Results 11 to 20 of about 166 (151)
Современная математика: Фундаментальные направления, 2022 We describe the semiclassical asymptotic behavior of the solution of the Cauchy problem for the Schrödinger equation with a delta potential localized on a surface of codimension 1.
A. I. Shafarevich, O. A. Shchegortsova
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Strong Phase-Space Semiclassical Asymptotics [PDF]
SIAM Journal on Mathematical Analysis, 2011 Wigner and Husimi transforms have long been used for the phase-space reformulation of Schrödinger-type equations, and the study of the corresponding semiclassical limits. Most of the existing results provide approximations in appropriate weak topologies. In this work we are concerned with semiclassical limits in the strong topology, i.e.
Agissilaos Athanassoulis, Thierry Paul
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Semiclassical Approach to the Nonlocal Kinetic Model of Metal Vapor Active Media
Mathematics, 2021 A semiclassical approach based on the WKB–Maslov method is developed for the kinetic ionization equation in dense plasma with approximations characteristic of metal vapor active media excited by a contracted discharge.
Alexander V. Shapovalov +1 more
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Semiclassical asymptotics of nonlinear Fokker-Plank equation for distributions of asset returns [PDF]
Компьютерные исследования и моделирование, 2009 The semiclassical approximation method is applied for solution construction of the Fokker-Planck equation with quadratic nonlocal nonlinearity and various coefficients in models of asset returns estimation.
Andrey Yur'evich Trifonov +2 more
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Semiclassical Estimates¶in Asymptotically Euclidean Scattering [PDF]
Communications in Mathematical Physics, 2000 11 pages, 4 figures, AMS ...
Vasy, András, Zworski, Maciej
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Semiclassical asymptotics for a class of singular Schrödinger operators [PDF]
, 2021 Let $Ω\subset \mathbb{R}^d$ be bounded with $C^1$ boundary. In this paper we consider Schrödinger operators $-Δ+ W$ on $Ω$ with $W(x)\approx\mathrm{dist}(x, \partialΩ)^{-2}$ as $\mathrm{dist}(x, \partialΩ)\to 0$. Under weak assumptions on $W$ we derive a two-term asymptotic formula for the sum of the eigenvalues of such operators.
Rupert L. Frank, Simon Larson
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Bulletin of Mathematical Sciences, 2016 We discuss the asymptotics of the eigenvalue counting function for partial differential operators and related expressions paying the most attention to the sharp asymptotics.
Victor Ivrii
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Heat Kernels Estimates for Hermitian Line Bundles on Manifolds of Bounded Geometry
Mathematics, 2021 We consider a family of semiclassically scaled second-order elliptic differential operators on high tensor powers of a Hermitian line bundle (possibly, twisted by an auxiliary Hermitian vector bundle of arbitrary rank) on a Riemannian manifold of bounded
Yuri A. Kordyukov
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The Einstein-Ehrenfest system of (0, M)-type and asymptotical solutions of the multidimensional nonlinear Fokker-Planck-Kolmogorov equation [PDF]
Компьютерные исследования и моделирование, 2010 Semiclassical approximation formalism is developed for the multidimensional Fokker-Planck-Kolmogorov equation with non-local and nonlinear drift vector with respect to a small diffusion coefficient D, D0, in the class of trajectory concentrated functions.
Roman Olegovich Rezaev +2 more
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GLOBAL FOURIER INTEGRAL OPERATORS AND SEMICLASSICAL ASYMPTOTICS [PDF]
Reviews in Mathematical Physics, 2000 In this paper we introduce a class of semiclassical Fourier integral operators with global complex phases approximating the fundamental solutions (propagators) for time-dependent Schrödinger equations. Our construction is elementary, it is inspired by the joint work of the first author with Yu. Safarov and D. Vasiliev.
Laptev, A., Sigal, I. M.
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