Quantum Brownian Motion Revisited

Lampo, Aniello; March, Miguel Ángel García; Lewenstein, Maciej

doi:10.1007/978-3-030-16804-9

Cited by 14 publications

(6 citation statements)

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“…Although the Caldeira–Leggett model has been used extensively for quantum dissipative systems, this method does not ensure that the density operator is positive semidefinite as time evolves. However, it has been shown that master equations of the Lindblad form preserve the positivity of the density operator at all times. , In 1993, Diósi converted the Caldeira–Leggett master equation to the Lindblad form with the addition of two terms. − The modified Caldeira–Leggett equation in the phase space representation takes the form ,,, where D xx = γℏ 2 /(12 mk B T ), D px = γΩℏ 2 /(6π k B T ), and Ω is the cutoff frequency for the harmonic bath. Again, we only include the lowest-order quantum term in the modified Caldeira–Leggett equation.…”

Section: Theoretical Formulationmentioning

confidence: 99%

Moving Boundary Truncated Grid Method: Application to the Time Evolution of Distribution Functions in Phase Space

Lee

Chou

2020

J. Phys. Chem. A

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The moving boundary truncated grid (TG) method, previously developed to integrate the time-dependent Schrödinger equation and the imaginary time Schrödinger equation, is extended to the time evolution of distribution functions in phase space. A variable number of phase space grid points in the Eulerian representation are used to integrate the equation of motion for the distribution function, and the boundaries of the TG are adaptively determined as the distribution function evolves in time. Appropriate grid points are activated and deactivated for propagation of the distribution function, and no advance information concerning the dynamics in phase space is required. The TG method is used to integrate the equations of motion for phase space distribution functions, including the Klein–Kramers, Wigner–Moyal, and modified Caldeira–Leggett equations. Even though the initial distribution function is nonnegative, the solutions to the Wigner–Moyal and modified Caldeira–Leggett equations may develop negative basins in phase space originating from interference effects. Trajectory-based methods for propagation of the distribution function do not permit the formation of negative regions. However, the TG method can correctly capture the negative basins. Comparisons between the computational results obtained from the full grid and TG calculations demonstrate that the TG method not only significantly reduces the computational effort but also permits accurate propagation of various distribution functions in phase space.

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Section: Theoretical Formulationmentioning

confidence: 99%

Moving Boundary Truncated Grid Method: Application to the Time Evolution of Distribution Functions in Phase Space

Lee

Chou

2020

J. Phys. Chem. A

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“…Rubber molecules have a backbone of many covalent bonds which can rotate rapidly because of thermal agitation. Such long molecules convert their form easily at specific temperatures due to Brownian motion 12 , 13 . When no force is applied, they make random conformations but may adopt specific conformations if an external force is loaded.…”

Section: Introductionmentioning

confidence: 99%

Current challenges in thermodynamic aspects of rubber foam

Suethao

Ponloa

Phongphanphanee

et al. 2021

Sci Rep

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Natural rubber (NR) foam can be prepared by the Dunlop method using concentrated natural latex with chemical agents. Most previous studies have focused on the thermodynamic parameters of solid rubber in extension. The main objective of this study is to investigate the effect of the NR matrix concentration on the static and dynamic properties of NR foams, especially the new approach of considering the thermodynamic aspects of NR foam in compression. We found that the density and compression strength of NR foams increased with increasing NR matrix concentration. The mechanical properties of NR foam were in agreement with computational modelling. Moreover, thermodynamic aspects showed that the ratio of internal energy force to the compression force, Fu/F, and the entropy, S, increased with increasing matrix concentration. The activation enthalpy, ∆Ha, also increased with increasing matrix concentration in the NR foam, indicating the greater relaxation time of the backbone of the rubber molecules. New scientific concepts of thermodynamic parameters of the crosslinked NR foam in compression mode are proposed and discussed. Our results will improve both the knowledge and the development of rubber foams based on the structure–properties relationship, especially the new scientific concept of the thermodynamical parameters under compression.

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“…The relation between the MSD and the time interval of the so called ultraslow Brownian motions is x 2 t ∼ (ln t) γ [32]. There are different approaches to build a quantum analog of the Brownian motion [33][34][35][36]. For examples, the method of the path integral is used to study the quantum Brownian motion [35].…”

Section: Introductionmentioning

confidence: 99%

The Brownian Motion in an Ideal Quantum Qas

Zhou,

Zhang,

Dai

2020

Preprint

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A Brownian particle in an ideal quantum gas is considered. The mean square displacement (MSD) is derived. The Bose-Einstein or Fermi-Dirac distribution, other than the Maxwell-Boltzmann distribution, provides a different stochastic force compared with the classical Brownian motion. The MSD, which depends on the thermal wavelength and the density of medium particles, reflects the quantum effect on the Brownian particle explicitly. The result shows that the MSD in an ideal Bose gas is shorter than that in a Fermi gas. The behavior of the quantum Brownian particle recovers the classical Brownian particle as the temperature raises. At low temperatures, the quantum effect becomes obvious. For example, there is a random motion of the Brownian particle due to the fermionic exchange interaction even the temperature is near the absolute zero.

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Quantum Brownian Motion Revisited

Cited by 14 publications

References 0 publications

Moving Boundary Truncated Grid Method: Application to the Time Evolution of Distribution Functions in Phase Space

Moving Boundary Truncated Grid Method: Application to the Time Evolution of Distribution Functions in Phase Space

Current challenges in thermodynamic aspects of rubber foam

The Brownian Motion in an Ideal Quantum Qas

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