Uncertainty relations for Non-Hermitian systems - Namrata Shukla

Robertson's formalized version of the Heisenberg uncertainty relation contains a state of interest and two incompatible observables that are Hermitian operators. We 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 also valid in the PT-broken phase. In contrast to the usual quantum theory, a good observable can also be a non-Hermitian operator for such systems. We show that 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.ORobertson's formalized version of the Heisenberg uncertainty relation contains a state of interest and two incompatible observables that are Hermitian operators. We 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 also valid in the PT-broken phase. In contrast to the usual quantum theory, a good observable can also be a non-Hermitian operator for such systems. We show that 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.

IQST seminar by Namrata Shukla Topic: Uncertainty relations for Non-Hermitian systems Time: Sep 28, 2022 03:00 PM Edmonton Join Zoom Meeting https://ucalgary.zoom.us/j/94003392108?pwd=ZXRsa2Rwc0Q5cm5DUjkrZFNoS1FaUT09 Meeting ID: 940 0339 2108 Passcode: 265540 One tap mobile +16475580588,,94003392108#,,,,*265540# Canada +17789072071,,94003392108#,,,,*265540# Canada Dial by your location +1 647 558 0588 Canada +1 778 907 2071 Canada +1 780 666 0144 Canada +1 204 272 7920 Canada +1 438 809 7799 Canada +1 587 328 1099 Canada +1 647 374 4685 Canada +1 253 215 8782 US (Tacoma) +1 301 715 8592 US (Washington DC) +1 309 205 3325 US +1 312 626 6799 US (Chicago) +1 346 248 7799 US (Houston) +1 386 347 5053 US +1 564 217 2000 US +1 646 558 8656 US (New York) +1 646 931 3860 US +1 669 444 9171 US +1 669 900 6833 US (San Jose) +1 719 359 4580 US Meeting ID: 940 0339 2108 Passcode: 265540 Find your local number: https://ucalgary.zoom.us/u/aAM9bybKL Join by SIP 94003392108@zoomcrc.com