Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Semiclassical approximations for adiabatic slow-fast systems   In this letter we give a systematic derivation and justification of the
semiclassical model for the slow degrees of freedom in adiabatic slow-fast
systems first found by Littlejohn and Flynn [5]. The classical Hamiltonian
obtains a correction due to the variation of the adiabatic subspaces and the
symplectic form is modified by the curvature of the Berry connection. We show
that this classical system can be used to approximate quantum mechanical
expectations and the time-evolution of operators also in sub-leading order in
the combined adiabatic and semiclassical limit. In solid state physics the
corresponding semiclassical description of Bloch electrons has led to
substantial progress during the recent years, see [1]. Here, as an
illustration, we show how to compute the Piezo-current arising from a slow
deformation of a crystal in the presence of a constant magnetic field.

5
The categories of this paper are: gr-qc
32
The categories of this paper are: atom-ph
11
The categories of this paper are: hep-lat
12
The categories of this paper are: nucl-th
26
The categories of this paper are: bayes-an
2
The categories of this paper are: math
8
The categories of this paper are: hep-ex
25
The categories of this paper are: patt-sol
16
The categories of this paper are: stat
22
The categories of this paper are: chao-dyn
7
The categories of this paper are: hep-th
1
The categories of this paper are: cs
28
The categories of this paper are: alg-geom
24
The categories of this paper are: dg-ga
21
The categories of this paper are: adap-org
30
The categories of this paper are: q-alg