Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Ergodic Isoenergetic Molecular Dynamics for Microcanonical-Ensemble
  Averages   Considerable research has led to ergodic isothermal dynamics which can
replicate Gibbs' canonical distribution for simple ( small ) dynamical
problems. Adding one or two thermostat forces to the Hamiltonian motion
equations can give an ergodic isothermal dynamics to a harmonic oscillator, to
a quartic oscillator, and even to the "Mexican-Hat" ( double-well ) potential
problem. We consider here a time-reversible dynamical approach to Gibbs'
"microcanonical" ( isoenergetic ) distribution for simple systems. To enable
isoenergetic ergodicity we add occasional random rotations to the velocities.
This idea conserves energy exactly and can be made to cover the entire energy
shell with an ergodic dynamics. We entirely avoid the Poincar\'e-section holes
and island chains typical of Hamiltonian chaos. We illustrate this idea for the
simplest possible two-dimensional example, a single particle moving in a
periodic square-lattice array of scatterers, the "cell model".

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The categories of this paper are: acc-phys
31
The categories of this paper are: ao-sci
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
9
The categories of this paper are: nlin
10
The categories of this paper are: q-bio
12
The categories of this paper are: nucl-th
30
The categories of this paper are: q-alg
13
The categories of this paper are: quant-ph
33
The categories of this paper are: plasm-ph
25
The categories of this paper are: patt-sol
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The categories of this paper are: hep-lat
32
The categories of this paper are: atom-ph
6
The categories of this paper are: astro-ph
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The categories of this paper are: funct-an