Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Rank-adaptive time integration of tree tensor networks   A rank-adaptive integrator for the approximate solution of high-order tensor
differential equations by tree tensor networks is proposed and analyzed. In a
recursion from the leaves to the root, the integrator updates bases and then
evolves connection tensors by a Galerkin method in the augmented subspace
spanned by the new and old bases. This is followed by rank truncation within a
specified error tolerance. The memory requirements are linear in the order of
the tensor and linear in the maximal mode dimension. The integrator is robust
to small singular values of matricizations of the connection tensors. Up to the
rank truncation error, which is controlled by the given error tolerance, the
integrator preserves norm and energy for Schrodinger equations, and it
dissipates the energy in gradient systems. Numerical experiments with a basic
quantum spin system illustrate the behavior of the proposed algorithm.

31
The categories of this paper are: ao-sci
32
The categories of this paper are: atom-ph
15
The categories of this paper are: nucl-ex
19
The categories of this paper are: eess
7
The categories of this paper are: hep-th
27
The categories of this paper are: comp-gas
28
The categories of this paper are: alg-geom
37
The categories of this paper are: supr-con
33
The categories of this paper are: plasm-ph
5
The categories of this paper are: gr-qc
17
The categories of this paper are: q-fin
16
The categories of this paper are: stat
9
The categories of this paper are: nlin
18
The categories of this paper are: econ
8
The categories of this paper are: hep-ex
20
The categories of this paper are: acc-phys