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Updated: Jun 22, 2026

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
Published on: December 4, 2017
Nonperturbative approach to quantum Brownian motion
1Indian Institute of Science Education and Research Kolkata, Mohanpur Campus, Mohanpur, 741252, India.
Abstract:
Starting from the Caldeira-Leggett model, we derive the equation describing the quantum Brownian motion, which has been originally proposed by Dekker purely from phenomenological basis containing extra anomalous diffusion terms. This nonperturbative approach yields explicit analytical expressions for the temperature dependence of the diffusion constants. At high temperatures, additional momentum diffusion terms are suppressed and classical Langevin equation can be recovered and at the same time positivity of the density matrix is satisfied. At low temperatures, the diffusion constants have a finite positive value. However, below a certain critical temperature, the master equation does not satisfy the positivity condition as proposed by Dekker.
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