Repeatability of measurements: Non-Hermitian observables and quantum Coriolis force

Journal Article · Fri Aug 26 00:00:00 EDT 2016 · Physical Review A

DOI:https://doi.org/10.1103/PhysRevA.94.022121· OSTI ID:1414087

Gardas, Bartłomiej ^[1]; Deffner, Sebastian ^[2]; Saxena, Avadh  ^[2]

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1. Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Univ. of Silesia, Katowice (Poland). Inst. of Physics
2. Los Alamos National Lab. (LANL), Los Alamos, NM (United States). Center for Nonlinear Studies

A noncommuting measurement transfers, via the apparatus, information encoded in a system's state to the external “observer.” Classical measurements determine properties of physical objects. In the quantum realm, the very same notion restricts the recording process to orthogonal states as only those are distinguishable by measurements. Thus, even a possibility to describe physical reality by means of non-Hermitian operators should volens nolens be excluded as their eigenstates are not orthogonal. We show that non-Hermitian operators with real spectra can be treated within the standard framework of quantum mechanics. Further, we propose a quantum canonical transformation that maps Hermitian systems onto non-Hermitian ones. Similar to classical inertial forces this map is accompanied by an energetic cost, pinning the system on the unitary path.

• Research Organization: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
• Sponsoring Organization: USDOE
• Grant/Contract Number: AC52-06NA25396
• OSTI ID: 1414087
• Alternate ID(s): OSTI ID: 1307797
• Report Number(s): LA-UR-16-21217; PLRAAN; TRN: US1800622
• Journal Information: Physical Review A, Vol. 94, Issue 2; ISSN 2469-9926
• Publisher: American Physical Society (APS)
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
Atomic and Nuclear Physics
Quantum measurement
quantum mechanics