Related papers: Evaluating Sums over the Matsubara Frequencies
Computing accurate periodic responses in strongly nonlinear or even non-smooth vibration systems remains a fundamental challenge in nonlinear dynamics. Existing numerical methods, such as the Harmonic Balance Method (HBM) and the Shooting…
We present a quantum algorithm for calculating the vibronic spectrum of a molecule, a useful but classically hard problem in chemistry. We show several advantages over previous quantum approaches: vibrational anharmonicity is naturally…
Perturbative superstring theory is revisited, with the goal of giving a simpler and more direct demonstration that multi-loop amplitudes are gauge-invariant (apart from known anomalies), satisfy space-time supersymmetry when expected, and…
Iterative algorithms aimed at solving some problems are discussed. For certain problems, such as finding a common point in the intersection of a finite number of convex sets, there often exist iterative algorithms that impose very little…
Infinite series of the type Sum{n=1,infinity}(alpha/2)_n_2F_1(-n, b; gamma; y)/(n n!) are investigated. Closed-form sums are obtained for alpha a positive integer alpha=1,2,3, ... The limiting case of b --> infinity, after y is replaced…
One of the core research questions in the theory of quantum computing is to find out to what precise extent the classical simulation of a noisy quantum circuits is possible and where potential quantum advantages can set in. In this work, we…
A new version of the delta expansion is presented, which, unlike the conventional delta expansion, can be used to do nonperturbative calculations in a self-interacting scalar quantum field theory having broken symmetry. We calculate the…
We show that a spectrum of frequencies obtained by a random perturbation of the integers allows one to represent any measurable function on R by an almost everywhere converging sum of harmonics almost surely.
We discuss a new approach of scalar field theory where the small field contributions are treated perturbatively and the large field configurations (which are responsible for the asymptotic behavior of the perturbative series) are neglected.…
We present a generalization of the discrete Lehmann representation (DLR) to three-point correlation and vertex functions in imaginary time and Matsubara frequency. The representation takes the form of a linear combination of judiciously…
At high temperature the infrared modes of a weakly coupled quantum field theory can be treated nonperturbatively in real time using the classical field approximation. We use this to introduce a nonperturbative approach to the calculation of…
A finite-temperature many-body perturbation theory is presented that expands in power series the electronic grand potential, chemical potential, internal energy, and entropy on an equal footing. Sum-over-states and sum-over-orbitals…
We use the spectral theory of Hilbert-Maass forms for real quadratic fields to obtain the asymptotics of some sums involving the number of representations as a sum of two squares in the ring of integers.
A detailed description is provided of a new Worm Algorithm, enabling the accurate computation of thermodynamic properties of quantum many-body systems in continuous space, at finite temperature. The algorithm is formulated within the…
The hypercomputers compute functions or numbers, or more generally solve problems or carry out tasks, that cannot be computed or solved by a Turing machine. Several numerical simulations of a possible hypercomputational algorithm based on…
Numerical simulation is an important non-perturbative tool to study quantum field theories defined in non-commutative spaces. In this contribution, a selection of results from Monte Carlo calculations for non-commutative models is…
We consider the SUBSET SUM problem and its important variants in this paper. In the SUBSET SUM problem, a (multi-)set $X$ of $n$ positive numbers and a target number $t$ are given, and the task is to find a subset of $X$ with the maximal…
Most observables at particle colliders involve physics at a wide variety of distance scales. Due to asymptotic freedom of the strong interaction, the physics at short distances can be calculated reliably using perturbative techniques, while…
Finite-sum optimization has wide applications in machine learning, covering important problems such as support vector machines, regression, etc. In this paper, we initiate the study of solving finite-sum optimization problems by quantum…
The central aspect of my personal scientific activity, has focused on calculations useful for interpretation of High Energy accelerator experimental results, especially in a domain of precision tests of the Standard Model. My activities…