Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Slowly rocking symmetric, spatially periodic Hamiltonians: The role of
  escape and the emergence of giant transient directed transport   The nonintegrable Hamiltonian dynamics of particles placed in a symmetric,
spatially periodic potential and subjected to a periodically varying field is
explored. Such systems can exhibit a rich diversity of unusual transport
features. In particular, depending on the setting of the initial phase of the
drive, the possibility of a giant transient directed transport in a symmetric,
space-periodic potential when driven with an adiabatically varying field
arises. Here, we study the escape scenario and corresponding mean escape times
of particles from a trapping region with the subsequent generation of a
transient directed flow of an ensemble of particles. It is shown that for
adiabatically slow inclination modulations the unidirectional flow proceeds
over giant distances. The direction of escape and, hence, of the flow is
entirely governed whether the periodic force, modulating the inclination of the
potential, starts out initially positive or negative. In the phase space, this
transient directed flow is associated with a long-lasting motion taking place
within ballistic channels contained in the non-uniform chaotic layer. We
demonstrate that for adiabatic modulations all escaping particles move
ballistically into the same direction, leading to a giant directed current.

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The categories of this paper are: q-bio
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The categories of this paper are: gr-qc
12
The categories of this paper are: nucl-th
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The categories of this paper are: alg-geom
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The categories of this paper are: nucl-ex
34
The categories of this paper are: chem-ph
37
The categories of this paper are: supr-con
29
The categories of this paper are: funct-an
0
The categories of this paper are: hep-ph
33
The categories of this paper are: plasm-ph
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The categories of this paper are: hep-lat
35
The categories of this paper are: mtrl-th
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The categories of this paper are: econ
25
The categories of this paper are: patt-sol
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The categories of this paper are: stat
31
The categories of this paper are: ao-sci