#### 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)

Done