Document Type : Original Article
Authors
1 Department of Physics, Najafabad Branch, Islamic Azad University, Najafabad, Iran
2 Department of Mathematics, Najafabad Branch, Islamic Azad University, Najafabad, Iran
Abstract
The quantum theory of a damped harmonic oscillator has been continuously studied since 1939. For quantization, an oscillation oscillator usually uses a reservoir that includes a number of finite and discrete oscillators. However, a set of discrete oscillators is unable to study the quantum theory of an Ohmic damping (damping proportional to velocity). In this research, a continuous set of harmonic oscillators has been used to investigate Ohmic damping. Using a continuum reservoir instead of a discrete reservoir will enrich the results of the dynamic system. The results of this research can be used to study nano-mechanical systems and opto-mechanical systems.
Keywords
- H Dekker, Rep. 80 (1981)1.
- C I Um, K H Yeon, and T F George, Rep. 362 (2002) 63.
- U Weiss, “Quantum Dissipative Systems”, Singapore World Scientific (2008).
- H Bateman, Rev. 38 (1931) 815.
- M Blasone and P Jizba, J. Phys. 80 (2002) 645.
- M Blasone and P Jizba, Phys. 312 (2004) 354.
- D C Latimer, Phys. A: Math. Gen. 38 (2005) 2021.
- M C Baldiotti, R Fresneda, and D M Gitman, Lett. A 375 (2011) 1630.
- H Majima and A Suzuki, Phys. 326 (2011) 3000.
- E Celeghini, M Rasetti, and G Vitiello, Phys. 215 (1992) 156.
- V B Magalinskii, Phys. JETP 9 (1959) 1381.
- J Tuziemski and J K Korbicz, EPL(Europhys. Lett.) 112 (2015) 40008.
- D Boyanovsky and D Jasnow, Rev. A 96 (2017) 062108.
- L Ferialdi and A Smirne, Rev. A 96 (2017) 012109.
- M Carlesso and A Bassi, Rev. A 95 (2017) 052119.
- H Z Shen, et al., Phys. Rev. A 97 (2018) 042121.
- S H Lim, et al., Stat. Phys. 170 (2018) 351.
- P Bialas, J Spiechowicz, and J Łuczka, arXiv preprint at arXiv:1805. 04012 (2018).
- P Bialas and J Łuczka, Entropy 20 (2018) 123.
- G W Ford, Phys. 58 (2017) 244.
- D Shinichi, and F Yuki, Rev. A 101 (2020) 022105.
- K Fardin, Phys. J. Plus 135 (2020) 243.
- V P Tatarskii, Phys. Usp. 30 (1987) 134.
- H Grabert, U Weiss, and P Talkner, Phys. B: Condens. Matter 55 (1984) 87.
- B Huttner and S M Barnett, Rev. A 46 (1992) 4306.
- T G Philbin, New J. Phys. 12 (2010)
- T G Philbin, New J. Phys. 13 (2011)
- S A R Horsley, Rev. A 84 (2011) 063822.
- S A R Horsley, arXiv:1205.0486 (2012)
- A D O’Connell et al., Nature 464 (2010)
- J D Teufel et al., Nature 475 (2011)
- J Chan, et al., Nature 478 (2011) 89.
- M Aspelmeyer, et al., Opt. Soc. Am. B 27 (2010) 189.
- M Poot and H S J Zant, Rep. 511(2012) 273.
- A C Pipkin, “A Course on Integral Equations”, New York Springer (1991).
- N I Muskhelishvili, “Singular Integral Equations”, New York Dover (2008).
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