相关论文: Resummation of not summable series

We investigate the ground-state energy of the integrable two dimensional $O(3)$ sigma model in a magnetic field. By determining a large number of perturbative coefficients we explore the closest singularities of the corresponding Borel…

A revised new iterative method based on Green function defined by quadratures along a single trajectory is developed and applied to solve the ground state of the double-well potential. The result is compared to the one based on the original…

Highly accurate closed-form approximations are given for the ground state and first excited state wavefunctions and energies for a nonrelativistic particle in a one-dimensional double square well potential with a square barrier in between…

In this paper, we investigate an example of summation of non-logarithmic singularities of a specific type in a two-dimensional non-linear sigma model. As a result of the study, we obtained an explicit formula, which, upon formal expansion…

Feynman diagrams in the instanton background are used for the calculation of the tunneling amplitude, up to the two-loops order. Some mistakes made in the previous works are corrected. The same method is applied to the next-order…

Methods of summation of power series relevant to applications in quantum theory are reviewed, with particular attention to expansions in powers of the coupling constant and in inverse powers of an energy variable. Alternatives to the Borel…

We compute multi-instanton amplitudes in the sine-Gordon quantum mechanics (periodic cosine potential) by integrating out quasi-moduli parameters corresponding to separations of instantons and anti-instantons. We propose an extension of…

This article is concerned with a special class of the ``double-well-like'' potentials that occur naturally in the analysis of finite quantum systems. Special attention is paid, in particular, to the so-called Fokker-Planck potential, which…

The gap between ground and first excited state of the quantum-mechanical double well is calculated using the Renormalization Group equations to the second order in the derivative expansion, obtained within a class of proper time regulators.…

We present a method for extracting tunnelling amplitudes from perturbation expansions which are always divergent and not Borel-summable. We show that they can be evaluated by an analytic continuation of variational perturbation theory. The…

Assuming a toroidal space with finite volume, we derive analytically the full one-loop vacuum energy for a scalar field tunnelling between two degenerate vacua, taking into account discrete momentum. The Casimir energy is computed for an…

New lower bounds for the binding energy of a quantum-mechanical system of interacting particles are presented. The new bounds are expressed in terms of two-particle quantities and improve the conventional bounds of the Hall-Post type. They…

We present a method for evaluating divergent non-Borel-summable series by an analytic continuation of variational perturbation theory. We demonstrate the power of the method by an application to the exactly known partition function of the…

We develop methods for resummation of instanton lattice series. Using these tools, we investigate the consequences of the Weak Gravity Conjecture for large-field axion inflation. We find that the Sublattice Weak Gravity Conjecture implies a…

The effective action for low-energy excitations of Laughlin's states is obtained by systematic expansion in inverse powers of the magnetic field. It is based on the W-infinity symmetry of quantum incompressible fluids and the associated…

We present a strong-weak coupling duality for quantum mechanical potentials. Similarly to what happens in quantum field theory, it relates two problems with inverse couplings, leading to a mapping of the strong coupling regime into the weak…

The level splitting formula of an asymmetric double well potential is calculated taking into account the multi-instanton contributions (dilute gas approximation). Results can be related with known semiclassical ones obtained with a…

We discuss resummation strategies for free energy in quantum field theories at nonzero temperatures T. We point out that resummations should be performed for the short- and long-distance parts separately in order to avoid spurious…

We study weak coupling perturbative series in 4d N=2 and 5d N=1 supersymmetric gauge theories with Lagrangians. We prove that the perturbative series of these theories in zero instanton sector are Borel summable for various observables. Our…

An infinite sequence of potential well functions is considered. A trial wavefunction is used with the Schr$\ddot{\text{o}}$dinger equation to obtain an approximate ground state energy for each potential well function. We obtain an…