The generalized Langevin equation revisited: Analytical expressions for the persistence dynamics of a viscous fluid under a time dependent external force

Olivares-Rivas, Wilmer; Colmenares, Pedro J.

doi:10.1016/j.physa.2016.03.112

Cited by 14 publications

(12 citation statements)

References 36 publications

(101 reference statements)

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“…Recently, Lisý and Tóthova [16] did that and showed that in the framework of the generalized Langevin equation (GLE), this extra term in the Hamiltonian modifies the SFD and therefore, the time dependent friction will depend upon this strength. A similar result for a time dependent field was previously found by Olivares and Colmenares [17] . The incorporation of the field strength will require the reformulation of the functional integral approach that is out of scope in this research.…”

Section: Relevant Equations a Solution Of The Qclesupporting

confidence: 90%

Susceptibility of quasiclassical Brownian motion in harmonic nonlinear potentials

Colmenares

2020

Phys. Rev. E

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This work sets the exact equations for the quasiclassical response function and susceptibility of a Brownian particle immersed in a bath of quantum harmonic oscillators driving by nonlinear harmonic potentials. A delta force perturbation gives rise to a response whose susceptibility is the combination of a linear term, own of the harmonic oscillator, plus a nonlinear one involving an integral equation. It is provided a recursion method to find its solutions based on functional equations in the Banach space. The ODE for the response function is a highly nonlinear damped non-autonomous Duffing equation for which the aforementioned method is used to get its solution.

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Section: Relevant Equations a Solution Of The Qclesupporting

confidence: 90%

Susceptibility of quasiclassical Brownian motion in harmonic nonlinear potentials

Colmenares

2020

Phys. Rev. E

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“…A relationship between the susceptibilities is obtained [24,25]. Their explicit dependence on γ and ω 0 is shown in Sec.…”

Section: General Theorymentioning

confidence: 97%

“…In general, position and velocity relax to equilibrium at different rates. The velocity achieves the canonical distribution faster than position [25]. Then, the density p(q, t | q 0 ) given an initial thermal distribution of initial velocity v 0 is found by averaging the solution p(q, t | q 0 , v 0 ) over the Maxwell velocity distribution.…”

Section: General Theorymentioning

confidence: 99%

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Fokker-Planck equation of the reduced Wigner function associated to an Ohmic quantum Langevin dynamics

Colmenares¹

2018

Phys. Rev. E

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This article has to do with the derivation and solution of the Fokker-Planck equation associated to the momentum-integrated Wigner function of a particle subjected to a harmonic external field in contact with an ohmic thermal bath of quantum harmonic oscillators. The strategy employed is a simplified version of the phenomenological approach of Schramm, Jung, and Grabert of interpreting the operators as c numbers to derive the quantum master equation arising from a twofold transformation of the Wigner function of the entire phase space. The statistical properties of the random noise comes from the integral functional theory of Grabert, Schramm, and Ingold. By means of a single Wigner transformation, a simpler equation than that mentioned before is found. The Wigner function reproduces the known results of the classical limit. This allowed us to rewrite the underdamped classical Langevin equation as a first-order stochastic differential equation with time-dependent drift and diffusion terms.

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“…In order to find the expression for P (x, v, t), we resort to the stochastic Liouville equation [21] and Novikov's theorem [22], as described in Ref. [14]:…”

Section: A Dynamicsmentioning

confidence: 99%

Extracting work from a single reservoir in the non-Markovian underdamped regime

2016

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We derive optimal-work finite time protocols for a colloidal particle in a harmonic well in the general non-Markovian underdamped regime in contact with a single reservoir. Optimal work protocols with and without measurements of position and velocity are shown to be linear in time. In order to treat the underdamped regime one must address forcing the particle at the start and at the end of a protocol, conditions which dominate the short time behaviour of the colloidal particle. We find that for protocols without measurement the least work by an external agent decreases linearly for forced start-stop conditions while those only forced at starting conditions are quadratic (slower) at short times, while both decrease asymptotically to zero for quais-static processes. When measurements are performed protocols with start-end forcing are still more efficient at short times but can be overtaken by start-only protocols at a threshold time. Measurement protocols derive work from the reservoir but always below the predicted by the Sagawa's generalization of the second law. Velocity measurement protocols are more efficient in deriving work than position measurements.Published in Phys. Rev. E, 94, 062111 (2016).

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The generalized Langevin equation revisited: Analytical expressions for the persistence dynamics of a viscous fluid under a time dependent external force

Cited by 14 publications

References 36 publications

Susceptibility of quasiclassical Brownian motion in harmonic nonlinear potentials

Susceptibility of quasiclassical Brownian motion in harmonic nonlinear potentials

Fokker-Planck equation of the reduced Wigner function associated to an Ohmic quantum Langevin dynamics

Extracting work from a single reservoir in the non-Markovian underdamped regime

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