Asymptotic behavior of fundamental solutions for Schrödinger equations with rough potentials
Paper Title:
Short time asymptotics of the fundamental solutions for Schrödinger equations with non-smooth potentials
Published on:
12 March 2024
Primary Category:
Analysis of PDEs
Paper Authors:
Shun Takizawa
Bullets
Key Details
With smooth potentials, fundamental solutions have explicit short-time formulas found by Fujiwara
These formulas fail for non-smooth potentials, where dispersive estimates break down
This paper shows the principal asymptotic term still resembles the smooth case
The analysis hinges on wave packet transforms and classical trajectory computations
Explore the topics in this paper
AI generated summary
Asymptotic behavior of fundamental solutions for Schrödinger equations with rough potentials
This paper examines the short-time asymptotic behavior of fundamental solutions for time-dependent Schrödinger equations with non-smooth potentials that have at most quadratic spatial growth. It shows that the principal part of the asymptotic expansion resembles the smooth potential case, even though dispersive estimates can fail with rough potentials. The key techniques involve wave packet transforms and classical trajectory analysis.
Answers from this paper
You might also like
Solutions and dispersion for the space-time fractional nonlinear Schrodinger equation
Simplified title focusing on cubic nonlinear Schrödinger equation with rough potential
Simplified summary of fractional Schrödinger equations
Asymptotic behavior of singularly perturbed transport equations with fast and slow components
Modified scattering and absence of energy cascades for cubic NLS on Diophantine waveguides
Scattering behavior of small solutions for 2D semi-relativistic Hartree equations
Comments
No comments yet, be the first to start the conversation...
Sign up to comment on this paper