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

Abstract

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.

Authors:
 [1];  [2]; ORCiD logo [2]
  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
Publication Date:
Research Org.:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1414087
Report Number(s):
LA-UR-16-21217
Journal ID: ISSN 2469-9926; PLRAAN
Grant/Contract Number:
AC52-06NA25396
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Physical Review A
Additional Journal Information:
Journal Volume: 94; Journal Issue: 2; Journal ID: ISSN 2469-9926
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Atomic and Nuclear Physics; Quantum measurement, quantum mechanics

Citation Formats

Gardas, Bartłomiej, Deffner, Sebastian, and Saxena, Avadh. Repeatability of measurements: Non-Hermitian observables and quantum Coriolis force. United States: N. p., 2016. Web. doi:10.1103/PhysRevA.94.022121.
Gardas, Bartłomiej, Deffner, Sebastian, & Saxena, Avadh. Repeatability of measurements: Non-Hermitian observables and quantum Coriolis force. United States. doi:10.1103/PhysRevA.94.022121.
Gardas, Bartłomiej, Deffner, Sebastian, and Saxena, Avadh. 2016. "Repeatability of measurements: Non-Hermitian observables and quantum Coriolis force". United States. doi:10.1103/PhysRevA.94.022121. https://www.osti.gov/servlets/purl/1414087.
@article{osti_1414087,
title = {Repeatability of measurements: Non-Hermitian observables and quantum Coriolis force},
author = {Gardas, Bartłomiej and Deffner, Sebastian and Saxena, Avadh},
abstractNote = {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.},
doi = {10.1103/PhysRevA.94.022121},
journal = {Physical Review A},
number = 2,
volume = 94,
place = {United States},
year = 2016,
month = 8
}

Journal Article:
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