Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Spectral geometry in a rotating frame: properties of the ground state   We investigate spectral properties of the operator describing a quantum
particle confined to a planar domain $\Omega$ rotating around a fixed point
with an angular velocity $\omega$ and demonstrate several properties of its
principal eigenvalue $\lambda_1^\omega$. We show that as a function of rotating
center position it attains a unique maximum and has no other extrema provided
the said position is unrestricted. Furthermore, we show that as a function
$\omega$, the eigenvalue attains a maximum at $\omega=0$, unique unless
$\Omega$ has a full rotational symmetry. Finally, we present an upper bound to
the difference $\lambda_{1,\Omega}^\omega - \lambda_{1,B}^\omega$ where the
last named eigenvalue corresponds to a disk of the same area as $\Omega$.

32
The categories of this paper are: atom-ph
23
The categories of this paper are: solv-int
16
The categories of this paper are: stat
1
The categories of this paper are: cs
13
The categories of this paper are: quant-ph
11
The categories of this paper are: hep-lat
3
The categories of this paper are: physics
33
The categories of this paper are: plasm-ph
30
The categories of this paper are: q-alg
18
The categories of this paper are: econ
28
The categories of this paper are: alg-geom
7
The categories of this paper are: hep-th
24
The categories of this paper are: dg-ga
22
The categories of this paper are: chao-dyn
0
The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat