Related papers: WKB and Resurgence in the Mathieu Equation
Based on some recent progress on a relation between four dimensional super Yang-Mills gauge theory and quantum integrable system, we study the asymptotic spectrum of the quantum mechanical problems described by the Mathieu equation and the…
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…
The physical reason why one can calculate with similar accuracy, as compared to the experimental data, the absolute cross section associated with two-nucleon transfer processes between members of pairing rotational bands, making use of…
We analyze the semiclassical Einstein equations for quantum scalar fields satisfying modified dispersion relations. We first discuss in detail the renormalization procedure based on adiabatic subtraction and dimensional regularization. We…
We consider partial theta series associated with periodic sequences of coefficients, of the form $\Theta(\tau) := \sum_{n>0} n^\nu f(n) e^{i\pi n^2\tau/M}$, with $\nu$ non-negative integer and an $M$-periodic function $f : \mathbb{Z}…
The ``trans-Planckian'' challenge in cosmology appears when we trace the present physical wavelengths of fluctuations backwards in time. They become smaller and smaller until crossing the Planck scale where conventional QFT is challenged,…
This technical note addresses the challenge of accurate turbulence characterization using robust, bandwidth-limited sensors which fail to resolve the high-wavenumber dissipation range. To correct the resulting underestimation of turbulent…
We provide a brief introduction to the high density effective theory of QCD. As an application, we consider the instanton correction to the perturbatively generated gap in the color superconducting phase. We show that the instanton…
The quest to find a nonperturbative formulation of topological string theory has recently seen two unrelated developments. On the one hand, via quantization of the mirror curve associated to a toric Calabi-Yau background, it has been…
In this paper, we study the exact WKB methods for solutions of the Schr\"{o}dinger equations corresponding to quantum Seiberg-Witten curves in 4d $\mathcal{N}=2$ theories with surface defects. The tools are Borel summation and…
Let $R$ be an iterable weak coarse premouse and let $N$ be a premouse with Mitchell-Steel indexing, produced by a fully backgrounded $L[\mathbb{E}]$-construction of $R$. We identify and correct a problem with the process of resurrection…
The primary objective of this work is to investigate the cosmological phase transitions in the early Universe, with a focus on the electroweak phase transition in the Standard Model and its extensions. In the Standard Model, the…
The Anderson transition between localized and metallic states is traditionally analyzed by assuming a one-parameter scaling hypothesis. Although that hypothesis has been confirmed near two dimensions by epsilon = d-2 expansion of the…
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…
This paper presents the derivation of Schwinger's gauge invariant result of $Im \cal{L}_{eff}$ upto one loop approximation, for particle production in an uniform electric field through the method of complex trajectory WKB approximation…
Inflationary reheating is almost completely controlled by the Floquet indices, $\mu_k$. Using spectral theory we demonstrate that the stability bands (where $\mu_k = 0$) of the Mathieu and Lam\'e equations are destroyed even in Minkowski…
The transport of intensity equation (TIE) has revolutionized phase retrieval in optical microscopy, yet its application to complex media with absorption/scattering remains challenging. Here, we present a coupled TIE-TPE (transport of phase…
Plasma turbulence, and edge density fluctuations in particular, can under certain conditions broaden the cross-section of injected microwave beams significantly. This can be a severe problem for applications relying on well-localized…
By using the formulation of the reconstruction, we explicitly construct models of $k$-essence, which unify the inflation in the early universe and the late accelerating expansion of the present universe by a single scalar field. Due to the…
Under certain assumptions and independent of the instantons, we show that the logarithm expansion of dimensional regularization in quantum field theory needs a nonperturbative completion to have a renormalization-group flow valid at all…