Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Slowly changing potential problems in Quantum Mechanics: Adiabatic
  Theorems, Ergodic Theorems, and Scattering   We employ the recently developed multi-time scale averaging method to study
the large time behavior of slowly changing (in time) Hamiltonians. We treat
some known cases in a new way, such as the Zener problem, and we give another
proof of the Adiabatic Theorem in the gapless case. We prove a new Uniform
Ergodic Theorem for slowly changing unitary operators. This theorem is then
used to derive the adiabatic theorem, do the scattering theory for such
Hamiltonians, and prove some classical propagation estimates and Asymptotic
Completeness.

16
The categories of this paper are: stat
4
The categories of this paper are: cond-mat
36
The categories of this paper are: cmp-lg
37
The categories of this paper are: supr-con
25
The categories of this paper are: patt-sol
23
The categories of this paper are: solv-int
20
The categories of this paper are: acc-phys
3
The categories of this paper are: physics
30
The categories of this paper are: q-alg
0
The categories of this paper are: hep-ph
19
The categories of this paper are: eess
1
The categories of this paper are: cs
11
The categories of this paper are: hep-lat
31
The categories of this paper are: ao-sci
33
The categories of this paper are: plasm-ph
26
The categories of this paper are: bayes-an