Results 11 to 20 of about 48,968 (172)

Semiclassical asymptotics and entropy [PDF]

Journal of Physics: Conference Series, 2023
Abstract We study the entanglement of quantum states associated with submanifolds of Kaehler manifolds. As a motivating example, we discuss the semiclassical asymptotics of entanglement entropy of pure states on the two dimensional sphere with the standard metric.
Barron, Tatyana, Saikia, Manimugdha
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On Semiclassical Asymptotics for Nonlocal Equations

Russian Journal of Mathematical Physics, 2022
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Savin A.Yu., Nazaikinskii V.E.
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Semiclassical Asymptotics of Eigenvalues for Schrödinger Operators with Magnetic Fields [PDF]

Journal of Functional Analysis, 1995
The author studies the semi-classical asymptotics of eigenvalues for Schrödinger operators \(H(\lambda)\) with magnetic fields either on two-dimensional compact manifolds \(M\) or on \(\mathbb{R}^2\). Here \(H(\lambda)=1/2\nabla^{A_*}_\lambda\nabla^A_{\lambda}+\lambda^2V+\lambda v\), \(\lambda>0\), with \(\nabla^A_\lambda u=du+i\lambda uA\) \((i=\sqrt{-
Matsumoto, H.
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Semiclassical asymptotics of the Bloch–Torrey operator in two dimensions

Journal of the Mathematical Society of Japan
The Bloch--Torrey operator $-h^2Δ+e^{iα}x_1$ on a bounded smooth planar domain, subject to Dirichlet boundary conditions, is analyzed. Assuming $α\in\left[0,\frac{3π}{5}\right)$ and a non-degeneracy assumption on the left-hand side of the domain, asymptotics of the eigenvalues with the smallest real part in the limit $h \to 0$ are derived. The strategy
Hérau, Frédéric, Krejcirik, David, Raymond, Nicolas   +2 more
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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 ...
Guillemin V, Uribe A.
europepmc   +5 more sources

On Critical Behaviour in Systems of Hamiltonian Partial Differential Equations. [PDF]

J Nonlinear Sci, 2015
We study the critical behaviour of solutions to weakly dispersive Hamiltonian systems considered as perturbations of elliptic and hyperbolic systems of hydrodynamic type with two components.
Dubrovin B, Grava T, Klein C, Moro A.
europepmc   +2 more sources

Semiclassical asymptotics for Bergman projections with Gevrey weights

We extend the direct approach to the semiclassical asymptotics for Bergman projections, developed by Deleporte--Hitrik--Sjöstrand for real analytic exponential weights and Hitrik--Stone for smooth exponential weights, to the case of Gevrey weights. We prove that the amplitude of the asymptotic Bergman projection forms a Gevrey symbol whose asymptotic ...
Xiong, Haoren, Xu, Hang
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Semiclassical asymptotics for the Maxwell–Dirac system [PDF]

Journal of Mathematical Physics, 2003
We study the coupled system of Maxwell and Dirac equations from a semiclassical point of view. A rigorous nonlinear WKB-analysis, locally in time, for solutions of (critical) order O(ε) is performed, where the small semiclassical parameter ε≪1 denotes the microscopic/macroscopic scale ratio.
Sparber, Christoph, Markowich, Peter
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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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