Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quasi-normal frequencies: Key analytic results   The study of exact quasi-normal modes [QNMs], and their associated
quasi-normal frequencies [QNFs], has had a long and convoluted history -
replete with many rediscoveries of previously known results. In this article we
shall collect and survey a number of known analytic results, and develop
several new analytic results - specifically we shall provide several new QNF
results and estimates, in a form amenable for comparison with the extant
literature. Apart from their intrinsic interest, these exact and approximate
results serve as a backdrop and a consistency check on ongoing efforts to find
general model-independent estimates for QNFs, and general model-independent
bounds on transmission probabilities. Our calculations also provide yet another
physics application of the Lambert W function. These ideas have relevance to
fields as diverse as black hole physics, (where they are related to the damped
oscillations of astrophysical black holes, to greybody factors for the Hawking
radiation, and to more speculative state-counting models for the Bekenstein
entropy), to quantum field theory (where they are related to Casimir energies
in unbounded systems), through to condensed matter physics, (where one may
literally be interested in an electron tunelling through a physical barrier).

30
The categories of this paper are: q-alg
12
The categories of this paper are: nucl-th
16
The categories of this paper are: stat
26
The categories of this paper are: bayes-an
21
The categories of this paper are: adap-org
6
The categories of this paper are: astro-ph
20
The categories of this paper are: acc-phys
24
The categories of this paper are: dg-ga
35
The categories of this paper are: mtrl-th
31
The categories of this paper are: ao-sci
37
The categories of this paper are: supr-con
34
The categories of this paper are: chem-ph
32
The categories of this paper are: atom-ph
1
The categories of this paper are: cs
3
The categories of this paper are: physics
11
The categories of this paper are: hep-lat