Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Finite-Element Lattice Hamiltonian Matrix Eleents. Anharmonic
  Oscillators   The finite-element approach to lattice field theory is both highly accurate
(relative errors $\sim 1/N^2$, where $N$ is the number of lattice points) and
exactly unitary (in the sense that canonical commutation relations are exactly
preserved at the lattice sites). In this paper we construct matrix elements for
the time evolution operator for the anharmonic oscillator, for which the
continuum Hamiltonian is $H=p^2/2+\lambda q^{2k}/2k$. Construction of such
matrix elements does not require solving the implicit equations of motion. Low
order approximations turn out to be quite accurate. For example, the matrix
element of the time evolution operator in the harmonic oscillator ground state
gives a result for the $k=2$ anharmonic oscillator ground state energy accurate
to better than 1\%, while a two-state approximation reduces the error to less
than 0.1\%. Accurate wavefunctions are also extracted. Analogous results may be
obtained in the continuum, but there the computation is more difficult, and not
generalizable to field theories in more dimensions.

9
The categories of this paper are: nlin
15
The categories of this paper are: nucl-ex
29
The categories of this paper are: funct-an
24
The categories of this paper are: dg-ga
19
The categories of this paper are: eess
33
The categories of this paper are: plasm-ph
8
The categories of this paper are: hep-ex
3
The categories of this paper are: physics
36
The categories of this paper are: cmp-lg
18
The categories of this paper are: econ
37
The categories of this paper are: supr-con
31
The categories of this paper are: ao-sci
12
The categories of this paper are: nucl-th
11
The categories of this paper are: hep-lat
16
The categories of this paper are: stat
10
The categories of this paper are: q-bio