Energetics of a driven Brownian harmonic oscillator

Yaghoubi, Mohammad; Foulaadvand, M. Ebrahim; Bérut, Antoine; Łuczka, J.

doi:10.1088/1742-5468/aa9346

Cited by 13 publications

(6 citation statements)

References 46 publications

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“…1, and T is the base temperature of the setup. The position of the mirror can thus be treated as a classical degree of freedom, whose dynamics is governed by the Langevin equation [27,44]…”

mentioning

confidence: 99%

Nonequilibrium Many-Body Quantum Engine Driven by Time-Translation Symmetry Breaking

2020

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Quantum many-body systems out of equilibrium can host intriguing phenomena such as transitions to exotic dynamical states. Although this emergent behaviour can be observed in experiments, its potential for technological applications is largely unexplored. Here, we investigate the impact of collective effects on quantum engines that extract mechanical work from a many-body system. Using an opto-mechanical cavity setup with an interacting atomic gas as a working fluid, we demonstrate theoretically that such engines produce work under periodic driving. The stationary cycle of the working fluid features nonequilibrium phase transitions, resulting in abrupt changes of the work output. Remarkably, we find that our many-body quantum engine operates even without periodic driving. This phenomenon occurs when its working fluid enters a phase that breaks continuous time-translation symmetry: the emergent time-crystalline phase can sustain the motion of a load generating mechanical work. Our findings pave the way for designing novel nonequilibrium quantum machines.

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“…1, and T is the base temperature of the setup. The position of the mirror can thus be treated as a classical degree of freedom, whose dynamics is governed by the Langevin equation [27,44]…”

mentioning

confidence: 99%

Nonequilibrium Many-Body Quantum Engine Driven by Time-Translation Symmetry Breaking

2020

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“…2 one can see that for all considered potential wells with the Gaussian white noise driving the average total energy E(t) exhibits the same time dependence. Using Itô lemma [26] it is possible to confirm this observation in an analogous way to the damped harmonic oscillator [29]. Using the definition of the potential energy E p = k 2 x 2 one gets…”

Section: Gaussian White Noisementioning

confidence: 61%

“…( 13). The kinetic energy E k = 1 2 mv 2 requires different treatment [29], because the velocity v(t) fulfills the stochastic differential equation (12). Therefore, it is necessary to use the Itô lemma…”

Section: Gaussian White Noisementioning

confidence: 99%

Energetics of single-well undamped stochastic oscillators

Mandrysz

Dybiec

2019

Phys. Rev. E

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The paper discusses analytical and numerical results for non-harmonic, undamped, single-well, stochastic oscillators driven by additive noises. It focuses on average kinetic, potential and total energies together with the corresponding distributions under random drivings, involving Gaussian white, Ornstein-Uhlenbeck and Markovian dichotomous noises. It demonstrates that insensitivity of the average total energy to the single-well potential type, V (x) ∝ x 2n , under Gaussian white noise does not extend to other noise types. Nevertheless, in the longtime limit (t → ∞), the average energies grow as power-law with exponents dependent on the steepness of the potential n. Another special limit corresponds to n → ∞, i.e. to the infinite rectangular potential well, when the average total energy grows as a power-law with the same exponent for all considered noise types.

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“…Lemons' results are the same as those reported by Chandrasekhar. As well, an important amount of research and academic works related to HOBM has been reported in the literature [17][18][19][20][21][22][23]. Other interesting and recent publications of experimental academic works have been reported; for super paramagnetic colloids [24] and a repetition of Perrin's experiments [26].…”

Section: Introducctionmentioning

confidence: 96%

Harmonic oscillator Brownian motion: Langevin approach revisited

et al. 2021

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The original strategy applied by Langevin to Brownian movement problem is used to solve the case of a free particle under a harmonic potential. Such straightforward strategy consists in separating the noise termin the Langevin equation in order to solve a deterministic equation associated with the Mean Square Displacement (MSD). In this work, to achieve our goal we first calculate the variance for the stochastic harmonic oscillator and then the MSD appears immediately. We study the problem in the damped and lightly damped cases and show that, for times greater than the relaxation time, Langevin's original strategy is quite consistent with the exact theoretical solutions reported by Chandrasekhar and Lemons, these latter obtained using the statistical properties of a Gaussian white noise. Our results for the MSDs are compared with the exact theoretical solutions as well as with the numerical simulation.

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Energetics of a driven Brownian harmonic oscillator

Cited by 13 publications

References 46 publications

Nonequilibrium Many-Body Quantum Engine Driven by Time-Translation Symmetry Breaking

Nonequilibrium Many-Body Quantum Engine Driven by Time-Translation Symmetry Breaking

Energetics of single-well undamped stochastic oscillators

Harmonic oscillator Brownian motion: Langevin approach revisited

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