Alladi Ramakrishnan Hall

Uncertainty relation in PT invariant non-Hermitian system

Ranjan Modak

IIT-Tirupati

Robertson’s formalized version of the Heisenberg uncertainty relation
contains a state of interest and two incompatible observables that are
Hermitian operators. In the talk, we will show how one can construct
uncertainty relation for PT invariant non-Hermitian quantum systems by
introducing a more general condition of “good observable”. Our construction
is not limited to the PT-symmetric phase but is also valid in the PT broken
phase. We will show that in contrast to the usual quantum theory, a good
observable can also be a non-Hermitian operator for such systems. Moreover,
the non-Hermitian Hamiltonian itself qualifies as a good observable in the
PT-symmetric phase, but not in the broken phase. Consequently, this fact
can be used as a diagnostic tool to detect the PT phase transition in any
arbitrary finite-dimensional system.


Ref: N. Shukla, Ranjan Modak, and B P Mandal, arXiv: 2206.02844 (2022)