Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Quantum Toda Lattice Revisited   In this work we study the quantum Toda lattice, developing the asymptotic
Bethe ansatz method first used by Sutherland. Despite its known limitations we
find, on comparing with Gutzwiller's exact method, that it works well in this
particular problem and in fact becomes exact as $\hbar$ grows large. We
calculate ground state and excitation energies for finite sized lattices,
identify excitations as phonons and solitons on the basis of their quantum
numbers, and find their dispersions. These are similar to the classical
dispersions for small $\hbar$, and remain similar all the way up to $\hbar=1$,
but then deviate substantially as we go further into the quantum regime. On
comparing the sound velocities for various $\hbar$ obtained thus with that
predicted by conformal theory we conclude that the Bethe ansatz gives the
energies per particle accurate to O($1/N^2$). On that assumption we can find
correlation functions. Thus the Bethe ansatz method can be used to yield much
more than the thermodynamic properties which previous authors have calculated.

17
The categories of this paper are: q-fin
23
The categories of this paper are: solv-int
30
The categories of this paper are: q-alg
5
The categories of this paper are: gr-qc
8
The categories of this paper are: hep-ex
36
The categories of this paper are: cmp-lg
2
The categories of this paper are: math
35
The categories of this paper are: mtrl-th
24
The categories of this paper are: dg-ga
28
The categories of this paper are: alg-geom
11
The categories of this paper are: hep-lat
13
The categories of this paper are: quant-ph
22
The categories of this paper are: chao-dyn
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The categories of this paper are: stat
14
The categories of this paper are: math-ph
3
The categories of this paper are: physics