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Langevin equation for a dissipative macroscopic quantum system: Bohmian theory versus quantum mechanics

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Abstract

In this study, we solve analytically the Schrödinger equation for a macroscopic quantum oscillator as a central system coupled to a large number of environmental micro-oscillating particles. Then, the Langevin equation is obtained for the system using two approaches: Quantum Mechanics and Bohmian Theory. Our results show that the predictions of the two theories are inherently different in real conditions. Nevertheless, the Langevin equation obtained by Bohmian approach could be reduced to the quantum one, when the vibrational frequency of the central system is high enough compared to the frequency of the environmental particles.

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Authors and Affiliations

  1. Research Group on Foundations of Quantum Theory and Information, Department of Chemistry, Sharif University of Technology, P.O.Box 11365-9516, Tehran, Iran

    Hamid Reza Naeij & Afshin Shafiee

  2. School of Physics, Institute for Research in Fundamental Sciences (IPM), P.O.Box 19395-5531, Tehran, Iran

    Afshin Shafiee

Authors
  1. Hamid Reza Naeij
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  2. Afshin Shafiee
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Correspondence to Afshin Shafiee.

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Naeij, H.R., Shafiee, A. Langevin equation for a dissipative macroscopic quantum system: Bohmian theory versus quantum mechanics. Quantum Stud.: Math. Found. 7, 5–15 (2020). https://doi.org/10.1007/s40509-019-00195-5

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