Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Effective many-body parameters for atoms in non-separable Gaussian
  optical potentials   We analyze the properties of particles trapped in three-dimensional
potentials formed from superimposed Gaussian beams, fully taking into account
effects of potential anharmonicity and non-separability. Although these effects
are negligible in more conventional optical lattice experiments, they are
essential for emerging ultracold atom developments. We focus in particular on
two potentials utilized in current ultracold atom experiments: arrays of
tightly focused optical tweezers and a one-dimensional optical lattice with
transverse Gaussian confinement and highly excited transverse modes. Our main
numerical tools are discrete variable representations (DVRs), which combine
many favorable features of spectral and grid-based methods, such as the
computational advantage of exponential convergence and the convenience of an
analytical representation of Hamiltonian matrix elements. Optimizations, such
as symmetry adaptations and variational methods built on top of DVR methods,
are presented and their convergence properties discussed. We also present a
quantitative analysis of the degree of non-separability of eigenstates,
borrowing ideas from the theory of matrix product states (MPSs), leading to
both conceptual and computational gains. Beyond developing numerical
methodologies, we present results for construction of optimally localized
Wannier functions and tunneling and interaction matrix elements in optical
lattices and tweezers relevant for constructing effective models for many-body
physics.

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The categories of this paper are: q-bio
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The categories of this paper are: nucl-th
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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: alg-geom
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The categories of this paper are: dg-ga
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The categories of this paper are: astro-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: solv-int
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The categories of this paper are: chao-dyn
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The categories of this paper are: math
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The categories of this paper are: acc-phys
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The categories of this paper are: econ
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The categories of this paper are: nlin
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The categories of this paper are: cs
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The categories of this paper are: q-fin