Related papers: Bootstrap Method in Theoretical Physics
The modern S-Matrix Bootstrap provides non-perturbative bounds on low-energy aspects of scattering amplitudes, leveraging the constraints of unitarity, analyticity and crossing. Typically, the solutions saturating such bounds also saturate…
We consider many-body problems in classical mechanics where a wide range of time scales limits what can be computed. We apply the method of optimal prediction to obtain equations which are easier to solve numerically. We demonstrate by…
We employ the so-called companion matrix method from computational algebraic geometry, tailored for zero-dimensional ideals, to study the scattering equations. The method renders the CHY-integrand of scattering amplitudes computable using…
We study two-dimensional conformal field theories (CFTs) with boundaries via the conformal bootstrap. We derive a positive semi-definite program from crossing symmetry of three observables: the annulus partition function, the two-point…
In this paper we deploy for the first time Reinforcement-Learning algorithms in the context of the conformal-bootstrap programme to obtain numerical solutions of conformal field theories (CFTs). As an illustration, we use a soft…
We demonstrate that combining the positivity of density matrices with steady-state conditions yields a systematic bootstrap method for studying open quantum many-body systems governed by Lindblad master equations on infinite lattices, which…
Resampling methods such as the bootstrap have proven invaluable in the field of machine learning. However, the applicability of traditional bootstrap methods is limited when dealing with large streams of dependent data, such as time series…
This paper presents a novel phase-field-based methodology for solving minimum compliance problems in topology optimization under fixed external loads and body forces. The proposed framework characterizes the optimal structure through an…
LECTURE GIVEN AT TH2002. Given a set of Boolean variables, and some constraints between them, is it possible to find a configuration of the variables which satisfies all constraints? This problem, which is at the heart of combinatorial…
A method is described for dealing with effective theories of hadron scattering. It allows one to reduce the number of independent renormalization prescriptions in those theories and gives a possibility to make numerical predictions. As an…
We apply the bootstrap technique to find the moments of certain multi-trace and multi-matrix random matrix models suggested by noncommutative geometry. Using bootstrapping we are able to find the relationships between the coupling constant…
A bootstrap program is presented for algebraically solving the $R$-matrix of a generic integrable quantum spin chain from its Hamiltonian. The Yang-Baxter equation contains an infinite number of seemingly independent constraints on the…
Statistical multispecies models of multiarea marine ecosystems use a variety of data sources to estimate parameters using composite or weighted likelihood functions with associated weighting issues and questions on how to obtain variance…
Hybrid computational schemes combining the advantages of a method of moments formulation of a field integral equation and T-matrix method are developed in this paper. The hybrid methods are particularly efficient when describing the…
We study the statistical Ising model of spins on the infinite lattice using a bootstrap method that combines spin-flip identities with positivity conditions, including reflection positivity and Griffiths inequalities, to derive rigorous…
Large $N$ matrix quantum mechanics is central to holographic duality but not solvable in the most interesting cases. We show that the spectrum and simple expectation values in these theories can be obtained numerically via a `bootstrap'…
We introduce the notion of branon jets, states of collinear flux tube excitations. We argue for the analyticity, crossing and unitarity of the multi-particle scattering of these jets and, through the S-matrix bootstrap, place bounds on a…
We show that bootstrap methods based on the positivity of probability measures provide a systematic framework for studying both synchronous and asynchronous nonequilibrium stochastic processes on infinite lattices. First, we formulate…
In this work, we present a novel approach for solving stochastic shape optimization problems. Our method is the extension of the classical stochastic gradient method to infinite-dimensional shape manifolds. We prove convergence of the…
In recent years, randomized methods for numerical linear algebra have received growing interest as a general approach to large-scale problems. Typically, the essential ingredient of these methods is some form of randomized dimension…