Dimensionless Universal Parameters of the Kramers Problem

Gontchar, I. I.; Chushnyakova, M. V.; Блесман, А. И.

doi:10.1088/1742-6596/1210/1/012052

Cited by 7 publications

(5 citation statements)

References 13 publications

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“…In the present work, the number of modeled trajectories and 𝑡 𝐷 are chosen to obtain the value of 𝑅 𝐷 with the relative error not exceeding 2%. The computer code used in the present work was verified numerously [7,10,12].…”

Section: Numerical Modelmentioning

confidence: 93%

“…As in the case of the barrier composed by two smoothly joined parabolas (harmonic barrier) [10], this rate (measured in units of 𝜔 𝑐 = 2𝜋 𝜏 𝑐 ⁄ ) depends only upon the dimensionless scaling parameters 𝜑 and 𝐺 (see Eqs. ( 1) and (2) for the definitions of these parameters).…”

Section: Approximate Kramers Ratesmentioning

confidence: 99%

“…The decay rate is the main characteristic of this process. We operate with two dimensionless parameters [10] defining mostly the value of the rate: a governing parameter 𝐺 and a damping parameter 𝜑:…”

Section: Introductionmentioning

confidence: 99%

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Two ways for numerical solution of the Kramers problem for spatial diffusion over an edge-shaped barrier

Chushnyakova

Gontchar

Захаров

et al. 2020

J. Phys.: Conf. Ser.

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Thermal decay rate over an edge-shaped barrier at high dissipation is studied numerically through the computer modeling. Two sorts of the stochastic Langevin type equations are applied: (i) the Langevin equations for the coordinate and conjugate momentum (LEqp, the phase space diffusion) and (ii) the reduced Langevin equation (RLE, the spatial diffusion, overdamped motion). The latter method is much faster and self-similar; however, one can doubt about its applicability in the case of an edge-shaped barrier with a discontinuous force. The reason is that a formal condition of the applicability of the RLE is not fulfilled since the curvature of the potential profile at the barrier is equal to infinity. The present numerical study demonstrates that, for large friction, the decay rate calculated using the RLE agrees with the rate resulting from the more exact LEqp. Moreover, it turns out that the influence of the position of the absorbing border is similar to the case of harmonic potential known in the literature.

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Section: Numerical Modelmentioning

confidence: 93%

Section: Approximate Kramers Ratesmentioning

confidence: 99%

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Two ways for numerical solution of the Kramers problem for spatial diffusion over an edge-shaped barrier

Chushnyakova

Gontchar

Захаров

et al. 2020

J. Phys.: Conf. Ser.

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“…As in the case of the two parabolas barrier, this rate (measured in units of −1 ) depends only upon the dimensionless scaling parameters and [14].…”

Section: Modelmentioning

confidence: 98%

“…Thus, the problem is often referred to as the Kramers problem [12,13]. In [14] it was shown that the decay rate depends mostly upon two dimensionless parameters, namely a governing parameter and damping parameter . The definitions of these parameters read = ,…”

Section: Introductionmentioning

confidence: 99%

Accuracy of the analytical escape rate for a cusp barrier in the overdamping regime

Захаров

Chushnyakova

Gontchar

2020

J. Phys.: Conf. Ser.

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For the first time, the accuracy of the approximate analytical Kramers formula for the thermal decay rate over a cusp barrier, , is checked numerically for the overdamping regime. The numerical quasistationary rate, , which is believed to be exact within the statistical errors is evaluated by means of computer modeling of the stochastic Langevin-type dynamical equations. The agreement between and significantly depends upon the friction strength and the height of the barrier in comparison to the thermal energy. The difference between and decreases with the dimensionless damping parameter , however, does not become smaller than 10-20%. The unexpected growth of the difference between and with the governing parameter is observed.

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Activated decay of a metastable state: transient times for small and large dissipation

2021

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Dimensionless Universal Parameters of the Kramers Problem

Cited by 7 publications

References 13 publications

Two ways for numerical solution of the Kramers problem for spatial diffusion over an edge-shaped barrier

Two ways for numerical solution of the Kramers problem for spatial diffusion over an edge-shaped barrier

Accuracy of the analytical escape rate for a cusp barrier in the overdamping regime

Activated decay of a metastable state: transient times for small and large dissipation

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