Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Finite temperature quantum condensations in the space of states   If, for an isolated quantum system, we can find a partition of its space of
states $\mathbb{F}$ into two subspaces, $\mathbb{F}_\mathrm{cond}$ and
$\mathbb{F}_\mathrm{norm}$, such that, in the thermodynamic limit, $\dim
\mathbb{F}_\mathrm{cond}/ \dim \mathbb{F} \to 0$ and the ground state energies
of the system restricted to these subspaces cross each other for some value of
the Hamiltonian parameters, then, the system undergoes a first-order quantum
phase transition driven by that parameter. A proof of this general class of
phase transitions, which correspond to a condensation in the space of quantum
states, briefly, a quantum condensing, has been provided at zero temperature.
Here, we find its natural extension to finite temperature and suggest that
quantum condensing can have a pivotal role in establishing quantum supremacy
for optimization problems.

1
The categories of this paper are: cs
17
The categories of this paper are: q-fin
20
The categories of this paper are: acc-phys
3
The categories of this paper are: physics
18
The categories of this paper are: econ
21
The categories of this paper are: adap-org
7
The categories of this paper are: hep-th
27
The categories of this paper are: comp-gas
16
The categories of this paper are: stat
29
The categories of this paper are: funct-an
25
The categories of this paper are: patt-sol
12
The categories of this paper are: nucl-th
24
The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph
19
The categories of this paper are: eess
22
The categories of this paper are: chao-dyn