Statistical features of
quantum evolution
SUDHIR R JAIN
Nuclear Physics Division, Bhabha
Atomic Research Centre, Mumbai 400 085,
E-mail: srjain@barc.gov.in
Abstract. It is shown
that the integral of the uncertainty of energy with respect to
time is independent of the
particular Hamiltonian of the quantum
system for an arbitrary
pseudo-unitary (and hence PT-)
quantum evolution. The result
generalizes the time--energy
uncertainty principle for
pseudo-unitary quantum evolutions.
Further, employing random matrix theory developed for
pseudo-Hermitian
systems, time correlation functions are studied in
the framework of linear response
theory. The results given here
provide a quantum brachistochrone problem where the system will
evolve in a thermodynamic
environment with spectral complexity that
can be modelled
by random matrix theory.
Keywords. PT
symmetry; random matrix theory; time
correlation functions.
PACS Nos 03.65.Ge; 05.45.Mt