Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Transport in the One-Dimensional Schroedinger Equation   We prove a dispersive estimate for the one-dimensional Schroedinger equation,
mapping between weighted $L^p$ spaces with stronger time-decay ($t^{-3/2}$
versus $t^{-1/2}$) than is possible on unweighted spaces. To satisfy this
bound, the long-term behavior of solutions must include transport away from the
origin. Our primary requirements are that $(1+|x|)^3 V$ be integrable and
$-\Delta + V$ not have a resonance at zero energy. If a resonance is present
(for example in the free case), similar estimates are valid after projecting
away from a rank-one subspace corresponding to the resonance.

23
The categories of this paper are: solv-int
4
The categories of this paper are: cond-mat
22
The categories of this paper are: chao-dyn
24
The categories of this paper are: dg-ga
11
The categories of this paper are: hep-lat
20
The categories of this paper are: acc-phys
33
The categories of this paper are: plasm-ph
32
The categories of this paper are: atom-ph
3
The categories of this paper are: physics
31
The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th
26
The categories of this paper are: bayes-an
0
The categories of this paper are: hep-ph
7
The categories of this paper are: hep-th
8
The categories of this paper are: hep-ex
18
The categories of this paper are: econ