相关论文: Instantons in Quantum Mechanics and Resurgent Expa…

We consider specific quantum mechanical model problems for which perturbation theory fails to explain physical properties like the eigenvalue spectrum even qualitatively, even if the asymptotic perturbation series is augmented by…

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…

We consider expansions of eigenvalues and eigenvectors of models of quantum field theory. For a class of models known as generalized spin boson model we prove the existence of asymptotic expansions of the ground state and the ground state…

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…

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…

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…

An alternative perturbative expansion in quantum mechanics which allows a full expression of the scaling arbitrariness is introduced. This expansion is examined in the case of the anharmonic oscillator and is conveniently resummed using a…

In a large variety of quantum mechanical systems, we show that the full non-perturbative expression for energy eigenvalues, containing all orders of perturbative, non-perturbative and quasi-zero-mode terms, may be generated directly from…

The study of the convergence of power series expansions of energy eigenvalues for anharmonic oscillators in quantum mechanics differs from general understanding, in the case of quasi-exactly solvable potentials. They provide examples of…

We present a general analytic expansion in powers of $1/n$ of the resonant states of quantum-mechanical systems, where $n=1,2,3,\cdots$ is the excitation number. Explicit formulas are obtained for some potential barrier models.

We illustrate the physical significance and mathematical origin of resurgent trans-series expansions for energy eigenvalues in quantum mechanical problems with degenerate harmonic minima, by using the uniform WKB approach. We provide…

We derive out a complete series expression of Hamiltonian eigenvalues without any approximation and cut in the general quantum systems based on Wang's formal framework \cite{wang1}. In particular, we then propose a calculating approach of…

An effective description of an initial state is a method for representing the signatures of new physics in the short-distance structure of a quantum state. The expectation value of the energy-momentum tensor for a field in such a state…

The behavior of the quantum potential is studied for a particle in a linear and a harmonic potential by means of an extended phase space technique. This is done by obtaining an expression for the quantum potential in momentum space…

A quantum field has been coupled to a space-time with accelerating expansion. Dynamical modes are destabilised successively at shorter material wavelengths as they metamorphose from oscillators to repellers. Due to degeneracy of energy…

The intricate machinery of perturbative quantum field theory has largely been devoted to the 'dynamical' side of the theory: simple states are evolved in complicated ways. This article begins to address this lopsided treatment. Although it…

A central object in any axionic theory is its periodic potential, which is typically generated by instantons. The goal of this paper is to understand what physically happens to the theory when we lose control of the potential's instanton…

In the probabilistic approach to quantum many-body systems, the ground-state energy is the solution of a nonlinear scalar equation written either as a cumulant expansion or as an expectation with respect to a probability distribution of the…

Instanton -- antiinstanton pair is considered as a source of singularity at the Borel plane for the ground state energy of anharmonic oscillator. The problem of defining the short range instanton -- antiinstanton interaction reduces to…

In this paper, we sketch and emphasize the automatic emergence of a quantum potential (QP) in general Hamilton-Jacobi equation via commuting relations, quantum canonical transformations and without the straight effect of wave function. The…