Quantum work statistics of charged Dirac particles in time-dependent fields

Deffner, Sebastian; Saxena, Avadh

doi:10.1103/PhysRevE.92.032137

Quantum work statistics of charged Dirac particles in time-dependent fields

Journal Article · Mon Sep 28 00:00:00 EDT 2015 · Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

DOI:https://doi.org/10.1103/PhysRevE.92.032137· OSTI ID:1233562

Deffner, Sebastian ^[1]; Saxena, Avadh ^[1]

Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

The quantum Jarzynski equality is an important theorem of modern quantum thermodynamics. We show that the Jarzynski equality readily generalizes to relativistic quantum mechanics described by the Dirac equation. After establishing the conceptual framework we solve a pedagogical, yet experimentally relevant, system analytically. As a main result we obtain the exact quantum work distributions for charged particles traveling through a time-dependent vector potential evolving under Schrödinger as well as under Dirac dynamics, and for which the Jarzynski equality is verified. Thus, special emphasis is put on the conceptual and technical subtleties arising from relativistic quantum mechanics.

View Accepted Manuscript (DOE)

Research Organization:: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Sponsoring Organization:: USDOE

Grant/Contract Number:: AC52-06NA25396

OSTI ID:: 1233562

Alternate ID(s):: OSTI ID: 1222047

Report Number(s):: LA--UR-15-24887

Journal Information:: Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics, Journal Name: Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics Journal Issue: 3 Vol. 92; ISSN 1539-3755; ISSN PLEEE8

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

References (53)

Das Maxwellsche Gesetz der Geschwindigkeitsverteilung in der Relativtheorie Jüttner, Ferencz Annalen der Physik, Vol. 339, Issue 5 https://doi.org/10.1002/andp.19113390503	journal	January 1911
Quantum work statistics of linear and nonlinear parametric oscillators Deffner, Sebastian; Abah, Obinna; Lutz, Eric Chemical Physics, Vol. 375, Issue 2-3 https://doi.org/10.1016/j.chemphys.2010.04.042	journal	October 2010
Quantum work distribution for a driven diatomic molecule Leonard, Alison; Deffner, Sebastian Chemical Physics, Vol. 446 https://doi.org/10.1016/j.chemphys.2014.10.020	journal	January 2015
Relativistic fluctuation theorems Fingerle, Axel Comptes Rendus Physique, Vol. 8, Issue 5-6 https://doi.org/10.1016/j.crhy.2007.05.015	journal	June 2007
Quantum Computation and Quantum Information Nielsen, Michael A.; Chuang, Isaac L. Cambridge University Press https://doi.org/10.1017/CBO9780511976667	book	January 2011
The other QFT Hänggi, Peter; Talkner, Peter Nature Physics, Vol. 11, Issue 2 https://doi.org/10.1038/nphys3167	journal	February 2015
Experimental test of the quantum Jarzynski equality with a trapped-ion system An, Shuoming; Zhang, Jing-Ning; Um, Mark Nature Physics, Vol. 11, Issue 2 https://doi.org/10.1038/nphys3197	journal	December 2014
Diverse phenomena, common themes Jarzynski, Christopher Nature Physics, Vol. 11, Issue 2 https://doi.org/10.1038/nphys3229	journal	February 2015
Interview with Michael E. Fisher Ortiz de Zárate, José M. Europhysics News, Vol. 42, Issue 1 https://doi.org/10.1051/epn/2011101	journal	January 2011
The Nonequilibrium Thermodynamics of Small Systems Bustamante, Carlos; Liphardt, Jan; Ritort, Felix Physics Today, Vol. 58, Issue 7 https://doi.org/10.1063/1.2012462	journal	July 2005
Quantum fluctuation relations for ensembles of wave functions Campisi, Michele New Journal of Physics, Vol. 15, Issue 11 https://doi.org/10.1088/1367-2630/15/11/115008	journal	November 2013
Transient quantum fluctuation theorems and generalized measurements Prasanna Venkatesh, B.; Watanabe, Gentaro; Talkner, Peter New Journal of Physics, Vol. 16, Issue 1 https://doi.org/10.1088/1367-2630/16/1/015032	journal	January 2014
Non-equilibrium equalities with unital quantum channels Rastegin, Alexey E. Journal of Statistical Mechanics: Theory and Experiment, Vol. 2013, Issue 06 https://doi.org/10.1088/1742-5468/2013/06/P06016	journal	June 2013
The Quantum Theory of the Electron Dirac, P. A. M. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 117, Issue 778 https://doi.org/10.1098/rspa.1928.0023	journal	February 1928
Landau-Zener-Stückelberg interferometry in pair production from counterpropagating lasers Fillion-Gourdeau, François; Lorin, Emmanuel; Bandrauk, André D. Physical Review A, Vol. 86, Issue 3 https://doi.org/10.1103/PhysRevA.86.032118	journal	September 2012
Holevo's bound from a general quantum fluctuation theorem Kafri, Dvir; Deffner, Sebastian Physical Review A, Vol. 86, Issue 4 https://doi.org/10.1103/PhysRevA.86.044302	journal	October 2012
Entropy production and information fluctuations along quantum trajectories Leggio, B.; Napoli, A.; Messina, A. Physical Review A, Vol. 88, Issue 4 https://doi.org/10.1103/PhysRevA.88.042111	journal	October 2013
Nonequilibrium dynamics of a noisy quantum Ising chain: Statistics of work and prethermalization after a sudden quench of the transverse field Marino, Jamir; Silva, Alessandro Physical Review B, Vol. 89, Issue 2 https://doi.org/10.1103/PhysRevB.89.024303	journal	January 2014
Entropy production fluctuation theorem and the nonequilibrium work relation for free energy differences Crooks, Gavin E. Physical Review E, Vol. 60, Issue 3 https://doi.org/10.1103/PhysRevE.60.2721	journal	September 1999
Fluctuation theorems: Work is not an observable Talkner, Peter; Lutz, Eric; Hänggi, Peter Physical Review E, Vol. 75, Issue 5 https://doi.org/10.1103/PhysRevE.75.050102	journal	May 2007
Nonequilibrium work distribution of a quantum harmonic oscillator Deffner, Sebastian; Lutz, Eric Physical Review E, Vol. 77, Issue 2 https://doi.org/10.1103/PhysRevE.77.021128	journal	February 2008
Statistics of work performed on a forced quantum oscillator Talkner, Peter; Burada, P. Sekhar; Hänggi, Peter Physical Review E, Vol. 78, Issue 1 https://doi.org/10.1103/PhysRevE.78.011115	journal	July 2008
Quantum and classical fluctuation theorems from a decoherent histories, open-system analysis Subaşı, Y.; Hu, B. L. Physical Review E, Vol. 85, Issue 1 https://doi.org/10.1103/PhysRevE.85.011112	journal	January 2012
Validity of nonequilibrium work relations for the rapidly expanding quantum piston Quan, H. T.; Jarzynski, Christopher Physical Review E, Vol. 85, Issue 3 https://doi.org/10.1103/PhysRevE.85.031102	journal	March 2012
Quantum-trajectory approach to the stochastic thermodynamics of a forced harmonic oscillator Horowitz, Jordan M. Physical Review E, Vol. 85, Issue 3 https://doi.org/10.1103/PhysRevE.85.031110	journal	March 2012
Fluctuation theorems for non-Markovian quantum processes Leggio, B.; Napoli, A.; Breuer, H. -P. Physical Review E, Vol. 87, Issue 3 https://doi.org/10.1103/PhysRevE.87.032113	journal	March 2013
Fluctuation theorems for quantum processes Albash, Tameem; Lidar, Daniel A.; Marvian, Milad Physical Review E, Vol. 88, Issue 3 https://doi.org/10.1103/PhysRevE.88.032146	journal	September 2013
Work distribution and edge singularities for generic time-dependent protocols in extended systems Smacchia, Pietro; Silva, Alessandro Physical Review E, Vol. 88, Issue 4 https://doi.org/10.1103/PhysRevE.88.042109	journal	October 2013
Jarzynski equality for quantum stochastic maps Rastegin, Alexey E.; Życzkowski, Karol Physical Review E, Vol. 89, Issue 1 https://doi.org/10.1103/PhysRevE.89.012127	journal	January 2014
Generalized energy measurements and modified transient quantum fluctuation theorems Watanabe, Gentaro; Venkatesh, B. Prasanna; Talkner, Peter Physical Review E, Vol. 89, Issue 5 https://doi.org/10.1103/PhysRevE.89.052116	journal	May 2014
Work and quantum phase transitions: Quantum latency Mascarenhas, E.; Bragança, H.; Dorner, R. Physical Review E, Vol. 89, Issue 6 https://doi.org/10.1103/PhysRevE.89.062103	journal	June 2014
Nonequilibrium quantum fluctuations of work Allahverdyan, A. E. Physical Review E, Vol. 90, Issue 3 https://doi.org/10.1103/PhysRevE.90.032137	journal	September 2014
Interference of identical particles and the quantum work distribution Gong, Zongping; Deffner, Sebastian; Quan, H. T. Physical Review E, Vol. 90, Issue 6 https://doi.org/10.1103/PhysRevE.90.062121	journal	December 2014
Employing Trapped Cold Ions to Verify the Quantum Jarzynski Equality Huber, Gerhard; Schmidt-Kaler, Ferdinand; Deffner, Sebastian Physical Review Letters, Vol. 101, Issue 7 https://doi.org/10.1103/PhysRevLett.101.070403	journal	August 2008
Statistics of the Work Done on a Quantum Critical System by Quenching a Control Parameter Silva, Alessandro Physical Review Letters, Vol. 101, Issue 12 https://doi.org/10.1103/PhysRevLett.101.120603	journal	September 2008
Test of the Jarzynski and Crooks Fluctuation Relations in an Electronic System Saira, O. -P.; Yoon, Y.; Tanttu, T. Physical Review Letters, Vol. 109, Issue 18 https://doi.org/10.1103/PhysRevLett.109.180601	journal	October 2012
Single-Ion Heat Engine at Maximum Power Abah, O.; Roßnagel, J.; Jacob, G. Physical Review Letters, Vol. 109, Issue 20 https://doi.org/10.1103/PhysRevLett.109.203006	journal	November 2012
Resonantly Enhanced Pair Production in a Simple Diatomic Model Fillion-Gourdeau, François; Lorin, Emmanuel; Bandrauk, André D. Physical Review Letters, Vol. 110, Issue 1 https://doi.org/10.1103/PhysRevLett.110.013002	journal	January 2013
Extracting Quantum Work Statistics and Fluctuation Theorems by Single-Qubit Interferometry Dorner, R.; Clark, S. R.; Heaney, L. Physical Review Letters, Vol. 110, Issue 23 https://doi.org/10.1103/PhysRevLett.110.230601	journal	June 2013
Measuring the Characteristic Function of the Work Distribution Mazzola, L.; De Chiara, G.; Paternostro, M. Physical Review Letters, Vol. 110, Issue 23 https://doi.org/10.1103/PhysRevLett.110.230602	journal	June 2013
Nanoscale Heat Engine Beyond the Carnot Limit Roßnagel, J.; Abah, O.; Schmidt-Kaler, F. Physical Review Letters, Vol. 112, Issue 3 https://doi.org/10.1103/PhysRevLett.112.030602	journal	January 2014
Quantum Optomechanical Heat Engine Zhang, Keye; Bariani, Francesco; Meystre, Pierre Physical Review Letters, Vol. 112, Issue 15 https://doi.org/10.1103/PhysRevLett.112.150602	journal	April 2014
Experimental Reconstruction of Work Distribution and Study of Fluctuation Relations in a Closed Quantum System Batalhão, Tiago B.; Souza, Alexandre M.; Mazzola, Laura Physical Review Letters, Vol. 113, Issue 14 https://doi.org/10.1103/PhysRevLett.113.140601	journal	October 2014
Work Measurement as a Generalized Quantum Measurement Roncaglia, Augusto J.; Cerisola, Federico; Paz, Juan Pablo Physical Review Letters, Vol. 113, Issue 25 https://doi.org/10.1103/PhysRevLett.113.250601	journal	December 2014
Jarzynski Equality in P T -Symmetric Quantum Mechanics Deffner, Sebastian; Saxena, Avadh Physical Review Letters, Vol. 114, Issue 15 https://doi.org/10.1103/PhysRevLett.114.150601	journal	April 2015
Nonequilibrium Equality for Free Energy Differences Jarzynski, C. Physical Review Letters, Vol. 78, Issue 14 https://doi.org/10.1103/PhysRevLett.78.2690	journal	April 1997
Experimental Test of the Fluctuation Theorem for a Driven Two-Level System with Time-Dependent Rates Schuler, S.; Speck, T.; Tietz, C. Physical Review Letters, Vol. 94, Issue 18 https://doi.org/10.1103/PhysRevLett.94.180602	journal	May 2005
Assessing the Nonequilibrium Thermodynamics in a Quenched Quantum Many-Body System via Single Projective Measurements Fusco, L.; Pigeon, S.; Apollaro, T. J. G. Physical Review X, Vol. 4, Issue 3 https://doi.org/10.1103/PhysRevX.4.031029	journal	August 2014
Colloquium : Quantum fluctuation relations: Foundations and applications Campisi, Michele; Hänggi, Peter; Talkner, Peter Reviews of Modern Physics, Vol. 83, Issue 3 https://doi.org/10.1103/RevModPhys.83.771	journal	July 2011
Equilibrium Information from Nonequilibrium Measurements in an Experimental Test of Jarzynski's Equality Liphardt, J. Science, Vol. 296, Issue 5574 https://doi.org/10.1126/science.1071152	journal	June 2002
Equalities and Inequalities: Irreversibility and the Second Law of Thermodynamics at the Nanoscale Jarzynski, Christopher Annual Review of Condensed Matter Physics, Vol. 2, Issue 1 https://doi.org/10.1146/annurev-conmatphys-062910-140506	journal	March 2011
Quantum entropy production in phase space Deffner, Sebastian EPL (Europhysics Letters), Vol. 103, Issue 3 https://doi.org/10.1209/0295-5075/103/30001	journal	August 2013
Detailed Jarzynski equality applied to a logically irreversible procedure Bérut, A.; Petrosyan, A.; Ciliberto, S. EPL (Europhysics Letters), Vol. 103, Issue 6 https://doi.org/10.1209/0295-5075/103/60002	journal	September 2013

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