Results 11 to 20 of about 8,950 (170)
Reduction, the trace formula, and semiclassical asymptotics. [PDF]
Proc Natl Acad Sci U S A, 1987 We state a theorem that relates the theory of dimensional reduction in Hamiltonian mechanics to the spectral properties of elliptic operators with symmetries on compact manifolds. As an application, we show that the spectrum of the Schrödinger operator, -[unk]hΔ + V , as [unk]h → 0, contains geometric information ...
Guillemin V, Uribe A.
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Comparative asymptotics for discrete semiclassical orthogonal polynomials
Bulletin of Mathematical Sciences, 2023 We study the ratio [Formula: see text] asymptotically as [Formula: see text], where the polynomials [Formula: see text] are orthogonal with respect to a discrete linear functional and [Formula: see text] denote the falling factorial polynomials.
Diego Dominici
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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 Schr dinger-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. approximation
Athanassoulis, Agissilaos, Paul, Thierry
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Semiclassical Asymptotics for Weakly Nonlinear Bloch Waves [PDF]
Journal of Statistical Physics, 2004 References added; more explanations; inaccuracy concerning the initial data ...
Carles, Rémi +2 more
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Transverse Evolution Operator for the Gross-Pitaevskii Equation in Semiclassical Approximation [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2005 The Gross-Pitaevskii equation with a local cubic nonlinearity that describes a many-dimensional system in an external field is considered in the framework of the complex WKB-Maslov method.
Alexey Borisov +2 more
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Annals of Mathematics, 1999 We derive semiclassical asymptotics for the orthogonal polynomials P_n(z) on the line with respect to the exponential weight \exp(-NV(z)), where V(z) is a double-well quartic polynomial, in the limit when n, N \to \infty. We assume that \epsilon \le (n/N)
Bleher, Pavel, Its, Alexander
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Frontiers in Applied Mathematics and StatisticsThe purpose of this note is to review certain recent results concerning the pseudospectra and the eigenvalues asymptotics of non-selfadjoint semiclassical pseudo-differential operators subject to small random perturbations.
Martin Vogel
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Semiclassical Asymptotics Beyond All Orders for Simple Scattering Systems [PDF]
SIAM Journal on Mathematical Analysis, 1995 The scattering matrix \(S\) for the equation \(i\varepsilon {d\varphi(t)\over dt}= A(t)\varphi(t)\), when \(\varepsilon\to 0\), is considered. It is supposed that \(A\) is an analytic \(n\times n\) matrix whose eigenvalues are real and distinct for all \(t\). The asymptotics for the matrix \(S\) are given up to errors \(O(\exp(- k\varepsilon^{- 1}))\),
Joye, Alain, Pfister, Charles-Edouard
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Semiclassical Asymptotics of the Aharonov‐Bohm Interference Process [PDF]
Annalen der Physik, 2017 AbstractWe systematically derive the semiclassical limit of a charged particle's motion in the presence of an infinitely long and infinitesimally thin solenoid carrying magnetic flux. Our limit establishes the connection of the particle's quantum mechanical canonical angular momentum to the latter's classical counterpart.
Fischer, Stefan Georg +2 more
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Semiclassical asymptotics on covering manifolds and morse inequalities
Geometric and Functional Analysis, 1996 The paper contains a review of results which can be obtained by applying the Witten deformation method and general semi-classical asymptotics to the case of regular covering manifolds. The author formulates general semi-classical asymptotics and Morse type inequalities in a way which is more explicit, making use of the general notion of a model ...
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