Fast forward evolution in heat equation: Tunable heat transport in adiabatic regime
https://doi.org/10.17586/2220-8054-2023-14-4-421-427
Abstract
We consider the problem of fast forward evolution of the processes described in terms of the heat equation. The matter is considered on an adiabatically expanding time-dependent box. Attention is paid to acceleration of heat transfer processes. So called shortcuts to adiabaticity, implying fast forwarding of the adiabatic states are studied. Heat flux and temperature profiles are analyzed for standard and fast forwarded regimes.
About the Authors
J. Matrasulov
Faculty of Physics, National University of Uzbekistan
Uzbekistan
Uzbekistan
J. Matrasulov – Faculty of Physics, National University of Uzbekistan
Vuzgorodok, Tashkent 100174
J. R. Yusupov
Kimyo International University in Tashkent
Uzbekistan
Uzbekistan
J. R. Yusupov – Kimyo International University in Tashkent
156 Usman Nasyr Str., 100121, Tashkent
A. A. Saidov
Turin Polytechnic University in Tashkent
Uzbekistan
Uzbekistan
A. A. Saidov – Turin Polytechnic University in Tashkent
17 Niyazov Str.,100095, Tashkent
References
1. Masuda S., Nakamura K. Fast-forward problem in quantum mechanics. Phys. Rev. A, 2008, 78, P. 062108.
2. Khujakulov A., Nakamura K. Scheme for accelerating quantum tunneling dynamics. Phys. Rev. A, 2016, 93, P. 022101.
3. S. Masuda and K. Nakamura, Fast-forward of adiabatic dynamics in quantum mechanics, Proc. R. Soc. A 466, 1135 (2010).
4. Shumpei Masuda and Katsuhiro Nakamura, Acceleration of adiabatic quantum dynamics in electromagnetic fields. Phys. Rev. A, 2011, 84, P. 043434.
5. Setiawan I., Bobby Eka Gunara, Masuda S., Nakamura K. Fast forward of the adiabatic spin dynamics of entangled states. Phys. Rev. A, 2017, 96, P. 052106.
6. Nakamura K., Khujakulov A., Avazbaev S., Masuda S. Fast forward of adiabatic control of tunneling states. Phys. Rev.A, 2017, 95, P. 062108.
7. Babajanova G., Matrasulov J., Nakamura K. Quantum gas in the fast forward scheme of adiabatically expanding cavities: Force and equation of state. Phys. Rev. E, 2018, 97, P. 042104.
8. Katsuhiro Nakamura, Jasur Matrasulov, and Yuki Izumida. Fast-forward approach to stochastic heat engine. Phys. Rev. E, 2020, 102, P. 012129.
9. Guery-Odelin D., Ruschhaup A., Kiel A., Torrontegui E., Mart ´ ´ınez-Garaot S., Muga J.G. Shortcuts to adiabaticity: Concepts, methods, and applications. Rev. Mod. Phys., 2019, 91, P. 045001.
10. Erik Torrontegui, et al. Chapter 2 - Shortcuts to Adiabaticity, Advances in atomic, molecular, and optical physics, 2013, 62, P. 117.
11. Chen X., et al. Fast Optimal Frictionless Atom Cooling in Harmonic Traps: Shortcut to Adiabaticity. Phys. Rev. Lett., 2010, 104, P. 063002.
12. Demirplak M., Rice S.A. Adiabatic Population Transfer with Control Fields. J. Phys. Chem. A., 2003, 107, P. 9937.
13. Berry M.V. Transitionless quantum driving. Journal of Physics A: Mathematical and Theoretical, 2009, 42, P. 365303.
14. Martınez-Garaot S., et al. Vibrational Mode Multiplexing of Ultracold Atoms. Phys. Rev. Lett., 2013, 111, P. 213001.
15. A. del Campo. Shortcuts to Adiabaticity by Counterdiabatic Driving. Phys. Rev. Lett., 2013, 111, P. 100502.
16. Christopher Jarzynski, Sebastian Deffner, Ayoti Patra, and Yigit Subas¸ı, Fast forward to the classical adiabatic invariant. ˘ Phys. Rev. E, 2017, 95, P. 032122.
17. Widder D. The Heat Equation. Academic Press, 1975.
18. Cannon J.R. The One-Dimensional Heat Equation. Cambridge University Press, 1984.
19. Barbu V. Partial Differential Equations and Boundary Value Problems. Springer, 1998.
20. Kirkwood J. Mathematical Physics with Partial Differential Equations. Academic Press, 2013.
21. X-Sh. Yang. Modelling heat transfer of carbon nanotubes, Modelling Simul. Mater. Sci. Eng., 2005, 13, P. 893.
22. H.-D. Wang, B.-Y. Cao, Z.-Y. Guo. Heat flow choking in carbon nanotubes. Int. J. Heat Mass Transfer, 2010, 53, P. 1796.
23. Dames C., Chen S., Harris C.T. A hot-wire probe for thermal measurements of nanowires and nanotubes inside a transmission electron microscope. Rev. Sci. Instrum., 2007, 78, P. 104903.
24. Bruns D., Nojeh A., Phani A.S., Rottler J. Heat transport in carbon nanotubes: Length dependence of phononic conductivity from the Boltzmann transport equation and molecular dynamics, Phys. Rev. Lett. B, 2020, 101, P. 195408.
Review
For citations:
Matrasulov J., Yusupov J.R., Saidov A.A. Fast forward evolution in heat equation: Tunable heat transport in adiabatic regime. Nanosystems: Physics, Chemistry, Mathematics. 2023;14(4):421-427. https://doi.org/10.17586/2220-8054-2023-14-4-421-427
Views:
0
Email this article 