相关论文: Resummation of not summable series

For many physical quantities, theory supplies weak- and strong-coupling expansions of the types $\sum a_n \alpha ^n$ and $ \alpha ^p\sum b_n (\alpha^{-2/q) ^n$, respectively. Either or both of these may have a zero radius of convergence. We…

It has recently been observed [Phys. Rev. Lett. 113, 113002 (2014)] that the ground-state energy may be obtained directly as a simple sum of augmented Kohn-Sham orbital energies, where it was ascertained that the corresponding one-body…

We consider asymptotics of the ground state energy of heavy atoms and molecules in the self-generatedl magnetic field. Namely, we consider $$H=((D-A)\cdot\boldsymbol{\sigma})^2-V$$ with $$V=\sum_{1\le m\le M} \frac{Z_m}{|x-y_m|}$$ and a…

We present here a simple equation explicitly incorporating non-locality, which reproduces quantized energy levels of the bound states for the square well potentials. Introduction of this equation is motivated by studies of differential…

Using the general argument in Borel resummation of perturbation theory that links the divergent perturbation theory to the nonperturbative effect we argue that the nonperturbative effect associated with the perturbation theory should have a…

We provide an elementary proof of the dual representation of Expected Shortfall on the space of integrable random variables over a general probability space. Unlike the results in the extant literature, our proof only exploits basic…

For a quantum mechanical system with broken supersymmetry, we present a simple method of determining the ground state when the corresponding energy eigenvalue is sufficiently small. A concise formula is derived for the approximate ground…

Using a recent reformulation of quantum mechanics where the potential function is not required, we are able to obtain the energy spectrum and wave function associated with the infinite square well analytically. Therefore, this work…

The WKB and instanton answers for the tunnel splitting of the ground state in a symmetric double well potential are both reduced to an expression involving only the functionals of the potential, without the need for solving any auxilliary…

We derive a general WKB energy splitting formula in a double-well potential by incorporating both phase loss and anharmonicity effect in the usual WKB approximation. A bare application of the phase loss approach to the usual WKB method…

We consider the resummation of the perturbation series describing the energy displacement of a hydrogenic bound state in an electric field (known as the Stark effect or the LoSurdo-Stark effect), which constitutes a divergent formal power…

A new summation method is introduced to convert a relatively wide family of infinite sums and local expansions into integrals. The integral representations yield global information such as analytic continuability, position of singularities,…

Sum rules have played an important role in the development of many branches of physics since the earliest days of quantum mechanics. We present examples of one-dimensional quantum mechanical sum rules and apply them in two familiar systems,…

We use various methods of Borel integration to calculate the binding ground energies and masses of b-bbar and t-tbar quarkonia. The methods take into account the leading infrared renormalon structure of the hard+soft part of the binding…

A novel method of summation for power series is developed. The method is based on the self-similar approximation theory. The trick employed is in transforming, first, a series expansion into a product expansion and in applying the…

By using the WKB quantization we deduce an analytical formula for the energy splitting in a double--well potential which is the usual Landau formula with additional quantum corrections. Then we analyze the accuracy of our formula for the…

The path-integral approach to the double well has long been limited by the dilute instanton gas approximation. We show that if the finite Euclidean-time structure is taken seriously by using exact saddles, the dilute gas can be sidestepped,…

For the Cos(2x)-Potential the coefficients of the weak- and strong coupling perturbation series of the ground state energy are constructed recursively. They match the well-known expansion coefficients of the Mathieu equation's…

There is a continuing effort to support and prepare the precision physics programs for the present and planned future colliders such as HL-LHC, FCC, CLIC, CEPC, and CPPC. We discuss new results from IR-improved amplitude-based resummation…

The theory of resurgence uniquely associates a factorially divergent formal power series with a collection of exponentially small non-perturbative corrections paired with a set of complex numbers known as Stokes constants. When the Borel…