given phase can suppress or enhance…
We perform certain alternating binomial summations with parameters that occur in the analysis of algorithms. A combination of integral and special function and special number representations is used. The results are sufficiently general to…
Simulating quantum circuits using classical computers lets us analyse the inner workings of quantum algorithms. The most complete type of simulation, strong simulation, is believed to be generally inefficient. Nevertheless, several…
We derive analytic results for scalar massless bosonic vacuum sum-integrals at two loops. Building upon a recent factorization proof of massive two-loop vacuum integrals, we are able to solve the corresponding Matsubara sums and map the…
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…
Spin wave computing device where an algorithm can be encoded by recording a corresponding magnetization pattern onto a hard magnetic material was previously proposed1 and a particular implementation of a vector-matrix algorithm was…
This article presents a new method to compute matrices from numerical simulations based on the ideas of sparse sampling and compressed sensing. The method is useful for problems where the determination of the entries of a matrix constitutes…
An algorithm is proposed for determining asymptotics of the sum of a perturbative series in the strong coupling limit using given values of the expansion coefficients. Operation of the algorithm is illustrated by test examples, method for…
The efficiency of exact subset sum problem algorithms which compute individual subset sums is defined as $e=min(T/z, 1)$, where $z$ is the number of subset sums computed. $e$ is related to these algorithms' computational complexity. This…
Using N=1 superspace techniques in four dimensions we show how to perturbatively compute the superpotential generated for the glueball superfield upon integrating out massive charged fields. The technique applies to arbitrary gauge groups…
First attempts in the application of Numerical Stochastic Perturbation Theory (NSPT) to the problem of pushing one loop further the computation of SU(3) (SU(2)) pertubative beta function (in different schemes) are reviewed and the relevance…
Practical application of the harmonic summing technique in the power-spectrum analysis for searching pulsars has exhibited the technique's effectiveness. In this paper, theoretical verification of harmonic summing considering power's…
Discrete translational symmetry plays a fundamental role in condensed matter physics and lattice gauge theories, enabling the analysis of systems that would otherwise be intractable. Despite this, many open problems remain. Quantum…
Yukawa theory at vanishing temperature provides (one of the ingredients for) an effective description of the thermodynamics of a variety of cold and dense fermionic systems. We study the role of masses and the renormalization group flow in…
The probabilistic satisfiability of a logical expression is a fundamental concept known as the partition function in statistical physics and field theory, an evaluation of a related graph's Tutte polynomial in mathematics, and the…
We construct a group field theory which realizes the sum of gravity amplitudes over all three dimensional topologies trough a perturbative expansion. We prove this theory to be uniquely Borel summable. This shows how to define a…
We present a method for calculating any (nested) harmonic sum to arbitrary accuracy for all complex values of the argument. The method utilizes the relation between harmonic sums and (derivatives of) Hurwitz zeta functions, which allows a…
Summation by parts is used to find the sum of a finite series of generalized harmonic numbers involving a specific polynomial or rational function. The Euler-Maclaurin formula for sums of powers is used to find the sums of some finite…
A computing program in Matlab is given that computes amplitudes in scalar $\phi^3$ theory. The program is partitioned into several parts and a simple guide is given for its use.