Related papers: On Exactness Of The Supersymmetric WKB Approximati…
We explain when the first-order Hamilton-Jacobi equations for black holes (and domain walls) in (gauged) supergravity, reduce to the usual first-order equations derived from a fake superpotential. This turns out to be equivalent to the…
We have obtained a set of coupled differential equations from the continuous limit of the transfer matrix method. Decoupling such a set of equations yields an extension to the Wentzel-Kramers-Brillouin (WKB) approximation for the…
The equivalence between logarithmic Sobolev inequalities and hypercontractivity of solutions of Hamilton-Jacobi equations has been proved in [5]. We consider a semi-Lagrangian approximation scheme for the Hamilton-Jacobi equation and we…
{}From Feynman's path integral, we derive quasi-classical quantization rules in supersymmetric quantum mechanics (SUSY-QM). First, we derive a SUSY counterpart of Gutzwiller's formula, from which we obtain the quantization rule of Comtet,…
The conventional Hamiltonian $H= p^2+ V_N(x)$, where the potential $V_N(x)$ is a polynomial of degree $N$, has been studied intensively since the birth of quantum mechanics. In some cases, its spectrum can be determined by combining the WKB…
We prove an existence and uniqueness theorem for exact WKB solutions of general singularly perturbed linear second-order ODEs in the complex domain. These include the one-dimensional time-independent complex Schr\"odinger equation. Notably,…
The paper deals with Hawking radiation related to non-static spherically symmetric black hole. Quantum corrections are incorporated using Hamilton-Jacobi method beyond semi-classical approximation. It is found that different order…
A procedure for the numerical approximation of high-dimensional Hamilton-Jacobi-Bellman (HJB) equations associated to optimal feedback control problems for semilinear parabolic equations is proposed. Its main ingredients are a…
We consider exact WKB analysis to a ${\cal PT}$ symmetric quantum mechanics defined by the potential, $V(x) = \omega^2 x^2 + g x^2(i x)^{\varepsilon=2}$ with $\omega \in {\mathbb R}_{\ge 0}$, $g \in {\mathbb R} _{> 0}$. We in particular aim…
\(\Un{N}\) coherent states over Grassmann manifold, \(\grsmn{N}{n}\simeq\Un{N}/ (\Un{n}\times \Un{N-n})\), are formulated to be able to argue the WKB-exactness, so called the localization of Duistermaat-Heckman, in the path integral…
We calculate the Yukawa corrections of order ${\cal O}(\alpha_{ew}m_{t(b)}^2/m_W^2)$, ${\cal O}(\alpha_{ew}m_{t(b)}^3/m_W^3)$ and ${\cal O}(\alpha_{ew}m_{t(b)}^4/m_W^4)$ to the widths of the decays $\tilde t_2\to \tilde t_1 + (h^0,H^0,A^0)$…
In this thesis, we develop WKB techniques for the finite difference Schrodinger equation, following the construction of the WKB approach for the standard differential Schrodinger equation. In particular, we will develop an all-order WKB…
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…
By using the WKB quantization we deduce an analytical formula for the energy splitting in a double--well potential which is the usual Landau formula with additional quantum corrections. Then we analyze the accuracy of our formula for the…
Poles of solutions to the Painleve-I equation are intimately related to the theory of the cubic anharmonic oscillator. In particular, poles of integrale tritronquee are in 1-1 correspondence with cubic oscillators that admit the…
In this paper, we revisit the well known Bohr-Sommerfeld quantization rule (BS) of order 2 for a self-adjoint 1-D semiclassical pseudo-differential operator, within the algebraic and microlocal framework of B. Helffer and J. Sj\"{o}strand.…
We consider a family of periodic scalar operators for which one can define flat bands in the sense of Floquet-Bloch theory. One puzzling question originating in recent physics literature is a quantisation rule for the values of parameters…
Based on spin-orbit coupling induced by q-plates, we present a feasible experimental proposal for preparing two-dimensional spatially inhomogeneous polarizations of light. We further investigate the quantum correlations between these…
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…
In this paper, the SQP method applied to a hyperbolic PDE-constrained optimization problem is considered. The model arises from the acoustic full waveform inversion in the time domain. The analysis is mainly challenging due to the involved…