Diffusion in the time-dependent double-well potential

Šubrt, Evžen; Chvosta, Petr

doi:10.1007/s10582-006-0074-x

Cited by 3 publications

(3 citation statements)

References 16 publications

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“…the Fokker-Planck equation or the Pauli master equation, must reflect the time dependence of the external parameters. Typically, then, one has to solve the diffusion equation including a timedependent potential [5]- [7], or the Pauli equation with the time-dependent transition rates [7]- [9]. But even the explicit solution of the evolution equation does not suit our purpose.…”

Section: Introductionmentioning

confidence: 99%

Exact analysis of work fluctuations in two-level systems

Šubrt

Chvosta

2007

J. Stat. Mech.

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This paper presents an exact probabilistic description of the work done by an external agent on a two-level system. We first develop a general scheme which is suitable for the treatment of functionals of the time-inhomogeneous Markov processes. Subsequently, we apply the procedure to the analysis of the isothermal-work probability density and we obtain its exact analytical forms in two specific settings. In both models, the state energies change with a constant velocity. On the other hand, the two models differ in their interstate transition rates. The explicit forms of the probability density allow a detailed discussion of the mean work. Moreover, we discuss the weight of the trajectories which display a smaller value of work than the corresponding equilibrium work. The results are controlled by a single dimensionless parameter which expresses the ratio of two underlying timescales: the velocity of the energy changes and the relaxation time in the case of frozen energies. If this parameter is large, the process is a strongly irreversible one and the work probability density differs substantially from a Gaussian curve.

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Section: Introductionmentioning

confidence: 99%

Exact analysis of work fluctuations in two-level systems

Šubrt

Chvosta

2007

J. Stat. Mech.

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“…[85][86][87] ), and may furthermore be relevant for a theoretical description of transport in ion-channels [88][89][90][91] . Our results can be extended in diverse ways, most immediately by including other types of interparticle interactions 92 and time-depended energy barriers 93 .…”

Section: Discussionmentioning

confidence: 94%

Single-file diffusion in a bi-stable potential: signatures of memory in the barrier-crossing of a tagged-particle

Lapolla,

Godec

2020

Preprint

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We investigate memory effects in barrier-crossing in the overdamped setting. We focus on the scenario where the hidden degrees of freedom relax on exactly the same time scale as the observable. As a prototypical model we analyze taggedparticle diffusion in a single-file confined to a bi-stable potential. We identify the signatures of memory and explain their origin. The emerging memory is a result of the projection of collective many-body eigenmodes onto the motion of a tagged-particle. We are interested in the 'confining' (all background particles in front of the tagged-particle) and 'pushing' (all background particles behind the tagged-particle) scenarios for which we find non-trivial and qualitatively different relaxation behavior. Notably and somewhat unexpectedly, at fixed particle number we find that the higher the barrier the more prominent are the signatures of memory. Our results can readily be tested experimentally and may be relevant for understanding transport in biological ion-channels.

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“…[103][104][105][106] Our results can be extended in diverse ways, most immediately by including other types of inter-particle interactions 81 and time-dependent energy barriers. 107…”

Section: Article Scitationorg/journal/jcpmentioning

confidence: 99%

Single-file diffusion in a bi-stable potential: Signatures of memory in the barrier-crossing of a tagged-particle

Lapolla

Godec

2020

The Journal of Chemical Physics

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We investigate memory effects in barrier-crossing in the overdamped setting. We focus on the scenario where the hidden degrees of freedom relax on exactly the same time scale as the observable. As a prototypical model, we analyze tagged-particle diffusion in a single file confined to a bi-stable potential. We identify the signatures of memory and explain their origin. The emerging memory is a result of the projection of collective many-body eigenmodes onto the motion of a tagged-particle. We are interested in the "confining" (all background particles in front of the tagged-particle) and "pushing" (all background particles behind the tagged-particle) scenarios for which we find non-trivial and qualitatively different relaxation behaviors. Notably and somewhat unexpectedly, at a fixed particle number, we find that the higher the barrier, the stronger the memory effects are. The fact that the external potential alters the memory is important more generally and should be taken into account in applications of generalized Langevin equations. Our results can readily be tested experimentally and may be relevant for understanding transport in biological ion-channels.

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Diffusion in the time-dependent double-well potential

Cited by 3 publications

References 16 publications

Exact analysis of work fluctuations in two-level systems

Exact analysis of work fluctuations in two-level systems

Single-file diffusion in a bi-stable potential: signatures of memory in the barrier-crossing of a tagged-particle

Single-file diffusion in a bi-stable potential: Signatures of memory in the barrier-crossing of a tagged-particle

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