Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantization and Corrections of Adiabatic Particle Transport in a
  Periodic Ratchet Potential   We study the transport of an overdamped particle adiabatically driven by an
asymmetric potential which is periodic in both space and time. We develop an
adiabatic perturbation theory after transforming the Fokker-Planck equation
into a time-dependent hermitian problem, and reveal an analogy with quantum
adiabatic particle transport. An analytical expression is obtained for the
ensemble average of the particle velocity in terms of the Berry phase of the
Bloch states. Its time average is shown to be quantized as a Chern number in
the deterministic or tight-binding limit, with exponentially small corrections.
In the opposite limit, where the thermal energy dominates the ratchet
potential, a formula for the average velocity is also obtained, showing a
second order dependence on the potential.

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The categories of this paper are: q-bio
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The categories of this paper are: funct-an
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The categories of this paper are: bayes-an
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The categories of this paper are: quant-ph
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The categories of this paper are: q-fin
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The categories of this paper are: nucl-ex
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The categories of this paper are: math
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The categories of this paper are: plasm-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: adap-org
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The categories of this paper are: gr-qc
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The categories of this paper are: eess
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-th
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The categories of this paper are: supr-con
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The categories of this paper are: q-alg