相关论文: Exact WKB Formulation of Quantization and Particle…
Particle production by slow-changing gravitational fields is usually described using quantum field theory in curved spacetime. Calculations require a definition of the vacuum state, which can be given using the adiabatic (WKB)…
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 complex time WKB (CWKB) approximation has been an effective technique to understand particle production in curved as well as in flat spacetime. Earlier we obtained the standard results on particle production in time dependent gauge in…
Cosmological particle production by a time-dependent scalar field is common in cosmology. We focus on the mechanism of asymmetry production when interaction explicitly violates symmetry and its motion is rapid enough to create particles by…
In this work, we develop and apply the WKB approximation to several examples of noncommutative quantum cosmology, obtaining the time evolution of the noncommutative universe, this is done starting from a noncommutative quantum formulation…
We explore the possibility of modifying the Lewis-Riesenfeld method of invariants developed originally to find exact solutions for time-dependent quantum mechanical systems for the situation in which an exact invariant can be constructed,…
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…
There are two well-known approaches to studying nonperturbative aspects of quantum mechanical systems: Saddle point analysis of the partition functions in Euclidean path integral formulation and the exact-WKB analysis based on the wave…
The problem of time emerging in the canonical quantization procedure of gravity signals a necessity to properly define a relational time parameter. Previous approaches, which are here briefly discussed, make use of the dependence of the…
We investigate the exact-WKB analysis for quantum mechanics in a periodic potential, with $N $ minima on $S^{1}$. We describe the Stokes graphs of a general potential problem as a network of Airy-type or degenerate Weber-type building…
In this work we study the particle production in time dependent periodic potential using the method of complex time WKB (CWKB) approximation. In the inflationary cosmology at the end of inflationary stage, the potential becomes time…
Solution of the Schr\"odinger's equation in the zero order WKB approximation is analyzed. We observe and investigate several remarkable features of the WKB$_0$ method. Solution in the whole region is built with the help of simple connection…
The diffusion approximation (DA) is widely used in the analysis of stochastic population dynamics, from population genetics to ecology and evolution. DA is an uncontrolled approximation that assumes the smoothness of the calculated quantity…
We revisit exact WKB quantization for radial Schr\"odinger problems from the modern resurgence perspective, with emphasis on how ``physically meaningful'' quantization paths should be chosen and interpreted. Using connection formulae at…
We study quasi-stationary states in quantum mechanics using the exact Wentzel--Kramers--Brillouin (WKB) analysis as a nonperturbative framework. Whereas previous works focused mainly on stable systems, we explore unstable states such as…
We formulate a ''minimal'' interpretational scheme for fairly general (minisuperspace) quantum cosmological models. Admitting as few exact mathematical structure as is reasonably possible at the fundamental level, we apply approximate…
This paper discusses how particle production from the vacuum can be explained by local analysis when the field theory is defined by differential geometry on curved manifolds. We have performed the local analysis in a mathematically rigorous…
We discuss the exact quantization of general one-dimensional potentials in view of the exact-WKB formalism. Building on our previous work, we perform analytic continuations across different sectors via the complexification to the spectral…
The WKB approximation plays an essential role in the development of quantum mechanics and various important results have been obtained from it. In this paper, we introduce another method, {\it the so-called uniform asymptotic…
The physical observables of quantum theory can be described by perturbation theory, which is often given by diverging power series. This divergence is connected to the existence of non-perturbative phenomena, where resurgence allows us to…