PROPAGATION OF SEMICLASSICAL WAVE PACKETS THROUGH AVOIDED EIGENVALUE CROSSINGS IN NONLINEAR SCHRÖDINGER EQUATIONS

DOI10.1017/S1474748014000346zbMath1342.35336MaRDI QIDQ2800014

Lysianne Hari

Publication date: 14 April 2016

Published in: Journal of the Institute of Mathematics of Jussieu (Search for Journal in Brave)

zbMATH Keywords

spectral gapBorn-Oppenheimer approximationadiabatic evolutionLandau-Zener formula

Mathematics Subject Classification ID

NLS equations (nonlinear Schrödinger equations) (35Q55) PDEs in connection with quantum mechanics (35Q40)

Related Items (2)

Propagation of coherent states through conical intersections ⋮ Propagation of wave packets for systems presenting codimension one crossings

Cites Work

• Unnamed Item
• A nonlinear Landau-Zener formula
• Nonlinear Schrödinger equation with time dependent potential
• Semiclassical wave packet dynamics in Schrödinger equations with periodic potentials
• Nonlinear coherent states and Ehrenfest time for Schrödinger equation
• Semiclassical propagation of coherent states for the Hartree equation
• A construction of the fundamental solution for the Schrödinger equation
• Proof of the Landau-Zener formula in an adiabatic limit with small eigenvalue gaps
• Lowest Landau level functional and Bargmann spaces for Bose-Einstein condensates
• Remarks on convergence of the Feynman path integrals
• Space-time decay for solutions of wave equations
• Restrictions of Fourier transforms to quadratic surfaces and decay of solutions of wave equations
• A Landau-Zener formula for non-degenerated involutive codimension 3 crossings
• The level crossing problem in semi-classical analysis. II: The Hermitian case.
• Generalized Strichartz inequalities for the wave equation
• Determination of non-adiabatic scattering wave functions in a Born-Oppenheimer model
• SEMI-CLASSICAL WAVE PACKET DYNAMICS FOR HARTREE EQUATIONS
• Mesures semi-classiques et croisement de modes
• A nonlinear adiabatic theorem for coherent states
• Propagation through Generic Level Crossings: A Surface Hopping Semigroup
• The Formula of FAA Di Bruno
• Spaces of Distributions with Weights. Multipliers inLp-spaces with Weights
• Non-adiabatic crossing of energy levels
• Coherent States for Systems ofL²-Supercritical Nonlinear Schrödinger Equations
• MOLECULAR PROPAGATION THROUGH SMALL AVOIDED CROSSINGS OF ELECTRON ENERGY LEVELS
• Classification and normal forms for avoided crossings of quantum-mechanical energy levels
• Semiclassical determination of exponentially small intermode transitions for 1 + 1 spacetime scattering systems
• Adiabatic decoupling and time-dependent Born-Oppenheimer theory

This page was built for publication: PROPAGATION OF SEMICLASSICAL WAVE PACKETS THROUGH AVOIDED EIGENVALUE CROSSINGS IN NONLINEAR SCHRÖDINGER EQUATIONS