Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Achieving the Landau bound to precision of quantum thermometry in
  systems with vanishing gap   We address estimation of temperature for finite quantum systems at thermal
equilibrium and show that the Landau bound to precision $\delta T^2 \propto
T^2$, originally derived for a classical {\em not too small} system being a
portion of a large isolated system at thermal equilibrium, may be also achieved
by energy measurement in microscopic {\em quantum} systems exhibiting vanishing
gap as a function of some control parameter. On the contrary, for any quantum
system with a non-vanishing gap $\Delta$, precision of any temperature
estimator diverges as $\delta T^2 \gtrsim T^4 e^{\Delta/T}$.

11
The categories of this paper are: hep-lat
5
The categories of this paper are: gr-qc
3
The categories of this paper are: physics
33
The categories of this paper are: plasm-ph
9
The categories of this paper are: nlin
14
The categories of this paper are: math-ph
34
The categories of this paper are: chem-ph
29
The categories of this paper are: funct-an
30
The categories of this paper are: q-alg
6
The categories of this paper are: astro-ph
23
The categories of this paper are: solv-int
37
The categories of this paper are: supr-con
1
The categories of this paper are: cs
17
The categories of this paper are: q-fin
15
The categories of this paper are: nucl-ex
32
The categories of this paper are: atom-ph