Igor Goychuk - Academia.edu (original) (raw)
Papers by Igor Goychuk
<p>(a) Effective anomalous transport exponent and (b) thermodynamic efficiency while workin... more <p>(a) Effective anomalous transport exponent and (b) thermodynamic efficiency while working against a constant force near the end point of the simulations ( sec or in dimensionless units). The thermodynamic efficiency decays over time as . The analysis considers the same particles as in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0091700#pone-0091700-g002" target="_blank">Figure 2</a>, but here the potential height is reduced by factor of . Ensemble averaging is performed over particles and random realizations of potential flashes. The inset in (a) shows the dependence of on the mean enzyme turnover frequency for .</p
<p>Single motor transport (full line) is almost perfectly locked to the potential fluctuati... more <p>Single motor transport (full line) is almost perfectly locked to the potential fluctuations (broken red line depicting a renewal process counting the number of potential fluctuations in units of ) occurring with mean turnover frequency Hz, in a potential (top inset) with amplitudes eV ( in dimensionless units) and eV ( eV), for nm. A particle with an effective radius nm (like a magnetic endosome <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0091700#pone.0091700-Robert1" target="_blank">[33]</a>) experiences asymptotically for sec an effective viscous friction enhanced by a factor of with respect to water. The bottom inset shows that on the relevant transient time scale the free particle subdiffuses with anomalous diffusion coefficient . Initially, diffusion is normal. The time-average over a single trajectory, , is shown for sec and compared with the theoretical subdiffusive ensemble-averaged result (red line). See <b>Methods</b>.</p
New Journal of Physics, Apr 1, 2022
We describe the phenomenon of a resonance-like, giant enhancement of diffusion in a basic model o... more We describe the phenomenon of a resonance-like, giant enhancement of diffusion in a basic model of nonlinear diffusion featured by a nonlinear in velocity friction and the corresponding multiplicative thermal noise. The model is consistent with thermal equilibrium in the absence of driving. Different from previous studies of this phenomenon, where the crucial nonlinearity originates from a periodic external potential while friction is linear, we focus on the case of a constant force driving, whereas the crucial nonlinearity stems from the friction. The basic model of such friction considered interpolates between linear viscous Stokes friction at small velocities and dry Coulomb-like friction at large velocities corresponding to a stress plateau in some nonlinear viscoelastic materials. Recently, a nonequilibrium phase transition to super-diffusion and super-transport was discovered within this basic model. We show that adding a tiny viscous friction part to major nonlinear friction regularizes in part this behavior. Diffusion becomes asymptotically normal. However, the phase transition translates into a giant enhancement of normal diffusion and mobility of particles at the transition point over the intuitively expected large force limit, where the linearization of friction occurs. Such a giant enhancement of diffusion is closely related to the largely enhanced kinetic temperature of the particles at and beyond the critical point. We provide analytical results obtained within an effective mass approximation which nicely agree with stochastic numerics.
Proceedings of the National Academy of Sciences of the United States of America, Nov 22, 2022
We investigate analytically and numerically a basic model of driven Brownian motion with a veloci... more We investigate analytically and numerically a basic model of driven Brownian motion with a velocity-dependent friction coefficient in nonlinear viscoelastic media featured by a stress plateau at intermediate shear velocities and profound memory effects. For constant force driving, we show that nonlinear oscillations of a microparticle velocity and position emerge by a Hopf bifurcation at a small critical force (first dynamical phase transition), where the friction’s nonlinearity seems to be wholly negligible. They also disappear by a second Hopf bifurcation at a much larger force value (second dynamical phase transition). The bifurcation diagram is found in an analytical form confirmed by numerics. Surprisingly, the particles’ inertial and the medium’s nonlinear properties remain crucial even in a parameter regime where they were earlier considered entirely negligible. Depending on the force and other parameters, the amplitude of oscillations can significantly exceed the size of the particles, and their period can span several time decades, primarily determined by the memory time of the medium. Such oscillations can also be thermally excited near the edges of dynamical phase transitions. The second dynamical phase transition combined with thermally induced stochastic limit cycle oscillations leads to a giant enhancement of diffusion over the limit of vast driving forces, where an effective linearization of stochastic dynamics occurs.
APS, Mar 20, 2003
The phenomenological linear response theory of non-Markovian stochastic resonance (SR) is put for... more The phenomenological linear response theory of non-Markovian stochastic resonance (SR) is put forward for stationary two-state renewal processes. In terms of a derivation of a non-Markov regression theorem we evaluate the characteristic SR-quantifiers; i.e., the spectral power amplification (SPA) and the signal-to-noise ratio (SNR), respectively. In clear contrast to Markovian-SR, a characteristic benchmark of genuine non-Markovian SR is its distinctive dependence of the SPA and SNR on small (adiabatic) driving frequencies; particularly, the adiabatic SNR becomes strongly suppressed over its Markovian counterpart. This non-Markovian SR-theory is elucidated for a fractal gating dynamics of a potassium ion channel possessing an infinite variance of closed sojourn times.
arXiv (Cornell University), Oct 22, 1999
In the regime of weak bath coupling and low temperature we demonstrate numerically for the spin-b... more In the regime of weak bath coupling and low temperature we demonstrate numerically for the spin-boson dynamics the equivalence between two widely used but seemingly different roads of approximation, namely the path integral approach and the Bloch-Redfield theory. The excellent agreement between these two methods is corroborated by a novel efficient analytical high-frequency approach: it well approximates the decay of quantum coherence via a series of damped coherent oscillations. Moreover, a suitably tuned control field can selectively enhance or suppress quantum coherence.
![Research paper thumbnail of Comment on "Large Fluctuations for Spatial Diffusion of Cold Atoms" [arXiv:1701.03357]](https://attachments.academia-assets.com/108716088/thumbnails/1.jpg)
](arXiv (Cornell University), Aug 14, 2017
An important criterion on finite kinetic temperature of the system of cold atoms is established. ... more An important criterion on finite kinetic temperature of the system of cold atoms is established. It is shown that the kinetic temperature becomes infinite in Fig. 1 of the commented paper in the course of time, i.e. the considered model system becomes asymptotically infinitely hot. Moreover, within this model the behavior of the squared width of the spatial distribution of atoms at the half of its maximum is very different from the variance of the particle positions. In particular, in the discussed Fig. 1 the former one increases sub-ballistically in time, while the variance grows super-ballistically, which corresponds to a heating phase. This leads to a profound ambiguity in definition and classification of anomalous diffusion. All in all, the model in the commented paper simply does not fit to experiments with cold atoms.
Bulletin of the American Physical Society, Mar 8, 2018
Viscoelastic subdiffusion governed by a fractional Langevin equation is studied numerically in a ... more Viscoelastic subdiffusion governed by a fractional Langevin equation is studied numerically in a random Gaussian environment modeled by stationary Gaussian potentials with decaying spatial correlations. This anomalous diffusion is archetypal for living cells, where cytoplasm is known to be viscoelastic and a spatial disorder also naturally emerges. We obtain some first important insights into it within a model one-dimensional study. Two basic types of potential correlations are studied: short-range exponentially decaying and algebraically slow decaying with an infinite correlation length, both for a moderate (several kBT , in the units of thermal energy), and strong (5-10 kBT) disorder. For a moderate disorder, it is shown that on the ensemble level viscoelastic subdiffusion can easily overcome the medium's disorder. Asymptotically, it is not distinguishable from the disorder-free subdiffusion. However, a strong scatter in single-trajectory averages is nevertheless seen even for a moderate disorder. It features a weak ergodicity breaking, which occurs on a very long yet transient time scale. Furthermore, for a strong disorder, a very long transient regime of logarithmic, Sinai-type diffusion emerges. It can last longer and be faster in the absolute terms for weakly decaying correlations as compare with the short-range correlations. Residence time distributions in a finite spatial domain are of a generalized log-normal type and are reminiscent also of a stretched exponential distribution. They can be easily confused for power-law distributions in view of the observed weak ergodicity breaking. This suggests a revision of some experimental data and their interpretation.
Physical Review Letters, 2019
We consider a two-state model of non-Markovian stochastic resonance (SR) within the framework of ... more We consider a two-state model of non-Markovian stochastic resonance (SR) within the framework of the theory of renewal processes. Residence time intervals are assumed to be mutually independent and characterized by some arbitrary non-exponential residence time distributions which are modulated in time by an externally applied signal. Making use of a stochastic path integral approach we obtain general integral equations governing the evolution of conditional probabilities in the presence of an input signal. These novel equations generalize earlier integral renewal equations by Cox and others to the case of driving-induced non-stationarity. On the basis of these new equations a response theory of two state renewal processes is formulated beyond the linear response approximation. Moreover, a general expression for the linear response function is derived. The connection of the developed approach with the phenomenological theory of linear response for manifest non-Markovian SR put forward in [ I. Goychuk and P. Hänggi, Phys. Rev. Lett. 91, 070601 (2003)] is clarified and its range of validity is scrutinized. The novel theory is then applied to SR in symmetric non-Markovian systems and to the class of single ion channels possessing a fractal kinetics.
Physical Review E
Hydrodynamic memory force or Basset force has been known since the 19th century. Its influence on... more Hydrodynamic memory force or Basset force has been known since the 19th century. Its influence on Brownian motion remains, however, mostly unexplored. Here we investigate its role in nonlinear transport and diffusion within a paradigmatic model of tilted washboard potential. In this model, a giant enhancement of driven diffusion over its potential-free limit [Phys. Rev. Lett. 87, 010602 (2001)] presents a well-established paradoxical phenomenon. In the overdamped limit, it occurs at a critical tilt of vanishing potential barriers. However, for weak damping, it takes place surprisingly at another critical tilt, where the potential barriers are clearly expressed. Recently we showed [Phys. Rev. Lett. 123, 180603 (2019)] that Basset force could make such a diffusion enhancement enormously large. In this paper, we discover that even for moderately strong damping, where the overdamped theory works very well when the memory effects are negligible, substantial hydrodynamic memory unexpectedly makes a strong impact. First, the diffusion boost occurs at nonvanishing potential barriers and can be orders of magnitude larger. Second, transient anomalous diffusion regimes emerge over many time decades and potential periods. Third, particles' mobility can also be dramatically enhanced, and a long transient supertransport regime emerges.
Physical review letters, 2021
We investigate a basic model of nonlinear Brownian motion in a thermal environment, where nonline... more We investigate a basic model of nonlinear Brownian motion in a thermal environment, where nonlinear friction interpolates between viscous Stokes and dry Coulomb friction. We show that superdiffusion and supertransport emerge as a nonequilibrium critical phenomenon when such a Brownian motion is driven out of thermal equilibrium by a constant force. Precisely at the edge of a phase transition, velocity fluctuations diverge asymptotically and diffusion becomes superballistic. The autocorrelation function of velocity fluctuations in this nonergodic regime exhibits a striking aging behavior.
arXiv: Mesoscale and Nanoscale Physics, 2015
Does electron transfer (ET) kinetics within a single-electron trajectory description always coinc... more Does electron transfer (ET) kinetics within a single-electron trajectory description always coincide with the ensemble description? This fundamental question of ergodic behavior is scrutinized within a very basic semi-classical curve-crossing problem of quantum Landau-Zener tunneling between two electronic states with overdamped classical reaction coordinate. It is shown that in the limit of non-adiabatic electron transfer (weak tunneling) well-described by the Marcus-Levich-Dogonadze (MLD) rate the answer is yes. However, in the limit of the so-called solvent-controlled adiabatic electron transfer a profound breaking of ergodicity occurs. The ensemble survival probability remains nearly exponential with the inverse rate given by the sum of the adiabatic curve crossing (Kramers) time and inverse MLD rate. However, near to adiabatic regime, the single-electron survival probability is clearly non-exponential but possesses an exponential tail which agrees well with the ensemble descrip...
Institute for Multiscale Simulation, Friedrich-Alexander University, Erlangen–Nuremberg, Germany.... more Institute for Multiscale Simulation, Friedrich-Alexander University, Erlangen–Nuremberg, Germany. ✉e-mail: igor.goychuk@fau.de In their Letter, Hu et al.1 claimed that the non-equilibrium dynamics of single protein molecules exhibits ageing over 13 decades of time, which covers the duration of the lifetime of many proteins. The Letter was the subject of a News and Views article2, and continues to attract the attention of many researchers. Here we re-examine the foundation of this claim and show that it is based on a fallacy. The numerical results shown in Fig. 2a of ref. 1 are obtained from Supplementary equation (1) in the same paper:
New Journal of Physics
This work justifies further paradigmatic importance of the model of viscoelastic subdiffusion in ... more This work justifies further paradigmatic importance of the model of viscoelastic subdiffusion in random environments for the observed subdiffusion in cellular biological systems. Recently, we showed [PCCP, 20, 24140 (2018)] that this model displays several remarkable features which makes it an attractive paradigm to explain the physical nature of subdiffusion occurring in biological cells. In particular, it combines viscoelasticity with distinct non-ergodic features. We extend this basic model to make it suitable for physical phenomena such as subdiffusion of lipids in disordered biological membranes upon including the inertial effects. For lipids, the inertial effects occur in the range of picoseconds, and a power-law decaying viscoelastic memory extends over the range of several nanoseconds. Thus, in the absence of disorder, diffusion would become normal on a time scale beyond this memory range. However, both experimentally and in some molecular-dynamical simulations the time range of lipid subdiffusion extends far beyond the viscoelastic memory range. We study three 1d models of correlated quenched Gaussian disorder to explain the puzzle: singular short-range (exponentially correlated), smooth short-range (Gaussiancorrelated), and smooth long-range (power-law correlated) disorder. For a moderate disorder strength, transient viscoelastic subdiffusion changes into the subdiffusion caused by the randomness of the environment. It is characterized by a time-dependent power-law exponent of subdiffusion α(t), which can show nonmonotonous behavior, in agreement with some recent molecular-dynamical simulations. Moreover, spatial distribution of test particles in this disorder-dominated regime is shown to be a non-Gaussian, exponential power distribution with index χ = 1.45 − 2.3, which also correlates well with molecular-dynamical findings and experiments. Furthermore, this subdiffusion is nonergodic with single-trajectory averages showing a broad scatter, in agreement with experimental observations for viscoelastic subdiffusion of various particles in living cells.
Physical Review E
Many experimental studies revealed subdiffusion of various nanoparticles in diverse polymer and c... more Many experimental studies revealed subdiffusion of various nanoparticles in diverse polymer and colloidal solutions, cytosol and plasma membrane of biological cells, which are viscoelastic and, at the same time, highly inhomogeneous randomly fluctuating environments. The observed subdiffusion often combines features of ergodic fractional Brownian motion (reflecting viscoelasticity) and nonergodic jumplike non-Markovian diffusional processes (reflecting disorder). Accordingly, several theories were proposed to explain puzzling experimental findings. Below we show that some of the significant and profound published experimental results are better rationalized within the viscoelastic subdiffusion approach in random environments, which is based on generalized Langevin dynamics in random potentials, than some earlier proposed theories.
Physical Review Letters
Diffusion in tilted washboard potentials can paradoxically exceed free normal diffusion. The effe... more Diffusion in tilted washboard potentials can paradoxically exceed free normal diffusion. The effect becomes much stronger in the underdamped case due to inertial effects. What happens upon inclusion of usually neglected fractional hydrodynamics memory effects (Basset-Boussinesq frictional force), which result in a heavy algebraic tail of the velocity autocorrelation function of the potential-free diffusion making it transiently superdiffusive? Will a giant enhancement of diffusion become even stronger, and the transient superdiffusion last even longer? These are the questions that we answer in this Letter based on an accurate numerical investigation. We show that a resonancelike enhancement of normal diffusion becomes indeed much stronger and sharper. Moreover, a long-lasting transient regime of superdiffusion, including Richardson-like diffusion, hδx 2 ðtÞi ∝ t 3 and ballistic supertransport, hδxðtÞi ∝ t 2 , is revealed.
The European Physical Journal B
The linear Boltzmann equation approach is generalized to describe fractional superdiffusive trans... more The linear Boltzmann equation approach is generalized to describe fractional superdiffusive transport of the Lévy walk type in external force fields. The time distribution between scattering events is assumed to have a finite mean value and infinite variance. It is completely characterized by the two scattering rates, one fractional and a normal one, which defines also the mean scattering rate. We formulate a general fractional linear Boltzmann equation approach and exemplify it with a particularly simple case of the Bohm and Gross scattering integral leading to a fractional generalization of the Bhatnagar, Gross and Krook kinetic equation. Here, at each scattering event the particle velocity is completely randomized and takes a value from equilibrium Maxwell distribution at a given fixed temperature. We show that the retardation effects are indispensable even in the limit of infinite mean scattering rate and argue that this novel fractional kinetic equation provides a viable alternative to the fractional Kramers-Fokker-Planck (KFP) equation by Barkai and Silbey and its generalization by Friedrich et al. based on the picture of divergent mean time between scattering events. The case of divergent mean time is also discussed at length and compared with the earlier results obtained within the fractional KFP.
<p>(a) Effective anomalous transport exponent and (b) thermodynamic efficiency while workin... more <p>(a) Effective anomalous transport exponent and (b) thermodynamic efficiency while working against a constant force near the end point of the simulations ( sec or in dimensionless units). The thermodynamic efficiency decays over time as . The analysis considers the same particles as in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0091700#pone-0091700-g002" target="_blank">Figure 2</a>, but here the potential height is reduced by factor of . Ensemble averaging is performed over particles and random realizations of potential flashes. The inset in (a) shows the dependence of on the mean enzyme turnover frequency for .</p
<p>Single motor transport (full line) is almost perfectly locked to the potential fluctuati... more <p>Single motor transport (full line) is almost perfectly locked to the potential fluctuations (broken red line depicting a renewal process counting the number of potential fluctuations in units of ) occurring with mean turnover frequency Hz, in a potential (top inset) with amplitudes eV ( in dimensionless units) and eV ( eV), for nm. A particle with an effective radius nm (like a magnetic endosome <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0091700#pone.0091700-Robert1" target="_blank">[33]</a>) experiences asymptotically for sec an effective viscous friction enhanced by a factor of with respect to water. The bottom inset shows that on the relevant transient time scale the free particle subdiffuses with anomalous diffusion coefficient . Initially, diffusion is normal. The time-average over a single trajectory, , is shown for sec and compared with the theoretical subdiffusive ensemble-averaged result (red line). See <b>Methods</b>.</p
New Journal of Physics, Apr 1, 2022
We describe the phenomenon of a resonance-like, giant enhancement of diffusion in a basic model o... more We describe the phenomenon of a resonance-like, giant enhancement of diffusion in a basic model of nonlinear diffusion featured by a nonlinear in velocity friction and the corresponding multiplicative thermal noise. The model is consistent with thermal equilibrium in the absence of driving. Different from previous studies of this phenomenon, where the crucial nonlinearity originates from a periodic external potential while friction is linear, we focus on the case of a constant force driving, whereas the crucial nonlinearity stems from the friction. The basic model of such friction considered interpolates between linear viscous Stokes friction at small velocities and dry Coulomb-like friction at large velocities corresponding to a stress plateau in some nonlinear viscoelastic materials. Recently, a nonequilibrium phase transition to super-diffusion and super-transport was discovered within this basic model. We show that adding a tiny viscous friction part to major nonlinear friction regularizes in part this behavior. Diffusion becomes asymptotically normal. However, the phase transition translates into a giant enhancement of normal diffusion and mobility of particles at the transition point over the intuitively expected large force limit, where the linearization of friction occurs. Such a giant enhancement of diffusion is closely related to the largely enhanced kinetic temperature of the particles at and beyond the critical point. We provide analytical results obtained within an effective mass approximation which nicely agree with stochastic numerics.
Proceedings of the National Academy of Sciences of the United States of America, Nov 22, 2022
We investigate analytically and numerically a basic model of driven Brownian motion with a veloci... more We investigate analytically and numerically a basic model of driven Brownian motion with a velocity-dependent friction coefficient in nonlinear viscoelastic media featured by a stress plateau at intermediate shear velocities and profound memory effects. For constant force driving, we show that nonlinear oscillations of a microparticle velocity and position emerge by a Hopf bifurcation at a small critical force (first dynamical phase transition), where the friction’s nonlinearity seems to be wholly negligible. They also disappear by a second Hopf bifurcation at a much larger force value (second dynamical phase transition). The bifurcation diagram is found in an analytical form confirmed by numerics. Surprisingly, the particles’ inertial and the medium’s nonlinear properties remain crucial even in a parameter regime where they were earlier considered entirely negligible. Depending on the force and other parameters, the amplitude of oscillations can significantly exceed the size of the particles, and their period can span several time decades, primarily determined by the memory time of the medium. Such oscillations can also be thermally excited near the edges of dynamical phase transitions. The second dynamical phase transition combined with thermally induced stochastic limit cycle oscillations leads to a giant enhancement of diffusion over the limit of vast driving forces, where an effective linearization of stochastic dynamics occurs.
APS, Mar 20, 2003
The phenomenological linear response theory of non-Markovian stochastic resonance (SR) is put for... more The phenomenological linear response theory of non-Markovian stochastic resonance (SR) is put forward for stationary two-state renewal processes. In terms of a derivation of a non-Markov regression theorem we evaluate the characteristic SR-quantifiers; i.e., the spectral power amplification (SPA) and the signal-to-noise ratio (SNR), respectively. In clear contrast to Markovian-SR, a characteristic benchmark of genuine non-Markovian SR is its distinctive dependence of the SPA and SNR on small (adiabatic) driving frequencies; particularly, the adiabatic SNR becomes strongly suppressed over its Markovian counterpart. This non-Markovian SR-theory is elucidated for a fractal gating dynamics of a potassium ion channel possessing an infinite variance of closed sojourn times.
arXiv (Cornell University), Oct 22, 1999
In the regime of weak bath coupling and low temperature we demonstrate numerically for the spin-b... more In the regime of weak bath coupling and low temperature we demonstrate numerically for the spin-boson dynamics the equivalence between two widely used but seemingly different roads of approximation, namely the path integral approach and the Bloch-Redfield theory. The excellent agreement between these two methods is corroborated by a novel efficient analytical high-frequency approach: it well approximates the decay of quantum coherence via a series of damped coherent oscillations. Moreover, a suitably tuned control field can selectively enhance or suppress quantum coherence.
arXiv (Cornell University), Aug 14, 2017
An important criterion on finite kinetic temperature of the system of cold atoms is established. ... more An important criterion on finite kinetic temperature of the system of cold atoms is established. It is shown that the kinetic temperature becomes infinite in Fig. 1 of the commented paper in the course of time, i.e. the considered model system becomes asymptotically infinitely hot. Moreover, within this model the behavior of the squared width of the spatial distribution of atoms at the half of its maximum is very different from the variance of the particle positions. In particular, in the discussed Fig. 1 the former one increases sub-ballistically in time, while the variance grows super-ballistically, which corresponds to a heating phase. This leads to a profound ambiguity in definition and classification of anomalous diffusion. All in all, the model in the commented paper simply does not fit to experiments with cold atoms.
Bulletin of the American Physical Society, Mar 8, 2018
Viscoelastic subdiffusion governed by a fractional Langevin equation is studied numerically in a ... more Viscoelastic subdiffusion governed by a fractional Langevin equation is studied numerically in a random Gaussian environment modeled by stationary Gaussian potentials with decaying spatial correlations. This anomalous diffusion is archetypal for living cells, where cytoplasm is known to be viscoelastic and a spatial disorder also naturally emerges. We obtain some first important insights into it within a model one-dimensional study. Two basic types of potential correlations are studied: short-range exponentially decaying and algebraically slow decaying with an infinite correlation length, both for a moderate (several kBT , in the units of thermal energy), and strong (5-10 kBT) disorder. For a moderate disorder, it is shown that on the ensemble level viscoelastic subdiffusion can easily overcome the medium's disorder. Asymptotically, it is not distinguishable from the disorder-free subdiffusion. However, a strong scatter in single-trajectory averages is nevertheless seen even for a moderate disorder. It features a weak ergodicity breaking, which occurs on a very long yet transient time scale. Furthermore, for a strong disorder, a very long transient regime of logarithmic, Sinai-type diffusion emerges. It can last longer and be faster in the absolute terms for weakly decaying correlations as compare with the short-range correlations. Residence time distributions in a finite spatial domain are of a generalized log-normal type and are reminiscent also of a stretched exponential distribution. They can be easily confused for power-law distributions in view of the observed weak ergodicity breaking. This suggests a revision of some experimental data and their interpretation.
Physical Review Letters, 2019
We consider a two-state model of non-Markovian stochastic resonance (SR) within the framework of ... more We consider a two-state model of non-Markovian stochastic resonance (SR) within the framework of the theory of renewal processes. Residence time intervals are assumed to be mutually independent and characterized by some arbitrary non-exponential residence time distributions which are modulated in time by an externally applied signal. Making use of a stochastic path integral approach we obtain general integral equations governing the evolution of conditional probabilities in the presence of an input signal. These novel equations generalize earlier integral renewal equations by Cox and others to the case of driving-induced non-stationarity. On the basis of these new equations a response theory of two state renewal processes is formulated beyond the linear response approximation. Moreover, a general expression for the linear response function is derived. The connection of the developed approach with the phenomenological theory of linear response for manifest non-Markovian SR put forward in [ I. Goychuk and P. Hänggi, Phys. Rev. Lett. 91, 070601 (2003)] is clarified and its range of validity is scrutinized. The novel theory is then applied to SR in symmetric non-Markovian systems and to the class of single ion channels possessing a fractal kinetics.
Physical Review E
Hydrodynamic memory force or Basset force has been known since the 19th century. Its influence on... more Hydrodynamic memory force or Basset force has been known since the 19th century. Its influence on Brownian motion remains, however, mostly unexplored. Here we investigate its role in nonlinear transport and diffusion within a paradigmatic model of tilted washboard potential. In this model, a giant enhancement of driven diffusion over its potential-free limit [Phys. Rev. Lett. 87, 010602 (2001)] presents a well-established paradoxical phenomenon. In the overdamped limit, it occurs at a critical tilt of vanishing potential barriers. However, for weak damping, it takes place surprisingly at another critical tilt, where the potential barriers are clearly expressed. Recently we showed [Phys. Rev. Lett. 123, 180603 (2019)] that Basset force could make such a diffusion enhancement enormously large. In this paper, we discover that even for moderately strong damping, where the overdamped theory works very well when the memory effects are negligible, substantial hydrodynamic memory unexpectedly makes a strong impact. First, the diffusion boost occurs at nonvanishing potential barriers and can be orders of magnitude larger. Second, transient anomalous diffusion regimes emerge over many time decades and potential periods. Third, particles' mobility can also be dramatically enhanced, and a long transient supertransport regime emerges.
Physical review letters, 2021
We investigate a basic model of nonlinear Brownian motion in a thermal environment, where nonline... more We investigate a basic model of nonlinear Brownian motion in a thermal environment, where nonlinear friction interpolates between viscous Stokes and dry Coulomb friction. We show that superdiffusion and supertransport emerge as a nonequilibrium critical phenomenon when such a Brownian motion is driven out of thermal equilibrium by a constant force. Precisely at the edge of a phase transition, velocity fluctuations diverge asymptotically and diffusion becomes superballistic. The autocorrelation function of velocity fluctuations in this nonergodic regime exhibits a striking aging behavior.
arXiv: Mesoscale and Nanoscale Physics, 2015
Does electron transfer (ET) kinetics within a single-electron trajectory description always coinc... more Does electron transfer (ET) kinetics within a single-electron trajectory description always coincide with the ensemble description? This fundamental question of ergodic behavior is scrutinized within a very basic semi-classical curve-crossing problem of quantum Landau-Zener tunneling between two electronic states with overdamped classical reaction coordinate. It is shown that in the limit of non-adiabatic electron transfer (weak tunneling) well-described by the Marcus-Levich-Dogonadze (MLD) rate the answer is yes. However, in the limit of the so-called solvent-controlled adiabatic electron transfer a profound breaking of ergodicity occurs. The ensemble survival probability remains nearly exponential with the inverse rate given by the sum of the adiabatic curve crossing (Kramers) time and inverse MLD rate. However, near to adiabatic regime, the single-electron survival probability is clearly non-exponential but possesses an exponential tail which agrees well with the ensemble descrip...
Institute for Multiscale Simulation, Friedrich-Alexander University, Erlangen–Nuremberg, Germany.... more Institute for Multiscale Simulation, Friedrich-Alexander University, Erlangen–Nuremberg, Germany. ✉e-mail: igor.goychuk@fau.de In their Letter, Hu et al.1 claimed that the non-equilibrium dynamics of single protein molecules exhibits ageing over 13 decades of time, which covers the duration of the lifetime of many proteins. The Letter was the subject of a News and Views article2, and continues to attract the attention of many researchers. Here we re-examine the foundation of this claim and show that it is based on a fallacy. The numerical results shown in Fig. 2a of ref. 1 are obtained from Supplementary equation (1) in the same paper:
New Journal of Physics
This work justifies further paradigmatic importance of the model of viscoelastic subdiffusion in ... more This work justifies further paradigmatic importance of the model of viscoelastic subdiffusion in random environments for the observed subdiffusion in cellular biological systems. Recently, we showed [PCCP, 20, 24140 (2018)] that this model displays several remarkable features which makes it an attractive paradigm to explain the physical nature of subdiffusion occurring in biological cells. In particular, it combines viscoelasticity with distinct non-ergodic features. We extend this basic model to make it suitable for physical phenomena such as subdiffusion of lipids in disordered biological membranes upon including the inertial effects. For lipids, the inertial effects occur in the range of picoseconds, and a power-law decaying viscoelastic memory extends over the range of several nanoseconds. Thus, in the absence of disorder, diffusion would become normal on a time scale beyond this memory range. However, both experimentally and in some molecular-dynamical simulations the time range of lipid subdiffusion extends far beyond the viscoelastic memory range. We study three 1d models of correlated quenched Gaussian disorder to explain the puzzle: singular short-range (exponentially correlated), smooth short-range (Gaussiancorrelated), and smooth long-range (power-law correlated) disorder. For a moderate disorder strength, transient viscoelastic subdiffusion changes into the subdiffusion caused by the randomness of the environment. It is characterized by a time-dependent power-law exponent of subdiffusion α(t), which can show nonmonotonous behavior, in agreement with some recent molecular-dynamical simulations. Moreover, spatial distribution of test particles in this disorder-dominated regime is shown to be a non-Gaussian, exponential power distribution with index χ = 1.45 − 2.3, which also correlates well with molecular-dynamical findings and experiments. Furthermore, this subdiffusion is nonergodic with single-trajectory averages showing a broad scatter, in agreement with experimental observations for viscoelastic subdiffusion of various particles in living cells.
Physical Review E
Many experimental studies revealed subdiffusion of various nanoparticles in diverse polymer and c... more Many experimental studies revealed subdiffusion of various nanoparticles in diverse polymer and colloidal solutions, cytosol and plasma membrane of biological cells, which are viscoelastic and, at the same time, highly inhomogeneous randomly fluctuating environments. The observed subdiffusion often combines features of ergodic fractional Brownian motion (reflecting viscoelasticity) and nonergodic jumplike non-Markovian diffusional processes (reflecting disorder). Accordingly, several theories were proposed to explain puzzling experimental findings. Below we show that some of the significant and profound published experimental results are better rationalized within the viscoelastic subdiffusion approach in random environments, which is based on generalized Langevin dynamics in random potentials, than some earlier proposed theories.
Physical Review Letters
Diffusion in tilted washboard potentials can paradoxically exceed free normal diffusion. The effe... more Diffusion in tilted washboard potentials can paradoxically exceed free normal diffusion. The effect becomes much stronger in the underdamped case due to inertial effects. What happens upon inclusion of usually neglected fractional hydrodynamics memory effects (Basset-Boussinesq frictional force), which result in a heavy algebraic tail of the velocity autocorrelation function of the potential-free diffusion making it transiently superdiffusive? Will a giant enhancement of diffusion become even stronger, and the transient superdiffusion last even longer? These are the questions that we answer in this Letter based on an accurate numerical investigation. We show that a resonancelike enhancement of normal diffusion becomes indeed much stronger and sharper. Moreover, a long-lasting transient regime of superdiffusion, including Richardson-like diffusion, hδx 2 ðtÞi ∝ t 3 and ballistic supertransport, hδxðtÞi ∝ t 2 , is revealed.
The European Physical Journal B
The linear Boltzmann equation approach is generalized to describe fractional superdiffusive trans... more The linear Boltzmann equation approach is generalized to describe fractional superdiffusive transport of the Lévy walk type in external force fields. The time distribution between scattering events is assumed to have a finite mean value and infinite variance. It is completely characterized by the two scattering rates, one fractional and a normal one, which defines also the mean scattering rate. We formulate a general fractional linear Boltzmann equation approach and exemplify it with a particularly simple case of the Bohm and Gross scattering integral leading to a fractional generalization of the Bhatnagar, Gross and Krook kinetic equation. Here, at each scattering event the particle velocity is completely randomized and takes a value from equilibrium Maxwell distribution at a given fixed temperature. We show that the retardation effects are indispensable even in the limit of infinite mean scattering rate and argue that this novel fractional kinetic equation provides a viable alternative to the fractional Kramers-Fokker-Planck (KFP) equation by Barkai and Silbey and its generalization by Friedrich et al. based on the picture of divergent mean time between scattering events. The case of divergent mean time is also discussed at length and compared with the earlier results obtained within the fractional KFP.