Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Differential equation for partition functions and a duality
  pseudo-forest   We consider finite quantum systems defined by a mixed set of commutation and
anti-commutation relations between components of the Hamiltonian operator.
These relations are represented by an anti-commutativity graph which contains a
necessary and sufficient information for computing the full quantum partition
function. We derive a second-order differential equation for an extended
partition function $z[\beta, \beta', J]$ which describes a transformation from
a "parent" partition function $z[0, \beta', J]$ (or anti-commutativity graph)
to a "child" partition function $z[\beta, 0, J]$ (or anti-commutativity graph).
The procedure can be iterated and then one forms a pseudo-forest of duality
transformations between quantum systems, i.e. a directed graph in which every
vertex (or quantum system) has at most one incoming edge (from its parent
system). The pseudo-forest has a single tree connected to a constant partition
function, many pseudo-trees connected to self-dual systems and all other
pseudo-trees connected to closed cycles of transformations between mutually
dual systems. We also show how the differential equation for the extended
partition function can be used to study disordered systems such as the SYK
model.

30
The categories of this paper are: q-alg
5
The categories of this paper are: gr-qc
1
The categories of this paper are: cs
32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
28
The categories of this paper are: alg-geom
18
The categories of this paper are: econ
16
The categories of this paper are: stat
12
The categories of this paper are: nucl-th
34
The categories of this paper are: chem-ph
37
The categories of this paper are: supr-con
17
The categories of this paper are: q-fin
0
The categories of this paper are: hep-ph
9
The categories of this paper are: nlin
25
The categories of this paper are: patt-sol
8
The categories of this paper are: hep-ex