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:
-
[2]
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Univ. of Silesia, Katowice (Poland). Inst. of Physics
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States). Center for Nonlinear Studies
- Publication Date:
- Research Org.:
- Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
- Sponsoring Org.:
- USDOE
- OSTI Identifier:
- 1414087
- Alternate Identifier(s):
- OSTI ID: 1307797
- Report Number(s):
- LA-UR-16-21217
Journal ID: ISSN 2469-9926; PLRAAN; TRN: US1800622
- Grant/Contract Number:
- AC52-06NA25396
- Resource Type:
- 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. https://doi.org/10.1103/PhysRevA.94.022121
Gardas, Bartłomiej, Deffner, Sebastian, and Saxena, Avadh. Fri .
"Repeatability of measurements: Non-Hermitian observables and quantum Coriolis force". United States. https://doi.org/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 = {Fri Aug 26 00:00:00 EDT 2016},
month = {Fri Aug 26 00:00:00 EDT 2016}
}
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Works referenced in this record:
Tilted optical lattices with defects as realizations of symmetry in Bose-Einstein condensates
journal, February 2016
- Kreibich, Manuel; Main, Jörg; Cartarius, Holger
- Physical Review A, Vol. 93, Issue 2
Jarzynski Equality in -Symmetric Quantum Mechanics
journal, April 2015
- Deffner, Sebastian; Saxena, Avadh
- Physical Review Letters, Vol. 114, Issue 15
Theory of Bose-Einstein condensation in trapped gases
journal, April 1999
- Dalfovo, Franco; Giorgini, Stefano; Pitaevskii, Lev P.
- Reviews of Modern Physics, Vol. 71, Issue 3
Must a Hamiltonian be Hermitian?
journal, November 2003
- Bender, Carl M.; Brody, Dorje C.; Jones, Hugh F.
- American Journal of Physics, Vol. 71, Issue 11
Pseudo-Hermiticity versus PT-symmetry III: Equivalence of pseudo-Hermiticity and the presence of antilinear symmetries
journal, August 2002
- Mostafazadeh, Ali
- Journal of Mathematical Physics, Vol. 43, Issue 8
Time-dependent version of crypto-Hermitian quantum theory
journal, October 2008
- Znojil, Miloslav
- Physical Review D, Vol. 78, Issue 8
Quantum Brachistochrone Problem and the Geometry of the State Space in Pseudo-Hermitian Quantum Mechanics
journal, September 2007
- Mostafazadeh, Ali
- Physical Review Letters, Vol. 99, Issue 13
A new notation for quantum mechanics
journal, July 1939
- Dirac, P. A. M.
- Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 35, Issue 3
Canonical Transformations in Quantum Mechanics
journal, June 1994
- Anderson, A.
- Annals of Physics, Vol. 232, Issue 2
Observation of non-Hermitian degeneracies in a chaotic exciton-polariton billiard
journal, October 2015
- Gao, T.; Estrecho, E.; Bliokh, K. Y.
- Nature, Vol. 526, Issue 7574
A single quantum cannot be cloned
journal, October 1982
- Wootters, W. K.; Zurek, W. H.
- Nature, Vol. 299, Issue 5886
Geometric phase for non-Hermitian Hamiltonian evolution as anholonomy of a parallel transport along a curve
journal, September 2008
- Sinitsyn, N. A.; Saxena, Avadh
- Journal of Physics A: Mathematical and Theoretical, Vol. 41, Issue 39
Observation of parity–time symmetry in optics
journal, January 2010
- Rüter, Christian E.; Makris, Konstantinos G.; El-Ganainy, Ramy
- Nature Physics, Vol. 6, Issue 3
Consistency of PT-symmetric quantum mechanics
journal, January 2016
- Brody, Dorje C.
- Journal of Physics A: Mathematical and Theoretical, Vol. 49, Issue 10
Optical polarization evolution near a non-Hermitian degeneracy
journal, October 2011
- Berry, M. V.
- Journal of Optics, Vol. 13, Issue 11
Dynamical invariants for pseudo-Hermitian Hamiltonians
journal, January 2016
- Simeonov, Lachezar S.; Vitanov, Nikolay V.
- Physical Review A, Vol. 93, Issue 1
Time-dependent pseudo-Hermitian Hamiltonians defining a unitary quantum system and uniqueness of the metric operator
journal, June 2007
- Mostafazadeh, Ali
- Physics Letters B, Vol. 650, Issue 2-3
Invisibility in non-Hermitian tight-binding lattices
journal, September 2010
- Longhi, Stefano
- Physical Review A, Vol. 82, Issue 3
Convective and absolute -symmetry breaking in tight-binding lattices
journal, November 2013
- Longhi, Stefano
- Physical Review A, Vol. 88, Issue 5
Complex Extension of Quantum Mechanics
journal, December 2002
- Bender, Carl M.; Brody, Dorje C.; Jones, Hugh F.
- Physical Review Letters, Vol. 89, Issue 27
Localization Transitions in Non-Hermitian Quantum Mechanics
journal, July 1996
- Hatano, Naomichi; Nelson, David R.
- Physical Review Letters, Vol. 77, Issue 3
Geometry and the Foucault Pendulum
journal, June 1995
- Oprea, John
- The American Mathematical Monthly, Vol. 102, Issue 6
Second-Quantization Representation for Systems of Atoms, Nuclei, and Electrons
journal, November 1971
- Girardeau, M. D.
- Physical Review Letters, Vol. 27, Issue 21
Non-hermitian quantum thermodynamics
journal, March 2016
- Gardas, Bartłomiej; Deffner, Sebastian; Saxena, Avadh
- Scientific Reports, Vol. 6, Issue 1
Biorthogonal quantum mechanics
journal, December 2013
- Brody, Dorje C.
- Journal of Physics A: Mathematical and Theoretical, Vol. 47, Issue 3
-symmetric cubic anharmonic oscillator as a physical model
journal, July 2005
- Mostafazadeh, Ali
- Journal of Physics A: Mathematical and General, Vol. 38, Issue 29
Wave-packet collapse and the core quantum postulates: Discreteness of quantum jumps from unitarity, repeatability, and actionable information
journal, May 2013
- Zurek, Wojciech H.
- Physical Review A, Vol. 87, Issue 5
Time-dependent $\mathcal {P}$$\mathcal {T}$-symmetric quantum mechanics
journal, November 2013
- Gong, Jiangbin; Wang, Qing-hai
- Journal of Physics A: Mathematical and Theoretical, Vol. 46, Issue 48
Covariant time derivatives for dynamical systems
journal, July 2001
- Thiffeault, Jean-Luc
- Journal of Physics A: Mathematical and General, Vol. 34, Issue 29
Quantum origin of quantum jumps: Breaking of unitary symmetry induced by information transfer in the transition from quantum to classical
journal, November 2007
- Zurek, Wojciech Hubert
- Physical Review A, Vol. 76, Issue 5
Bemerkung �ber die angen�herte G�ltigkeit der klassischen Mechanik innerhalb der Quantenmechanik
journal, July 1927
- Ehrenfest, P.
- Zeitschrift f�r Physik, Vol. 45, Issue 7-8
Topological Transition in a Non-Hermitian Quantum Walk
journal, February 2009
- Rudner, M. S.; Levitov, L. S.
- Physical Review Letters, Vol. 102, Issue 6
Extension of -symmetric quantum mechanics to quantum field theory with cubic interaction
journal, July 2004
- Bender, Carl M.; Brody, Dorje C.; Jones, Hugh F.
- Physical Review D, Vol. 70, Issue 2
-symmetric Hamiltonians and their application in quantum information
journal, May 2015
- Croke, Sarah
- Physical Review A, Vol. 91, Issue 5
Optical Realization of Relativistic Non-Hermitian Quantum Mechanics
journal, June 2010
- Longhi, Stefano
- Physical Review Letters, Vol. 105, Issue 1
Non-Hermitian Heisenberg representation
journal, September 2015
- Znojil, Miloslav
- Physics Letters A, Vol. 379, Issue 36
Non-Hermitian techniques of canonical transformations in quantum mechanics
journal, February 1995
- Lee, Haewon; l’Yi, W. S.
- Physical Review A, Vol. 51, Issue 2
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- Deffner, Sebastian; Campbell, Steve
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