Quantum theory of friction

Barnett, Stephen M.; Cresser, J. D.

doi:10.1103/physreva.72.022107

Cited by 29 publications

(56 citation statements)

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“…Lindblad master equations have been extensively used to describe phenomena in e.g. quantum optics, semiconductor physics and atomic physics, ranging from the decay of an atom to a quantum-mechanical description of Brownian motion [3][4][5].…”

Section: Introductionmentioning

confidence: 99%

Canonical form of master equations and characterization of non-Markovianity

et al. 2014

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Master equations govern the time evolution of a quantum system interacting with an environment, and may be written in a variety of forms. Time-independent or memoryless master equations, in particular, can be cast in the well-known Lindblad form. Any time-local master equation, Markovian or non-Markovian, may in fact also be written in a Lindblad-like form. A diagonalisation procedure results in a unique, and in this sense canonical, representation of the equation, which may be used to fully characterize the non-Markovianity of the time evolution. Recently, several different measures of non-Markovianity have been presented which reflect, to varying degrees, the appearance of negative decoherence rates in the Lindblad-like form of the master equation. We therefore propose using the negative decoherence rates themselves, as they appear in the canonical form of the master equation, to completely characterize non-Markovianity. The advantages of this are especially apparent when more than one decoherence channel is present. We show that a measure proposed by Rivas et al. is a surprisingly simple function of the canonical decoherence rates, and give an example of a master equation that is non-Markovian for all times t > 0, but to which nearly all proposed measures are blind. We also give necessary and sufficient conditions for trace distance and volume measures to witness non-Markovianity, in terms of the Bloch damping matrix.

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Section: Introductionmentioning

confidence: 99%

Canonical form of master equations and characterization of non-Markovianity

et al. 2014

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“…Important contributions to QLBEs have been made in [9][10][11][12] and can be reviewed in [6]. Mostly, the analysis is based on using scattering theory to describe the effects of a single collision with a gas particle which is assumed to be in a momentum eigenstate.…”

Section: Introductionmentioning

confidence: 99%

Quantum position diffusion and its implications for the quantum linear Boltzmann equation

Kamleitner

Cresser

2010

Phys. Rev. A

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“…From this perspective, it seems necessary for the environment to measure, and hence interact with, both the momentum and the position of the particle. This approach was taken by Barnett and Cresser, who developed the Lindblad master equation associated with simulatenous measurement of both these observables [49]. Note that they maintain the classical assumption of elastic, momentum-exchange collisions.…”

Section: Brownian Motionmentioning

confidence: 99%

“…Equation 13 can be "extended" to conform to Lindblad's form by the addition of a spatial diffusion term, −D qq [p, [p, ρ]], which will complete the form if D qq D pp ≥ γ 2 /16 [26,49]. This reveals a quantum effect-friction, momentum diffusion and spatial diffusion are all connected, there cannot be one without the other.…”

Section: Brownian Motionmentioning

confidence: 99%

Reflections on Friction in Quantum Mechanics

Rezek

2010

Entropy

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Distinctly quantum friction effects of three types are surveyed: internal friction, measurement-induced friction, and quantum-fluctuation-induced friction. We demonstrate that external driving will lead to quantum internal friction, and critique the measurement-based interpretation of friction. We conclude that in general systems will experience internal and external quantum friction over and beyond the classical frictional contributions. Keywords: quantum friction; dissipation; open systemClassification: PACS 03. 05.70.Ln Friction is the price for moving too fast. An attempt to induce a rapid change in the state of a system would be accompanied by additional entropy generation and will be encumbered by energy costs. As an example of friction we can consider a body moving rapidly against a stationary background. Its kinetic energy is dissipated, generating heat and entropy in the environment. The amount of dissipation is proportional to the velocity. Another archtypical case of friction is a driven gas compression process. For a system that is thermally decoupled from its environment, rapid changes in the piston position that compresses the gas will result in internal heating of the gas and entropy generation. To restore the system to its slow quasi-static compression equivalent, heat has to be removed from the gas. This additional heat is equivalent to extra work against friction.Friction is typically modeled by a phenomenological theory within classical mechanics. How does it extend to the quantum domain? Can a first principles model of friction be developed? There are ample examples of quantum frictional phenomena. These include friction observed in micro-mechanical systems at low temperatures [1], in superfluid theory [2], and even in quantum cosmology [3] and more. Are such quantum examples of friction essentially classical phenomena that endure into the quantum

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Quantum theory of friction

Cited by 29 publications

References 40 publications

Canonical form of master equations and characterization of non-Markovianity

Canonical form of master equations and characterization of non-Markovianity

Quantum position diffusion and its implications for the quantum linear Boltzmann equation

Reflections on Friction in Quantum Mechanics

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