Related papers: $1/\epsilon$ problem in resurgence
We investigate the resurgence structure in quantum mechanical models originating in 2d non-linear sigma models with emphasis on nearly supersymmetric and quasi-exactly solvable parameter regimes. By expanding the ground state energy in…
We study the integrable bi-Yang-Baxter deformation of the $SU(2)$ principal chiral model (PCM) and its finite action uniton solutions. Under an adiabatic compactification on an $S^1$, we obtain a quantum mechanics with an elliptic…
We present a formalism for semiclassical time evolution in quantum mechanics, building on a century of work. We identify complex saddle points in real time, real saddle points in complex time, and complex saddle points in complex time that…
A technique to reconstruct one-dimensional, reflectionless potentials and the associated quantum wave functions starting from a finite number of known energy spectra is discussed. The method is demonstrated using spectra that scale like the…
After setting up a general model for supersymmetric classical mechanics in more than one dimension we describe systems with centrally symmetric potentials and their Poisson algebra. We then apply this information to the investigation and…
We discuss two distinct aspects in supersymmetric quantum mechanics. First, we introduce a new class of operators A and $\bar{A}$ in terms of anticommutators between the momentum operator and N+1 arbitrary superpotentials. We show that…
The energy loss due to a quadratic velocity dependent force on a quantum particle bouncing on a perfectly reflecting surface is obtained for a full cycle of motion. We approach this problem by means of a new effective phenomenological…
We consider $1/Q$ corrections to hard processes in QCD where Q is a large mass scale, concentrating on shape variables in $e^{+}e^{-}$ annihilation. While the evidence for such corrections can be and has been established by means of the…
We analyze the problem of one dimensional quantum particle falling in a constant gravitational field, also known as the {\it bouncing ball}, employing a semiclassical approach known as momentous effective quantum mechanics. In this…
A method of fundamental solutions has been used to show its effectiveness in solving some well known problems of 1D quantum mechanics (barrier penetrations, over-barrier reflections, resonance states), i.e. those in which we look for…
In this work we explicitly show resurgence relations between perturbative and one instanton sectors of the resonance energy levels for cubic and quartic anharmonic potentials in one-dimensional quantum mechanics. Both systems satisfy the…
An investigation of the validity of the semiclassical approximation to quantum electrodynamics in 1+1 dimensions is given. The criterion for validity used here involves the impact of quantum fluctuations introduced through a two-point…
We calculate one-loop quantum energies in a renormalizable self-interacting theory in one spatial dimension by summing the zero-point energies of small oscillations around a classical field configuration, which need not be a solution of the…
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 study the Dirac equation in 3+1 dimensions with a general combination of scalar, vector and tensor interactions with arbitrary strengths, all of them described by central Coulomb potentials acting on a particular plane of motion. For the…
The motivation of this work is to get an additional insight into the irreversible energy dissipation on the quantum level. The presented examination procedure is based on the Feynman path integral method that is applied and widened towards…
The resonant state of the open quantum system is studied from the viewpoint of the outgoing momentum flux. We show that the number of particles is conserved for a resonant state, if we use an expanding volume of integration in order to take…
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…
We present a nonrelativistic one-particle quantum mechanics whose perturbative S-matrix exhibits a renormalon divergence that we explicitely compute. The potential of our model is the sum of the 2d Dirac $\delta$-potential -- known to…
We propose a new dark energy model for solving the cosmological fine-tuning and coincidence problems. A default assumption is that the fine-tuning problem disappears if we do not interpret dark energy as vacuum energy. The key idea to…