Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Composite Bound States and Broken U(1) symmetry in the Chemical Master
  Equation derivation of the Gray-Scott Model   We give a first principles derivation of the stochastic partial differential
equations that describe the chemical reactions of the Gray-Scott model (GS):
$U+2V {\stackrel {\lambda}{\rightarrow}} 3 V;$ and $V {\stackrel
{\mu}{\rightarrow}} P$, $U {\stackrel {\nu}{\rightarrow}} Q$, with a constant
feed rate for $U$. We find that the conservation of probability ensured by the
chemical master equation leads to a modification of the usual differential
equations for the GS model which now involves two composite fields and also
intrinsic noise terms. One of the composites is $\psi_1 = \phi_v^2$, where $ <
\phi_v >_{\eta} = v$ is the concentration of the species $V$ and the averaging
is over the internal noise $\eta_{u,v,\psi_1}$. The second composite field is
the product of three fields $ \chi = \lambda \phi_u \phi_v^2$ and requires a
noise source to ensure probability conservation. A third composite $\psi_2 =
\phi_{u} \phi_{v}$ can be also be identified from the noise-induced reactions.
The Hamiltonian that governs the time evolution of the many-body wave function,
associated with the master equation, has a broken U(1) symmetry related to
particle number conservation. By expanding around the (broken symmetry) zero
energy solution of the Hamiltonian (by performing a Doi shift) one obtains from
our path integral formulation the usual reaction diffusion equation, at the
classical level. The Langevin equations that are derived from the chemical
master equation have multiplicative noise sources for the density fields
$\phi_u, \phi_v, \chi$ that induce higher order processes such as $n
\rightarrow n$ scattering for $n > 3$. The amplitude of the noise acting on $
\phi_v$ is itself stochastic in nature.

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The categories of this paper are: q-fin
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The categories of this paper are: adap-org
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The categories of this paper are: nucl-th
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The categories of this paper are: chem-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: atom-ph
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The categories of this paper are: eess
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The categories of this paper are: gr-qc
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The categories of this paper are: math
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The categories of this paper are: chao-dyn
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The categories of this paper are: nlin
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The categories of this paper are: physics
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-ex
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The categories of this paper are: math-ph
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The categories of this paper are: comp-gas