Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Correlated Electron-Nuclear Dynamics with Conditional Wave Functions   The molecular Schr\"odinger equation is rewritten in terms of non-unitary
equations of motion for the nuclei (or electrons) that depend parametrically on
the configuration of an ensemble of generally defined electronic (or nuclear)
trajectories. This scheme is exact and does not rely on the tracing-out of
degrees of freedom. Hence, the use of trajectory-based statistical techniques
can be exploited to circumvent the calculation of the computationally demanding
Born-Oppenheimer potential-energy surfaces and non-adiabatic coupling elements.
The concept of potential-energy surface is restored by establishing a formal
connection with the exact factorization of the full wave function. This
connection is used to gain insight from a simplified form of the exact
propagation scheme.

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The categories of this paper are: gr-qc
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The categories of this paper are: q-bio
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The categories of this paper are: adap-org
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The categories of this paper are: math-ph
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The categories of this paper are: solv-int
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The categories of this paper are: comp-gas
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The categories of this paper are: stat
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The categories of this paper are: acc-phys
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The categories of this paper are: q-fin
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The categories of this paper are: plasm-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: cs
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The categories of this paper are: hep-ex
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The categories of this paper are: alg-geom
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The categories of this paper are: nucl-th
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The categories of this paper are: nucl-ex