Quantum thermal engine with spin 1/2 system and geometric phases and interference obtained by unitary transformations of mixed states
Abstract
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.
Keywords
quantum Carnot engine spin 1/2 working medium geometric phases of thermal mixed states parallel transport equations comparison with mixed NMR and neutron states
References
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Abstract
References
- 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.
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- 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.
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- 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.
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Details
| Primary Language | English |
|---|---|
| Subjects | Metrology, Applied and Industrial Physics |
| Journal Section | Research Articles |
| Authors | |
| Early Pub Date | March 18, 2025 |
| Publication Date | June 1, 2025 |
| Submission Date | November 24, 2023 |
| Acceptance Date | March 24, 2024 |
| Published in Issue | Year 2025 Volume: 28 Issue: 2 |
