Araştırma Makalesi
BibTex RIS Kaynak Göster

Quantum thermal engine with spin 1/2 system and geometric phases and interference obtained by unitary transformations of mixed states

Yıl 2025, Cilt: 28 Sayı: 2, 45 - 50, 01.06.2025

Yacob Ben-aryeh

https://doi.org/10.5541/ijot.1395683

Öz

Quantum Carnot engine whose working medium is a two-dimensional spin 1/2 system, with a time-dependent magnetic field in the symmetric z direction is described. The dynamic of this engine is obtained by using four steps, where in two steps the system is coupled alternatively to hot and cold heat baths, and in the other two steps the time development is adiabatic and isentropic (with constant entropy). The conditions for getting a reversible Carnot cycle and the role of time duration for its irreversibility are discussed. Since the calculations are made for the expectation values of the Hamiltonian, only dynamical phases are obtained which cannot be used for interference effects. An alternative method is developed for getting geometric phases, which can be used in interferometry. Parallel transport equations for pure states are generalized to mixed states by which dynamical phases are eliminated. The geometric phases are derived by unitary SU(2) transformations, including time-dependent parameters which are a function of the magnetic fields interactions. A special form of the unitary transformation for the mixed thermal states is developed, by which geometric phases are obtained, which are different from those obtained in NMR and neutron interferometry.

Anahtar Kelimeler

quantum Carnot engine spin 1/2 working medium geometric phases of thermal mixed states parallel transport equations comparison with mixed NMR and neutron states

Kaynakça

  • R. Kosloff and Y. Rezek, “The Quantum Harmonic Otto Cycle,” Entropy, vol. 19, no. 4, p. 136, Mar. 2017, doi: 10.3390/e19040136.
  • H. S. Leff, “Thermal efficiency at maximum work output: New results for old heat engines,” Am J Phys, vol. 55, no. 7, pp. 602–610, Jul. 1987, doi: 10.1119/1.15071.
  • J. Roßnagel et al., “A single-atom heat engine,” Science (1979), vol. 352, no. 6283, pp. 325–329, Apr. 2016, doi: 10.1126/science.aad6320.
  • O. Abah et al., “Single-Ion Heat Engine at Maximum Power,” Phys Rev Lett, vol. 109, no. 20, p. 203006, Nov. 2012, doi: 10.1103/PhysRevLett.109.203006.
  • M. Esposito, R. Kawai, K. Lindenberg, and C. Van den Broeck, “Efficiency at Maximum Power of Low-Dissipation Carnot Engines,” Phys Rev Lett, vol. 105, no. 15, Oct. 2010, Art. no. 150603, doi: 10.1103/PhysRevLett.105.150603.
  • E. Geva and R. Kosloff, “A quantum-mechanical heat engine operating in finite time. A model consisting of spin-1/2 systems as the working fluid,” J Chem Phys, vol. 96, no. 4, pp. 3054–3067, Feb. 1992, doi: 10.1063/1.461951.
  • B. Lin and J. Chen, “Optimal analysis of the performance of an irreversible quantum heat engine with spin systems,” J Phys A Math Gen, vol. 38, no. 1, pp. 69–79, Jan. 2005, doi: 10.1088/0305-4470/38/1/004.
  • F. L. Curzon and B. Ahlborn, “Efficiency of a Carnot engine at maximum power output,” Am J Phys, vol. 43, no. 1, pp. 22–24, Jan. 1975, doi: 10.1119/1.10023.
  • M. V. Berry, “Quantal phase factors accompanying adiabatic changes,” Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences, vol. 392, no. 1802, pp. 45–57, Mar. 1984, doi: 10.1098/rspa.1984.0023.
  • Y. Ben-Aryeh, “Berry and Pancharatnam topological phases of atomic and optical systems,” Journal of Optics B: Quantum and Semiclassical Optics, vol. 6, no. 4, pp. R1–R18, Apr. 2004, doi: 10.1088/1464-4266/6/4/R01.
  • Y. Aharonov and J. Anandan, “Phase change during a cyclic quantum evolution,” Phys Rev Lett, vol. 58, no. 16, pp. 1593–1596, Apr. 1987, doi: 10.1103/PhysRevLett.58.1593.
  • E. Sjöqvist et al., “Geometric Phases for Mixed States in Interferometry,” Phys Rev Lett, vol. 85, no. 14, pp. 2845–2849, Oct. 2000, doi: 10.1103/PhysRevLett.85.2845.
  • E. Sjöqvist, “Quantal phase in split-beam interferometry,” Phys Rev A (Coll Park), vol. 63, no. 3, Feb. 2001, Art. no. 035602, doi: 10.1103/PhysRevA.63.035602.
  • S. Pancharatnam, “Generalized theory of interference, and its applications,” Proceedings of the Indian Academy of Sciences - Section A, vol. 44, no. 5, pp. 247–262, Nov. 1956, doi: 10.1007/BF03046050.
  • A. G. Wagh and V. C. Rakhecha, “On measuring the Pancharatnam phase. I. Interferometry,” Phys Lett A, vol. 197, no. 2, pp. 107–111, Jan. 1995, doi: 10.1016/0375-9601(94)00914-B.
  • Ghosh and A. Kumar, “Experimental measurement of mixed state geometric phase by quantum interferometry using NMR,” Phys Lett A, vol. 349, no. 1–4, pp. 27–36, Jan. 2006, doi: 10.1016/j.physleta.2005.08.092.
  • M. Ericsson, D. Achilles, J. T. Barreiro, D. Branning, N. A. Peters, and P. G. Kwiat, “Measurement of Geometric Phase for Mixed States Using Single Photon Interferometry,” Phys Rev Lett, vol. 94, no. 5, Feb. 2005, Art. no. 050401, doi: 10.1103/PhysRevLett.94.050401.
  • J. Du et al., “Observation of Geometric Phases for Mixed States using NMR Interferometry,” Phys Rev Lett, vol. 91, no. 10, Sep. 2003, Art. no. 100403, doi: 10.1103/PhysRevLett.91.100403.
  • J. Klepp, S. Sponar, Y. Hasegawa, E. Jericha, and G. Badurek, “Noncyclic Pancharatnam phase for mixed state evolution in neutron polarimetry,” Phys Lett A, vol. 342, no. 1–2, pp. 48–52, Jul. 2005, doi: 10.1016/j.physleta.2005.05.038.

Yıl 2025, Cilt: 28 Sayı: 2, 45 - 50, 01.06.2025

Yacob Ben-aryeh

https://doi.org/10.5541/ijot.1395683

Öz

Kaynakça

  • R. Kosloff and Y. Rezek, “The Quantum Harmonic Otto Cycle,” Entropy, vol. 19, no. 4, p. 136, Mar. 2017, doi: 10.3390/e19040136.
  • H. S. Leff, “Thermal efficiency at maximum work output: New results for old heat engines,” Am J Phys, vol. 55, no. 7, pp. 602–610, Jul. 1987, doi: 10.1119/1.15071.
  • J. Roßnagel et al., “A single-atom heat engine,” Science (1979), vol. 352, no. 6283, pp. 325–329, Apr. 2016, doi: 10.1126/science.aad6320.
  • O. Abah et al., “Single-Ion Heat Engine at Maximum Power,” Phys Rev Lett, vol. 109, no. 20, p. 203006, Nov. 2012, doi: 10.1103/PhysRevLett.109.203006.
  • M. Esposito, R. Kawai, K. Lindenberg, and C. Van den Broeck, “Efficiency at Maximum Power of Low-Dissipation Carnot Engines,” Phys Rev Lett, vol. 105, no. 15, Oct. 2010, Art. no. 150603, doi: 10.1103/PhysRevLett.105.150603.
  • E. Geva and R. Kosloff, “A quantum-mechanical heat engine operating in finite time. A model consisting of spin-1/2 systems as the working fluid,” J Chem Phys, vol. 96, no. 4, pp. 3054–3067, Feb. 1992, doi: 10.1063/1.461951.
  • B. Lin and J. Chen, “Optimal analysis of the performance of an irreversible quantum heat engine with spin systems,” J Phys A Math Gen, vol. 38, no. 1, pp. 69–79, Jan. 2005, doi: 10.1088/0305-4470/38/1/004.
  • F. L. Curzon and B. Ahlborn, “Efficiency of a Carnot engine at maximum power output,” Am J Phys, vol. 43, no. 1, pp. 22–24, Jan. 1975, doi: 10.1119/1.10023.
  • M. V. Berry, “Quantal phase factors accompanying adiabatic changes,” Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences, vol. 392, no. 1802, pp. 45–57, Mar. 1984, doi: 10.1098/rspa.1984.0023.
  • Y. Ben-Aryeh, “Berry and Pancharatnam topological phases of atomic and optical systems,” Journal of Optics B: Quantum and Semiclassical Optics, vol. 6, no. 4, pp. R1–R18, Apr. 2004, doi: 10.1088/1464-4266/6/4/R01.
  • Y. Aharonov and J. Anandan, “Phase change during a cyclic quantum evolution,” Phys Rev Lett, vol. 58, no. 16, pp. 1593–1596, Apr. 1987, doi: 10.1103/PhysRevLett.58.1593.
  • E. Sjöqvist et al., “Geometric Phases for Mixed States in Interferometry,” Phys Rev Lett, vol. 85, no. 14, pp. 2845–2849, Oct. 2000, doi: 10.1103/PhysRevLett.85.2845.
  • E. Sjöqvist, “Quantal phase in split-beam interferometry,” Phys Rev A (Coll Park), vol. 63, no. 3, Feb. 2001, Art. no. 035602, doi: 10.1103/PhysRevA.63.035602.
  • S. Pancharatnam, “Generalized theory of interference, and its applications,” Proceedings of the Indian Academy of Sciences - Section A, vol. 44, no. 5, pp. 247–262, Nov. 1956, doi: 10.1007/BF03046050.
  • A. G. Wagh and V. C. Rakhecha, “On measuring the Pancharatnam phase. I. Interferometry,” Phys Lett A, vol. 197, no. 2, pp. 107–111, Jan. 1995, doi: 10.1016/0375-9601(94)00914-B.
  • Ghosh and A. Kumar, “Experimental measurement of mixed state geometric phase by quantum interferometry using NMR,” Phys Lett A, vol. 349, no. 1–4, pp. 27–36, Jan. 2006, doi: 10.1016/j.physleta.2005.08.092.
  • M. Ericsson, D. Achilles, J. T. Barreiro, D. Branning, N. A. Peters, and P. G. Kwiat, “Measurement of Geometric Phase for Mixed States Using Single Photon Interferometry,” Phys Rev Lett, vol. 94, no. 5, Feb. 2005, Art. no. 050401, doi: 10.1103/PhysRevLett.94.050401.
  • J. Du et al., “Observation of Geometric Phases for Mixed States using NMR Interferometry,” Phys Rev Lett, vol. 91, no. 10, Sep. 2003, Art. no. 100403, doi: 10.1103/PhysRevLett.91.100403.
  • J. Klepp, S. Sponar, Y. Hasegawa, E. Jericha, and G. Badurek, “Noncyclic Pancharatnam phase for mixed state evolution in neutron polarimetry,” Phys Lett A, vol. 342, no. 1–2, pp. 48–52, Jul. 2005, doi: 10.1016/j.physleta.2005.05.038.
Toplam 19 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Metroloji,Uygulamalı ve Endüstriyel Fizik
Bölüm Araştırma Makaleleri
Yazarlar

Yacob Ben-aryeh 0000-0002-6702-1530

Erken Görünüm Tarihi 18 Mart 2025
Yayımlanma Tarihi 1 Haziran 2025
Gönderilme Tarihi 24 Kasım 2023
Kabul Tarihi 24 Mart 2024
Yayımlandığı Sayı Yıl 2025 Cilt: 28 Sayı: 2

Kaynak Göster

APA Ben-aryeh, Y. (2025). Quantum thermal engine with spin 1/2 system and geometric phases and interference obtained by unitary transformations of mixed states. International Journal of Thermodynamics, 28(2), 45-50. https://doi.org/10.5541/ijot.1395683
AMA Ben-aryeh Y. Quantum thermal engine with spin 1/2 system and geometric phases and interference obtained by unitary transformations of mixed states. International Journal of Thermodynamics. Haziran 2025;28(2):45-50. doi:10.5541/ijot.1395683
Chicago Ben-aryeh, Yacob. “Quantum Thermal Engine With Spin 1/2 System and Geometric Phases and Interference Obtained by Unitary Transformations of Mixed States”. International Journal of Thermodynamics 28, sy. 2 (Haziran 2025): 45-50. https://doi.org/10.5541/ijot.1395683.
EndNote Ben-aryeh Y (01 Haziran 2025) Quantum thermal engine with spin 1/2 system and geometric phases and interference obtained by unitary transformations of mixed states. International Journal of Thermodynamics 28 2 45–50.
IEEE Y. Ben-aryeh, “Quantum thermal engine with spin 1/2 system and geometric phases and interference obtained by unitary transformations of mixed states”, International Journal of Thermodynamics, c. 28, sy. 2, ss. 45–50, 2025, doi: 10.5541/ijot.1395683.
ISNAD Ben-aryeh, Yacob. “Quantum Thermal Engine With Spin 1/2 System and Geometric Phases and Interference Obtained by Unitary Transformations of Mixed States”. International Journal of Thermodynamics 28/2 (Haziran 2025), 45-50. https://doi.org/10.5541/ijot.1395683.
JAMA Ben-aryeh Y. Quantum thermal engine with spin 1/2 system and geometric phases and interference obtained by unitary transformations of mixed states. International Journal of Thermodynamics. 2025;28:45–50.
MLA Ben-aryeh, Yacob. “Quantum Thermal Engine With Spin 1/2 System and Geometric Phases and Interference Obtained by Unitary Transformations of Mixed States”. International Journal of Thermodynamics, c. 28, sy. 2, 2025, ss. 45-50, doi:10.5541/ijot.1395683.
Vancouver Ben-aryeh Y. Quantum thermal engine with spin 1/2 system and geometric phases and interference obtained by unitary transformations of mixed states. International Journal of Thermodynamics. 2025;28(2):45-50.
 Kapak Resmi İndir