Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Jordan blocks and generalized bi-orthogonal bases: realizations in open
  wave systems   Dissipative systems can be described in terms of non-hermitian hamiltonians
H, whose left eigenvectors f^j and right eigenvectors f_j form a bi-orthogonal
system. Bi-orthogonal systems could suffer from two difficulties. (a) If the
eigenvectors do not span the whole space, then H can only be diagonalized to
blocks (the Jordan-block problem). (b) Normalization would not be possible and
many familiar-looking formulas would fail if (f^j,f_j) = 0 for some j (the
orthonormalization problem). Waves in open systems provide a well-founded
realization of a bi-orthogonal system, and it is shown that these two problems
can indeed occur and are both related to higher-order poles in the
frequency-domain Green's function. The resolution is then given by introducing
a generalized duality transformation involving extra basis vectors, whose time
evolution is modified by polynomials in the time t. One thus obtains a
nontrivial extension of the bi-orthogonal formalism for dissipative systems.

11
The categories of this paper are: hep-lat
19
The categories of this paper are: eess
6
The categories of this paper are: astro-ph
18
The categories of this paper are: econ
28
The categories of this paper are: alg-geom
32
The categories of this paper are: atom-ph
31
The categories of this paper are: ao-sci
17
The categories of this paper are: q-fin
23
The categories of this paper are: solv-int
33
The categories of this paper are: plasm-ph
4
The categories of this paper are: cond-mat
5
The categories of this paper are: gr-qc
37
The categories of this paper are: supr-con
26
The categories of this paper are: bayes-an
30
The categories of this paper are: q-alg
27
The categories of this paper are: comp-gas