Related papers: From exact-WKB towards singular quantum perturbati…
We study solutions of the functional eigenstate equation of a free quantum field Hamiltonian. Admissible solutions are to have a finite norm and a finite eigenvalue w.r.t. the norm and eigenvalue of the ground state of the free theory. We…
We provide a systematic formula, in terms of integer partitions, that generates perturbation theory explicitly at an arbitrary order. Our approach naturally includes an infinite number of perturbations and uses a single matrix equation that…
We provide an abstract framework for singular one-dimensional Schroedinger operators with purely discrete spectra to show when the spectrum plus norming constants determine such an operator completely. As an example we apply our findings to…
In these notes, using the method of differential constraints, novel exact kink-like solutions are obtained for certain classes of complex Ginzburg--Landau equations with cubic-quintic nonlinearity. The foregoing solutions are presented in…
The Wentzel-Kramers-Brillouin (WKB) perturbative series, a widely used technique for solving linear waves, is typically divergent and at best, asymptotic, thus impeding predictions beyond the first few leading-order effects. Here, we report…
Resonance phenomena are central to many quantum systems, where resonant states are typically characterized by pole singularities of the S-matrix. In this work, we employ the complex scaling method (CSM) in conjunction with exact WKB…
This work develops a new method to calculate non-perturbative corrections in one-dimensional Quantum Mechanics, based on trans-series solutions to the refined holomorphic anomaly equations of topological string theory. The method can be…
A set of exactly solvable one-dimensional quantum mechanical potentials is described. It is defined by a finite-difference-differential equation generating in the limiting cases the Rosen-Morse, harmonic, and P\"oschl-Teller potentials.…
We consider a quantum particle in a 1D interval submitted to a potential. The evolution of this particle is controlled using an external electric field. Taking into account the so-called polarizability term in the model (quadratic with…
A nonlinear scattering transform is studied for the two-dimensional Schrodinger equation at zero energy with a radial potential. First explicit examples are presented, both theoretically and computationally, of potentials with nontrivial…
We investigate almost-degenerate perturbation theory of eigenvalue problems, using spectral projectors, also named density matrices. When several eigenvalues are close to each other, the coefficients of the perturbative series become…
In this thesis, we construct an approximate series solution of the Wigner equation in terms of Airy functions, which are semiclassically concentrated on certain Lagrangian curves in two-dimensional phase space. These curves are defined by…
We derive self-consistent constraint conditions for collision terms in quantum kinetic theory using the Wigner function formalism. We present specific solutions for these collision terms that align with the constraints. we develop quantum…
Recent works have suggested that nonlinear (quadratic) effects in black hole perturbation theory may be important for describing a black hole ringdown. We show that the technique of uniform approximations can be used to accurately compute…
We apply exact WKB analysis to the spectral problem arising in black hole perturbation theory. The boundary conditions for quasinormal modes lead to exact quantization conditions for the complex frequencies. To solve these conditions, one…
The eigenstates of a real or complex cubic anharmonic oscillator are investigated using original and alternative methods. The procedure consists of determining global solutions of the Schr\"odinger equation that comply with the pertinent…
We solve the eigenvalue spectra for two quasi exactly solvable (QES) Schr\"odinger problems defined by the potentials $V(x;\gamma,\eta) = 4\gamma^{2}\cosh^{4}(x) + V_{1}(\gamma,\eta) \cosh^{2}(x) + \eta \left( \eta-1 \right)\tanh^{2}(x)$…
We explore the exact-WKB (EWKB) method through the analysis of Airy and Weber types, with an emphasis on the exact quantization of locally harmonic potentials in multiple sectors. The core innovation of our work lies in introducing a novel…
The Bogoliubov transformation in cosmological particle production can be explained by the Stokes phenomena of the corresponding ordinary differential equation. The calculation becomes very simple as far as the solution is described by a…
We draw attention on the fact that the Riccati-Pad\'e method developed some time ago enables the accurate calculation of bound-state eigenvalues as well as of resonances embedded either in the continuum or in the discrete spectrum. We apply…