Related papers: Multi-Instantons and Exact Results I: Conjectures,…
Certain quantum mechanical potentials give rise to a vanishing perturbation series for at least one energy level (which as we here assume is the ground state), but the true ground-state energy is positive. We show here that in a typical…
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…
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…
In view of experimentally obtainable resolutions, equal to the Compton wavelength of an electron, the conventional interpretation of quantum mechanics no longer seems to provide a sufficiently subtle tool. Based on the intrinsic properties…
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…
The energy levels of the double-well potential receive, beyond perturbation theory, contributions which are non-analytic in the coupling strength; these are related to instanton effects. For example, the separation between the energies of…
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…
The `strong-coupling' perturbation theory over the inverse interaction constant $1/g$ near the nontrivial solution of Lagrange equation is formulated. The ordinary `week-coupling' perturbation theory over $g$ is described also to compare…
Starting from our idea of combining the Feynman path integral spirit and the Dyson series kernel, we find an explicit and general form of time evolution operator that is a $c$-number function and a power series of perturbation including all…
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…
Quantum mechanics has many counter-intuitive consequences which contradict our intuition which is based on classical physics. Here we discuss a special aspect of quantum mechanics, namely the possibility of entanglement between two or more…
Two major deviations from causality in the existing formulations of quantum mechanics, related respectively to quantum chaos and indeterminate wave reduction, are eliminated within the new, universal concept of dynamic complexity. The…
We use exact WKB analysis to derive some concrete formulae in singular quantum perturbation theory, for Schr\"odinger eigenvalue problems on the real line with polynomial potentials of the form $(q^M + g q^N)$, where $N>M>0$ even, and…
We develop techniques to compute multi-instanton corrections to the 1/N expansion in matrix models described by orthogonal polynomials. These techniques are based on finding trans-series solutions, i.e. formal solutions with exponentially…
We develop a perturbation theory of quantum (and classical) master equations with slowly varying parameters, applicable to systems which are externally controlled on a time scale much longer than their characteristic relaxation time. We…
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…
The quantum mechanics formalism introduced new revolutionary concepts challenging our everyday perceptions. Arguably, quantum entanglement, which explains correlations that cannot be reproduced classically, is the most notable of them.…
We calculate the multi-instanton corrections to the ground state energy in large $N$ Matrix Quantum Mechanics. We find that they can be obtained, through a non-perturbative difference equation, from the multi-instanton series in…
We analyze quantitatively the accuracy of eigenfunction and eigenvalue calculations in the frame work of WKB and instanton semiclassical methods. We show that to estimate the accuracy it is enough to compare two linearly independent (with…