Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Two-level systems with periodic $N$-step driving fields: Exact dynamics
  and quantum state manipulations   In this work, we derive exact solutions of a dynamical equation, which can
represent all two-level Hermitian systems driven by periodic $N$-step driving
fields. For different physical parameters, this dynamical equation displays
various phenomena for periodic $N$-step driven systems. The time-dependent
transition probability can be expressed by a general formula that consists of
cosine functions with discrete frequencies, and, remarkably, this formula is
suitable for arbitrary parameter regimes. Moreover, only a few cosine functions
(i.e., one to three main frequencies) are sufficient to describe the actual
dynamics of the periodic $N$-step driven system. {Furthermore}, we find that a
beating in the transition probability emerges when two (or three) main
frequencies are similar. Some applications are also demonstrated in quantum
state manipulations by periodic $N$-step driving fields.

4
The categories of this paper are: cond-mat
1
The categories of this paper are: cs
28
The categories of this paper are: alg-geom
16
The categories of this paper are: stat
27
The categories of this paper are: comp-gas
21
The categories of this paper are: adap-org
6
The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci
33
The categories of this paper are: plasm-ph
29
The categories of this paper are: funct-an
11
The categories of this paper are: hep-lat
34
The categories of this paper are: chem-ph
14
The categories of this paper are: math-ph
12
The categories of this paper are: nucl-th
24
The categories of this paper are: dg-ga
23
The categories of this paper are: solv-int