Fast forward to the classical adiabatic invariant
Abstract
We show how the classical action, an adiabatic invariant, can be preserved under nonadiabatic conditions. Specifically, for a time-dependent Hamiltonian H = p2/2m + U (q,t) in one degree of freedom, and for an arbitrary choice of action I0, we construct a so-called fast-forward potential energy function VFF (q,t) that, when added to H, guides all trajectories with initial action I0 to end with the same value of action. Here, we use this result to construct a local dynamical invariant J (q,p,t) whose value remains constant along these trajectories. We illustrate our results with numerical simulations. Finally, we sketch how our classical results may be used to design approximate quantum shortcuts to adiabaticity.
- Authors:
-
- Univ. of Maryland, College Park, MD (United States). Inst. for Physical Science and Technology, Dept. of Chemistry and Biochemistry, and Dept. of Physics
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Univ. of Maryland Baltimore County (UMBC), Baltimore, MD (United States). Dept. of Physics
- Univ. of Maryland, College Park, MD (United States). Dept. of Physics
- Univ. of Maryland, College Park, MD (United States). Dept. of Chemistry and Biochemistry; Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
- Publication Date:
- Research Org.:
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
- Sponsoring Org.:
- USDOE; National Science Foundation (NSF); US Army Research Office (ARO)
- OSTI Identifier:
- 1458942
- Alternate Identifier(s):
- OSTI ID: 1346591
- Report Number(s):
- LA-UR-16-22608
Journal ID: ISSN 2470-0045; PLEEE8; TRN: US1901531
- Grant/Contract Number:
- AC52-06NA25396; W911NF-13-1-0390
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review E
- Additional Journal Information:
- Journal Volume: 95; Journal Issue: 3; Journal ID: ISSN 2470-0045
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Mathematics
Citation Formats
Jarzynski, Christopher, Deffner, Sebastian, Patra, Ayoti, and Suba??, Yi?it. Fast forward to the classical adiabatic invariant. United States: N. p., 2017.
Web. doi:10.1103/PhysRevE.95.032122.
Jarzynski, Christopher, Deffner, Sebastian, Patra, Ayoti, & Suba??, Yi?it. Fast forward to the classical adiabatic invariant. United States. https://doi.org/10.1103/PhysRevE.95.032122
Jarzynski, Christopher, Deffner, Sebastian, Patra, Ayoti, and Suba??, Yi?it. Wed .
"Fast forward to the classical adiabatic invariant". United States. https://doi.org/10.1103/PhysRevE.95.032122. https://www.osti.gov/servlets/purl/1458942.
@article{osti_1458942,
title = {Fast forward to the classical adiabatic invariant},
author = {Jarzynski, Christopher and Deffner, Sebastian and Patra, Ayoti and Suba??, Yi?it},
abstractNote = {We show how the classical action, an adiabatic invariant, can be preserved under nonadiabatic conditions. Specifically, for a time-dependent Hamiltonian H = p2/2m + U (q,t) in one degree of freedom, and for an arbitrary choice of action I0, we construct a so-called fast-forward potential energy function VFF (q,t) that, when added to H, guides all trajectories with initial action I0 to end with the same value of action. Here, we use this result to construct a local dynamical invariant J (q,p,t) whose value remains constant along these trajectories. We illustrate our results with numerical simulations. Finally, we sketch how our classical results may be used to design approximate quantum shortcuts to adiabaticity.},
doi = {10.1103/PhysRevE.95.032122},
journal = {Physical Review E},
number = 3,
volume = 95,
place = {United States},
year = {2017},
month = {3}
}
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Works referenced in this record:
Shortcuts to adiabaticity: suppression of pair production in driven Dirac dynamics
journal, December 2015
- Deffner, Sebastian
- New Journal of Physics, Vol. 18, Issue 1
High-Fidelity Rapid Ground-State Loading of an Ultracold Gas into an Optical Lattice
journal, August 2014
- Masuda, Shumpei; Nakamura, Katsuhiro; del Campo, Adolfo
- Physical Review Letters, Vol. 113, Issue 6
An Exact Quantum Theory of the Time‐Dependent Harmonic Oscillator and of a Charged Particle in a Time‐Dependent Electromagnetic Field
journal, August 1969
- Lewis, H. R.; Riesenfeld, W. B.
- Journal of Mathematical Physics, Vol. 10, Issue 8
Unitary deformations of counterdiabatic driving
journal, April 2015
- Takahashi, Kazutaka
- Physical Review A, Vol. 91, Issue 4
Ultracold quantum gases in optical lattices
journal, October 2005
- Bloch, Immanuel
- Nature Physics, Vol. 1, Issue 1
Classical and Quantum Shortcuts to Adiabaticity for Scale-Invariant Driving
journal, April 2014
- Deffner, Sebastian; Jarzynski, Christopher; del Campo, Adolfo
- Physical Review X, Vol. 4, Issue 2
Class of Exact Invariants for Classical and Quantum Time‐Dependent Harmonic Oscillators
journal, November 1968
- Lewis, H. R.
- Journal of Mathematical Physics, Vol. 9, Issue 11
Acceleration of adiabatic quantum dynamics in electromagnetic fields
journal, October 2011
- Masuda, Shumpei; Nakamura, Katsuhiro
- Physical Review A, Vol. 84, Issue 4
Classical and Quantum Shortcuts to Adiabaticity in a Tilted Piston
journal, October 2016
- Patra, Ayoti; Jarzynski, Christopher
- The Journal of Physical Chemistry B, Vol. 121, Issue 15
Fast-forward of adiabatic dynamics in quantum mechanics
journal, November 2009
- Masuda, Shumpei; Nakamura, Katsuhiro
- Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 466, Issue 2116
Generating shortcuts to adiabaticity in quantum and classical dynamics
journal, October 2013
- Jarzynski, Christopher
- Physical Review A, Vol. 88, Issue 4
Adiabatic Population Transfer with Control Fields
journal, November 2003
- Demirplak, Mustafa; Rice, Stuart A.
- The Journal of Physical Chemistry A, Vol. 107, Issue 46
Boosting work characteristics and overall heat-engine performance via shortcuts to adiabaticity: Quantum and classical systems
journal, December 2013
- Deng, Jiawen; Wang, Qing-hai; Liu, Zhihao
- Physical Review E, Vol. 88, Issue 6
Fast and stable manipulation of a charged particle in a Penning trap
journal, March 2015
- Kiely, A.; McGuinness, J. P. L.; Muga, J. G.
- Journal of Physics B: Atomic, Molecular and Optical Physics, Vol. 48, Issue 7
Shortcuts to adiabaticity: Fast-forward approach
journal, July 2012
- Torrontegui, E.; Martínez-Garaot, S.; Ruschhaupt, A.
- Physical Review A, Vol. 86, Issue 1
Fast transport of Bose–Einstein condensates
journal, January 2012
- Torrontegui, E.; Chen, Xi; Modugno, M.
- New Journal of Physics, Vol. 14, Issue 1
Transitionless quantum driving
journal, August 2009
- Berry, M. V.
- Journal of Physics A: Mathematical and Theoretical, Vol. 42, Issue 36
Paul Ehrenfest: The Genesis of the Adiabatic Hypothesis, 1911–1914
journal, January 2006
- Navarro, Luis; Pérez, Enric
- Archive for History of Exact Sciences, Vol. 60, Issue 2
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- Torrontegui, E.; Lizuain, I.; González-Resines, S.
- Physical Review A, Vol. 96, Issue 2
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journal, November 2017
- González-Resines, S.; Guéry-Odelin, D.; Tobalina, A.
- Physical Review Applied, Vol. 8, Issue 5
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journal, February 2019
- Bukov, Marin; Sels, Dries; Polkovnikov, Anatoli
- Physical Review X, Vol. 9, Issue 1
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journal, October 2019
- Guéry-Odelin, D.; Ruschhaupt, A.; Kiely, A.
- Reviews of Modern Physics, Vol. 91, Issue 4
Robust load transport by an overhead crane with respect to cable length uncertainties
journal, January 2020
- Martínez-Cercós, Daniel; Guéry-Odelin, David; Muga, Juan Gonzalo
- Journal of Vibration and Control, Vol. 26, Issue 17-18
Invariant-based inverse engineering of crane control parameters
text, January 2017
- González-Resines, S.; Guéry-Odelin, D.; Tobalina, A.
- arXiv