Research Article
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Quantum Irreversibility in a Misaligned Spin System

Year 2021, Volume: 25 Issue: 3, 841 - 848, 30.06.2021
https://doi.org/10.16984/saufenbilder.827989

Abstract

A single spin that is misaligned with respect to the static external magnetic field is investigated as a toy model to clarify the nature of irreversibility in terms of inner friction and irreversible work. The coherence generation and the effects of unwanted transitions are analyzed in detail. The behavior of inner friction and irreversible work as a function of protocol time are analyzed for a finite-time unitary transformation. The coherence generation is shown to be the common sign for the inner friction and irreversible work. The excess energy sourced by the unwanted transitions for a quasistatic transformation is found to be the only sign for irreversible work. The angle The angle dependencies of the inner friction and irreversible work are also analyzed explicitly. The selected model and the considered realistic parameters are available to be implemented for the finite-time operations on the nuclear magnetic resonance setups.

Supporting Institution

Research Fund of the Samsun University

Project Number

BAP.MÜF.5501.2020.001

References

  • [1] H.T. Quan, Y.X. Liu, C.P. Sun and F. Nori, “Quantum thermodynamic cycles and quantum heat engines,” Phys. Rev. E 76, 031105, 2007.
  • [2] O. Abah, J. Roßnagel, G. Jacob, S. Deffner, F. Schmidt-Kaler, K. Singer and E. Lutz, “Single-ion heat engine at maximum power,” Phys. Rev. Lett. 109, 203006, 2012.
  • [3] F. Altintas, A.Ü.C Hardal and Ö.E Müstacaplıoğlu, “Rabi model as a quantum coherent heat engine: from quantum biology to superconducting circuits,” Phys. Rev. A 91, 023816, 2015.
  • [4] R. Dillenschneider and E. Lutz, “Energetics of quantum correlations,” Europhys. Lett. 8, 50003, 2009.
  • [5] R. Uzdin, “Coherence-induced reversibility and collective operation of quantum heat machines via coherence recycling,” Rev. Appl. 6, 024004, 2016.
  • [6] D. Türkpençe, F. Altintas, M. Paternostro and Ö.E. Müstecaplıoglu, “A photonic Carnot engine powered by a spin-star network,” EPL 117, 50002, 2017.
  • [7] A. del Campo, J. Goold and M. Paternostro, “More bang for your buck: super-adiabatic quantum engines,” Sci. Rep. 4, 6208, 2015.
  • [8] O. Abah, M. Paternostro and E. Lutz, “Shortcut-to-adiabaticity quantum Otto refrigerator,” Phys. Rev. Research. 2, 023120, 2020.
  • [9] G. Xiao and J. Gong, “Construction and optimization of a quantum analog of the Carnot cycle,” Phys. Rev. E 92, 012118 2015.
  • [10] T.B. Batalhão, A.M. Souza, L. Mazzola, R. Auccaise, R.S. Sarthour, I.S. Oliveira, J. Goold, G. De Chiara, M. Paternostro and R.M. Serra, "Experimental reconstruction of work distribution and study of fluctuation relations in a closed quantum system," Phys. Rev. Lett. 113, 140601 2014.
  • [11] A.E. Allahverdyan, K.V. Hovhannisyan, A.V. Melkikh and S.G. Gevorkian, “Carnot cycle at finite power: attainability of maximal efficiency,” Phys. Rev. Lett. 111, 050601, 2013.
  • [12] F. Plastina, A. Alecce, T.J.G. Apollaro, G. Falcone, G. Francica, F. Galve, N. Lo Gullo and R. Zambrini, “Irreversible work and inner friction in quantum thermodynamic processes,” Phys. Rev. Lett. 113, 260601, 2014.
  • [13] G. Thomas and R. S. Johal, “Friction due to inhomogeneous driving of coupled spins in a quantum heat engine,” Eur. Phys. J. B 87, 166, 2014.
  • [14] A. Alecce, F. Galve, N.L. Gullo, L. Dell’Anna, F. Plastina and R. Zambrini, “Quantum Otto cycle with inner friction: finite-time and disorder effects,” New J. Phys. 17, 075007, 2015.
  • [15] S. Çakmak, F. Altintas, and Ö.E. Müstecaplıoglu, "Irreversibility in a unitary finite-rate protocol: the concept of internal friction," Phys. Scr. 91, 075101, 2016.
  • [16] S. Çakmak, F. Altintas, A. Gençten and Ö.E. Müstecaplıoglu, "Irreversible work and internal friction in a quantum Otto cycle of a single arbitrary spin," Eur. Phys. J. D. 71, 75, 2017.
  • [17] P.A. Camati, J.F.G. Santos and R.M. Serra, “Coherence effects in the performance of the quantum Otto heat engine,” Phys. Rev. A 99, 062103, 2019.
  • [18] G. Francica, J. Goold and F. Plastina, “Role of coherence in the nonequilibrium thermodynamics of quantum systems,” Phys. Rev. E 99, 042105, 2019.
  • [19] S. Çakmak and F. Altintas, “Quantum Carnot cycle with inner friction,” Quantum Inf. Process. 19, 248, 2020.
  • [20] A.D. Varizi, A.P. Vieira, C. Cormick, R.C. Drumond and G.T. Landi, “Quantum coherence and criticality in irreversible work,” Phys. Rev. Research. 2, 033279, 2020.
  • [21] N. Shiraishi and H. Tajima, "Efficiency versus speed in quantum heat engines: rigorous constraint from Lieb-Robinson bound," Phys. Rev. E 96, 022138, 2017.
  • [22] D. Türkpençe and F. Altintas, “Coupled quantum Otto heat engine and refrigerator with inner friction,” Quantum Inf. Process. 18, 255, 2019.
  • [23] A.E. Allahverdyan and Th.M. Nieuwenhuizen, “Minimal work principle: Proof and counterexamples,” Phys. Rev. E 71, 046107, 2005.
  • [24] J.P.S. Peterson, T.B. Batalhão, M. Herrera, A.M. Souza, R.S. Sarthour, I.S. Oliveira and R.M. Serra, "Experimental Characterization of a Spin Quantum Heat Engine," Phys. Rev. Lett. 123, 240601, 2019.
  • [25] R.J. de Assis, T.M. de Mendonça, C.J. Villas-Boas, A.M. de Souza, R.S. Sarthour, I.S. Oliveira and N.G. de Almeida, “Efficiency of a Quantum Otto Heat Engine Operating under a Reservoir at Effective Negative Temperatures,” Phys. Rev. Lett. 122, 240602, 2019.
Year 2021, Volume: 25 Issue: 3, 841 - 848, 30.06.2021
https://doi.org/10.16984/saufenbilder.827989

Abstract

İçsel sürtünme ve geri çevrilemez iş açısından tersinmezliğin doğasını açıklamak amacıyla dış durgun manyetik alana göre yanlış hizalanmış spin, model olarak incelendi. Eşevrelilik üretimi ve izinsiz geçişlerin etkileri dataylı olarak analiz edildi. İçsel sürtünmenin ve geri çevrilemez işin davranışı protokol zamanının fonksiyonu olarak sonlu-zamanlı üniter dönüşüm için analiz edildi. Eşevrelilik üretiminin, içsel sürtünme ve geri çevrilemez işin ortak işareti olduğu gösterildi. Sanki durağan dönüşümler için, istenmeyen geçişlerden kaynaklanan fazla enerjinin sadece geri çevrilemez işin göstergesi olduğu bulundu. Ayrıca, içsel sürtünme ve geri çevrilemez işin açıya göre değişimleri açıklandı. Seçilen model ve alınan gerçek parametreler ile sonlu-zamanlı operasyonlar nükleer manyetik rezonans düzeneği üzerinde uygulanabilir.

Project Number

BAP.MÜF.5501.2020.001

References

  • [1] H.T. Quan, Y.X. Liu, C.P. Sun and F. Nori, “Quantum thermodynamic cycles and quantum heat engines,” Phys. Rev. E 76, 031105, 2007.
  • [2] O. Abah, J. Roßnagel, G. Jacob, S. Deffner, F. Schmidt-Kaler, K. Singer and E. Lutz, “Single-ion heat engine at maximum power,” Phys. Rev. Lett. 109, 203006, 2012.
  • [3] F. Altintas, A.Ü.C Hardal and Ö.E Müstacaplıoğlu, “Rabi model as a quantum coherent heat engine: from quantum biology to superconducting circuits,” Phys. Rev. A 91, 023816, 2015.
  • [4] R. Dillenschneider and E. Lutz, “Energetics of quantum correlations,” Europhys. Lett. 8, 50003, 2009.
  • [5] R. Uzdin, “Coherence-induced reversibility and collective operation of quantum heat machines via coherence recycling,” Rev. Appl. 6, 024004, 2016.
  • [6] D. Türkpençe, F. Altintas, M. Paternostro and Ö.E. Müstecaplıoglu, “A photonic Carnot engine powered by a spin-star network,” EPL 117, 50002, 2017.
  • [7] A. del Campo, J. Goold and M. Paternostro, “More bang for your buck: super-adiabatic quantum engines,” Sci. Rep. 4, 6208, 2015.
  • [8] O. Abah, M. Paternostro and E. Lutz, “Shortcut-to-adiabaticity quantum Otto refrigerator,” Phys. Rev. Research. 2, 023120, 2020.
  • [9] G. Xiao and J. Gong, “Construction and optimization of a quantum analog of the Carnot cycle,” Phys. Rev. E 92, 012118 2015.
  • [10] T.B. Batalhão, A.M. Souza, L. Mazzola, R. Auccaise, R.S. Sarthour, I.S. Oliveira, J. Goold, G. De Chiara, M. Paternostro and R.M. Serra, "Experimental reconstruction of work distribution and study of fluctuation relations in a closed quantum system," Phys. Rev. Lett. 113, 140601 2014.
  • [11] A.E. Allahverdyan, K.V. Hovhannisyan, A.V. Melkikh and S.G. Gevorkian, “Carnot cycle at finite power: attainability of maximal efficiency,” Phys. Rev. Lett. 111, 050601, 2013.
  • [12] F. Plastina, A. Alecce, T.J.G. Apollaro, G. Falcone, G. Francica, F. Galve, N. Lo Gullo and R. Zambrini, “Irreversible work and inner friction in quantum thermodynamic processes,” Phys. Rev. Lett. 113, 260601, 2014.
  • [13] G. Thomas and R. S. Johal, “Friction due to inhomogeneous driving of coupled spins in a quantum heat engine,” Eur. Phys. J. B 87, 166, 2014.
  • [14] A. Alecce, F. Galve, N.L. Gullo, L. Dell’Anna, F. Plastina and R. Zambrini, “Quantum Otto cycle with inner friction: finite-time and disorder effects,” New J. Phys. 17, 075007, 2015.
  • [15] S. Çakmak, F. Altintas, and Ö.E. Müstecaplıoglu, "Irreversibility in a unitary finite-rate protocol: the concept of internal friction," Phys. Scr. 91, 075101, 2016.
  • [16] S. Çakmak, F. Altintas, A. Gençten and Ö.E. Müstecaplıoglu, "Irreversible work and internal friction in a quantum Otto cycle of a single arbitrary spin," Eur. Phys. J. D. 71, 75, 2017.
  • [17] P.A. Camati, J.F.G. Santos and R.M. Serra, “Coherence effects in the performance of the quantum Otto heat engine,” Phys. Rev. A 99, 062103, 2019.
  • [18] G. Francica, J. Goold and F. Plastina, “Role of coherence in the nonequilibrium thermodynamics of quantum systems,” Phys. Rev. E 99, 042105, 2019.
  • [19] S. Çakmak and F. Altintas, “Quantum Carnot cycle with inner friction,” Quantum Inf. Process. 19, 248, 2020.
  • [20] A.D. Varizi, A.P. Vieira, C. Cormick, R.C. Drumond and G.T. Landi, “Quantum coherence and criticality in irreversible work,” Phys. Rev. Research. 2, 033279, 2020.
  • [21] N. Shiraishi and H. Tajima, "Efficiency versus speed in quantum heat engines: rigorous constraint from Lieb-Robinson bound," Phys. Rev. E 96, 022138, 2017.
  • [22] D. Türkpençe and F. Altintas, “Coupled quantum Otto heat engine and refrigerator with inner friction,” Quantum Inf. Process. 18, 255, 2019.
  • [23] A.E. Allahverdyan and Th.M. Nieuwenhuizen, “Minimal work principle: Proof and counterexamples,” Phys. Rev. E 71, 046107, 2005.
  • [24] J.P.S. Peterson, T.B. Batalhão, M. Herrera, A.M. Souza, R.S. Sarthour, I.S. Oliveira and R.M. Serra, "Experimental Characterization of a Spin Quantum Heat Engine," Phys. Rev. Lett. 123, 240601, 2019.
  • [25] R.J. de Assis, T.M. de Mendonça, C.J. Villas-Boas, A.M. de Souza, R.S. Sarthour, I.S. Oliveira and N.G. de Almeida, “Efficiency of a Quantum Otto Heat Engine Operating under a Reservoir at Effective Negative Temperatures,” Phys. Rev. Lett. 122, 240602, 2019.
There are 25 citations in total.

Details

Primary Language English
Subjects Metrology, Applied and Industrial Physics
Journal Section Research Articles
Authors

Selçuk Çakmak 0000-0002-1284-0870

Project Number BAP.MÜF.5501.2020.001
Publication Date June 30, 2021
Submission Date November 18, 2020
Acceptance Date May 8, 2021
Published in Issue Year 2021 Volume: 25 Issue: 3

Cite

APA Çakmak, S. (2021). Quantum Irreversibility in a Misaligned Spin System. Sakarya University Journal of Science, 25(3), 841-848. https://doi.org/10.16984/saufenbilder.827989
AMA Çakmak S. Quantum Irreversibility in a Misaligned Spin System. SAUJS. June 2021;25(3):841-848. doi:10.16984/saufenbilder.827989
Chicago Çakmak, Selçuk. “Quantum Irreversibility in a Misaligned Spin System”. Sakarya University Journal of Science 25, no. 3 (June 2021): 841-48. https://doi.org/10.16984/saufenbilder.827989.
EndNote Çakmak S (June 1, 2021) Quantum Irreversibility in a Misaligned Spin System. Sakarya University Journal of Science 25 3 841–848.
IEEE S. Çakmak, “Quantum Irreversibility in a Misaligned Spin System”, SAUJS, vol. 25, no. 3, pp. 841–848, 2021, doi: 10.16984/saufenbilder.827989.
ISNAD Çakmak, Selçuk. “Quantum Irreversibility in a Misaligned Spin System”. Sakarya University Journal of Science 25/3 (June 2021), 841-848. https://doi.org/10.16984/saufenbilder.827989.
JAMA Çakmak S. Quantum Irreversibility in a Misaligned Spin System. SAUJS. 2021;25:841–848.
MLA Çakmak, Selçuk. “Quantum Irreversibility in a Misaligned Spin System”. Sakarya University Journal of Science, vol. 25, no. 3, 2021, pp. 841-8, doi:10.16984/saufenbilder.827989.
Vancouver Çakmak S. Quantum Irreversibility in a Misaligned Spin System. SAUJS. 2021;25(3):841-8.