Related papers: Non-perturbative instanton effects in the quartic …
We study the effect of anharmonicity in quantum anharmonic oscillators, by computing the energy gap between the ground and the 1st excited state using the numerical bootstrap method. Based on perturbative formulae of limiting coupling…
Numerical Stochastic Perturbation Theory (NSPT) has over the years proved to be a valuable tool, in particular being able to reach unprecedented orders for Lattice Gauge Theories, whose perturbative expansions are notoriously cumbersome.…
I show that the method of finding if the ground state energy is nonzero or not by saturating the functional integral directly with instanton-anti-instanton type fluctuations is not reliable either for the double or for the triple well…
We apply an asymptotic bootstrap estimate method to the non-perturbative study of unitary matrix integrals. The method combines exact recursion relations with asymptotic control of large modes to achieve very high numerical precision…
Within the framework of the instanton approach we present analytical results for the following model problems: (i) particle penetration through a parabolic potential barrier, where the instanton solution practically coincides with the exact…
We study the quantum-mechanical bootstrap as it applies to the bound states of several central potentials in three dimensions. As part of this effort, we show how the bootstrap approach may be applied to ``non-algebraic'' potentials, such…
We review the euclidean path-integral formalism in connection with the one-dimensional non-relativistic particle. The configurations which allow to construct a semiclassical approximation classify themselves into either topological…
Instantons play a crucial role in understanding non-perturbative dynamics in quantum field theories, including those with spontaneously broken gauge symmetries. In the broken phase, finite-size instanton-like configurations are no longer…
This paper examines methods of inference concerning quantile treatment effects (QTEs) in randomized experiments with matched-pairs designs (MPDs). Standard multiplier bootstrap inference fails to capture the negative dependence of…
In this second part of the treatment of instantons in quantum mechanics, the focus is on specific calculations related to a number of quantum mechanical potentials with degenerate minima. We calculate the leading multi-instanton…
In quantum mechanics and quantum field theory perturbation theory generically requires the inclusion of extra contributions non-perturbative in the coupling, such as instantons, to reproduce exact results. We show how full non-perturbative…
The bootstrap method aims to solve problems by imposing constraints on the space of physical observables, which often follow from physical assumptions such as positivity and symmetry. Here, we employ a bootstrap approach to study…
The purpose of the ``bootstrap program'' for integrable quantum field theories in 1+1 dimensions is to construct a model in terms of its Wightman functions explicitly. In this article, this program is mainly illustrated in terms of the…
The low-energy-level macroscopic wave functions of the Bose-Einstein condensate(BEC) trapped in a symmetric double-well and a periodic potential are obtained by solving the Gross-Pitaevskii equation numerically. The ground state tunnel…
Path integral implementation of the quantum instanton approximation currently belongs among the most accurate methods for computing quantum rate constants and kinetic isotope effects, but its use has been limited due to the rather high…
The nonperturbative effects in the high-energy processes involving strongly interacting particles are studied within the instanton liquid model of the QCD vacuum (ILM) by using the Wilson integral framework. The detailed analysis of…
A numerical bootstrap method is proposed to provide rigorous and nontrivial bounds in general quantum many-body systems with locality. In particular, lower bounds on ground state energies of local lattice systems are obtained by imposing…
This paper develops bootstrap methods for practical statistical inference in panel data quantile regression models with fixed effects. We consider random-weighted bootstrap resampling and formally establish its validity for asymptotic…
Current statistics literature on statistical inference of random fields typically assumes that the fields are stationary or focuses on models of non-stationary Gaussian fields with parametric/semiparametric covariance families, which may…
Instanton theory is an established method to calculate rate constants of chemical reactions including atom tunneling. Technical and methodological improvements increased its applicability. Still, a large number of energy and gradient…