Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hamiltonian chaos with a cold atom in an optical lattice   We consider a basic model of the lossless interaction between a moving
two-level atom and a standing-wave single-mode laser field. Classical treatment
of the translational atomic motion provides the semiclassical
Hamilton-Schrodinger equations which are a 5D nonlinear dynamical system with
two integrals of motion. The atomic dynamics can be regular or chaotic in
dependence on values of the control parameters, the atom-field detuning and
recoil frequency. We develop a semiclassical theory of the chaotic atomic
transport in terms of a random walk of the atomic electric dipole moment $u$.
Based on a jump-like behavior of this variable for atoms crossing nodes of the
standing wave, we construct a stochastic map that specifies the center-of-mass
motion. We find the relations between the detuning, recoil frequency and the
atomic energy, under which atoms may move in a optical lattice in a chaotic
way. We obtain the analytical conditions under which deterministic atomic
transport has fractal properties and explain a hierarchical structure of the
dynamical fractals. Quantum treatment of the atomic motion in a standing wave
is studied in the dressed state picture where the atom moves in two optical
potentials simultaneously. If the values of the detuning and a characteristic
atomic frequency are of the same order, than there is a probability of
nonadiabatic transitions of the atom upon crossing nodes of the standing wave.
At the same condition exactly, we observe sudden jumps in the atomic dipole
moment $u$ when the atom crosses the nodes. Those jumps are accompanied by
splitting of atomic wave packets at the nodes. Such a proliferation of wave
packets at the nodes of a standing wave is a manifestation of classical atomic
chaotic transport. At large values of the detuning, the quantum evolution is
shown to be adiabatic in accordance with a regular character of the classical
atomic motion.

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The categories of this paper are: astro-ph
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The categories of this paper are: funct-an
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The categories of this paper are: hep-ex
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The categories of this paper are: patt-sol
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The categories of this paper are: q-alg
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The categories of this paper are: econ
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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: cmp-lg
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The categories of this paper are: plasm-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: adap-org
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The categories of this paper are: nucl-ex
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The categories of this paper are: bayes-an
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The categories of this paper are: math-ph
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The categories of this paper are: quant-ph