Postdoctoral Research Project PN-III-P1-1.1-PD-2016-1423
2018 - 2020
Supported by CNCS - UEFISCDI, Contract number 11/02.05.2018, within PNCDI III
The study of quantum corrections in mesoscopic systems will be performed
by comparing kinetic theory and quantum field theory (QFT) results for
rigidly-rotating thermal states.
On the Minkowski space, kinetic theory predicts that rigidly-rotating
thermal states exhibit a speed of light surface (SOL), where co-rotating
observers travel at the speed of light and the stress-energy tensor
(SET) diverges. When this system is investigated using QFT, a
fundamental difference is found, namely that the rigidly-rotating
thermal states of the Klein-Gordon field are ill-defined everywhere due
to co-rotating modes having non-vanishing energy and infinite
statistical weight. On the other hand, the SET for the Dirac field is
well-defined up to the SOL, where the quantum corrections become
dominant.
In order to render the SET finite, the rotating system must be enclosed
inside a boundary which excludes the SOL. Recent QFT results confirm
that the SET is regular for both the Klein-Gordon and the Fermi-Dirac
fields, but so far a kinetic theory analysis of such systems has not
been performed. We propose as an objective of this project to perform a
comparative study between the QFT and the kinetic theory approaches by
employing numerical methods to evaluate mode sums (QFT) and the lattice
Boltzmann method for solving the relativistic Boltzmann equation.
Furthermore, it is natural to consider the problem of rigidly-rotating
thermal states in bounded spaces, such as the anti-de Sitter (adS) space
and the Einstein Static Universe (ESU). We propose to highlight the
properties of quantum corrections in such systems by comparing the
results obtained by solving the relativistic Boltzmann equation, as well
as the Klein-Gordon and Dirac equations on these space-times.