Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bogoliubov quasi-averages: spontaneous symmetry breaking and algebra of
  fluctuations   The paper advocates the Bogoliubov method of quasi-averages for quantum
systems. First, we elucidate its applications to study the phase transitions
with Spontaneous Symmetry Breaking (SSB). To this aim we consider example of
Bose-Einstein condensation (BEC) in continuous systems. Our analysis of
different type of generalised condensations demonstrates that the only
physically reliable quantities are those that defined by Bogoliubov
quasi-averages. In this connection we also give a solution of the problem posed
by Lieb, Seiringer and Yngvason in [SY07]. Second, using the scaled Bogoliubov
method of quasi-averages and taking the structural quantum phase transition as
a basic example, we scrutinise a relation between SSB and the critical quantum
fluctuations. Our analysis shows that again the quasi-averages give an adequate
tool for description of the algebra of critical quantum fluctuation operators
in the both commutative and noncommutative cases.

36
The categories of this paper are: cmp-lg
10
The categories of this paper are: q-bio
25
The categories of this paper are: patt-sol
37
The categories of this paper are: supr-con
35
The categories of this paper are: mtrl-th
28
The categories of this paper are: alg-geom
16
The categories of this paper are: stat
5
The categories of this paper are: gr-qc
7
The categories of this paper are: hep-th
22
The categories of this paper are: chao-dyn
4
The categories of this paper are: cond-mat
26
The categories of this paper are: bayes-an
20
The categories of this paper are: acc-phys
19
The categories of this paper are: eess
9
The categories of this paper are: nlin
27
The categories of this paper are: comp-gas