Related papers: Exact WKB Analysis and TBA Equations for the Stark…
A Bohr-Sommerfeld quantization rule is generalized for the case of the deformed commutation relation leading to minimal uncertainties in both coordinate and momentum operators. The correctness of the rule is verified by comparing obtained…
We propose an exact summation method to compute thermodynamic observables in integrable quantum field theories. The key idea is to use the matrix-tree theorem to write the Gaudin determinants that appear in the cluster expansion as a sum…
Thermodynamic properties of the one-dimensional (1D) quantum well (QW) with miscellaneous permutations of the Dirichlet (D) and Neumann (N) boundary conditions (BCs) at its edges in the perpendicular to the surfaces electric field…
The study of asymptotic properties of solutions to differential equations has a long and arduous history, with the most significant advances having been made in the development of quantum mechanics. A very powerful method of analysis is…
This is a continuation of developing mutation theory in exact WKB analysis using the framework of cluster algebras. Here we study the Schrodinger equation on a compact Riemann surface with turning points of simple-pole type. We show that…
We propose an extension of Wenzel-Kramers-Brillouin (WKB) approximation for solving the Schr\"odinger equation. A set of coupled differential equations is obtained by considering an ansatz of the wave function with an auxiliary condition on…
Most studies of PT-symmetric quantum-mechanical Hamiltonians have considered the Schroedinger eigenvalue problem on an infinite domain. This paper examines the consequences of imposing the boundary conditions on a finite domain. As is the…
We justify the WKB analysis for generalized nonlinear Schr{\"o}dinger equations (NLS), including the hyperbolic NLS and the Davey-Stewartson II system. Since the leading order system in this analysis is not hyperbolic, we work with analytic…
We extend topological string methods in order to perform WKB approximations for quantum mechanical problems with higher order potentials efficiently. This requires techniques for the evaluation of the relevant quantum periods for Riemann…
We develop a method that can constrain any local exchange-correlation potential to preserve ba-sic exact conditions. Using the method of Lagrange multipliers, we calculate for each set of given Kohn-Sham orbitals, a constraint-preserving…
By invoking supersymmetry, we found a condition under which the Stark effect problem for a polar and polarizable molecule subject to nonresonant electric fields becomes exactly solvable. The exact solvability condition for the interaction…
The exactly solvable Schr\"{o}dinger equations with the conventional shape-invariant potentials are known to be related with each other through point cannonical transformations. In this paper, we extend the idea to integral formulae called…
We investigate the thermodynamic and optical signatures of electrically charged black holes (BHs) in symmetric teleparallel gravity (STPG) with non-minimal electromagnetic coupling, incorporating quantum corrections and plasma dispersion…
We investigate asymptotic decay phenomenon towards the nonequilibrium steady state of the thermal diffusion in the presence of a tilted periodic potential. The parameter dependence of the decay rate is revealed by investigating the…
The broadening of lines by Stark effect is an important tool for inferring electron density and temperature in plasmas. Stark-effect calculations often rely on atomic data (transition rates, energy levels,...) not always exhaustive and/or…
This paper addresses the numerical implementation of the transparent boundary condition (TBC) and its various approximations for the free Schr\"odinger equation on a rectangular computational domain. In particular, we consider the exact TBC…
The evolution of the vacuum state in a time-dependent external electric field of arbitrary polarization is investigated within a nonperturbative framework of quantum kinetic equations (QKEs). In our previous work [Phys. Rev. Res. 6, 043009…
The first part of these lecture notes is devoted to an introduction to the theory of exact WKB analysis for second-order Schr\"odinger-type ordinary differential equations. It reviews the construction of the WKB solution, Borel summability,…
We present an exact single-electron picture that describes the correlated electron dynamics in strong laser fields. Our approach is based on the factorization of the electronic wavefunction as a product of a marginal and a conditional…
There is an interesting relation between the quantum periods on a certain limit of local $\mathbb{P}^1\times \mathbb{P}^1$ Calabi-Yau space and a TBA (Thermodynamic Bethe Ansatz) system appeared in the studies of ABJM…