STRONG AND WEAK SEMICLASSICAL LIMIT FOR SOME ROUGH HAMILTONIANS

DOI10.1142/S0218202512500388zbMath1255.35185arXiv1011.1651OpenAlexW3100645819MaRDI QIDQ4649858

Thierry Paul, Agissilaos G. Athanassoulis

Publication date: 15 November 2012

Published in: Mathematical Models and Methods in Applied Sciences (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1011.1651

zbMATH Keywords

semiclassical limitWigner transformnon-uniquely defined flow

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory (81Q20) Weak solutions to PDEs (35D30) Time-dependent Schrödinger equations and Dirac equations (35Q41) Strong solutions to PDEs (35D35)

Related Items (5)

On the selection of the classical limit for potentials with BV derivatives ⋮ Wigner measure propagation and conical singularity for general initial data ⋮ Classical limit for a system of non-linear random Schrödinger equations ⋮ Semiclassical regularization of Vlasov equations and wavepackets for nonlinear Schrödinger equations ⋮ Algebras of semiclassical pseudodifferential operators associated with Zoll-type domains in cotangent bundles

Cites Work

• Unnamed Item
• Unnamed Item
• Transport equation and Cauchy problem for BV vector fields
• Ordinary differential equations, transport theory and Sobolev spaces
• Coarse-scale representations and smoothed Wigner transforms
• High-frequency propagation for the Schrödinger equation on the torus
• Refraction of high-frequency waves density by sharp interfaces and semiclassical measures at the boundary
• Strong Phase-Space Semiclassical Asymptotics
• Wigner measures dynamics in a Coulomb potential
• Semiclassical expansion of Wigner functions
• Harmonic Analysis in Phase Space. (AM-122)
• Homogenization limits and Wigner transforms
• THE CLASSICAL LIMIT OF A SELF-CONSISTENT QUANTUM-VLASOV EQUATION IN 3D
• The limit from the Schrödinger‐Poisson to the Vlasov‐Poisson equations with general data in one dimension
• Passage from Quantum to Classical Molecular Dynamics in the Presence of Coulomb Interactions
• Semiclassical limit of quantum dynamics with rough potentials and well‐posedness of transport equations with measure initial data

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