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Igor Goychuk

Friedrich-Alexander-Universität Erlangen-Nürnberg, Chemical and BioEngineering, Temporary Position of DFG Principal Investigator

University of Augsburg, Institut für Physik, Adjunct

Universitaet Potsdam, Physics and Astronomy, Alumnus

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Papers by Igor Goychuk

Comment on "Large Fluctuations for Spatial Diffusion of Cold Atoms" [arXiv:1701.03357]

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.

Anomalous transport of large cargo particles at lower potential amplitude, larger turnover rates, and in the presence of loading force

<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

Normal transport for large cargo particles, large potential amplitude and small turnover rate, in the absence a of constant loading force

<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

Resonance-like enhancement of forced nonlinear diffusion as a nonequilibrium phase transition

New Journal of Physics, 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 ...

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Physical Review Letters, 2019

Memory can induce oscillations of microparticles in nonlinear viscoelastic media and cause a giant enhancement of driven diffusion

Proceedings of the National Academy of Sciences

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...

Stochastic modeling of excitable dynamics: improved Langevin model for mesoscopic channel noise

Influence of mesoscopic channel noise on excitable dynamics of living cells became a hot subject ... more Influence of mesoscopic channel noise on excitable dynamics of living cells became a hot subject within the last decade, and the traditional biophysical models of neuronal dynamics such as Hodgkin-Huxley model have been generalized to incorporate such effects. There still exists but a controversy on how to do it in a proper and computationally efficient way. Here we introduce an improved Langevin description of stochastic Hodgkin-Huxley dynamics with natural boundary conditions for gating variables. It consistently describes the channel noise variance in a good agreement with discrete state model. Moreover, we show by comparison with our improved Langevin model that two earlier Langevin models by Fox and Lu also work excellently starting from several hundreds of ion channels upon imposing numerically reflecting boundary conditions for gating variables.

Rate processes with non-Markovian dynamical disorder

Rate processes with dynamical disorder are investigated within a simple framework provided by uni... more Rate processes with dynamical disorder are investigated within a simple framework provided by unidirectional electron transfer (ET) with fluctuating transfer rate. The rate fluctuations are assumed to be described by a non-Markovian stochastic jump process which reflects conformational dynamics of an electron transferring donor-acceptor molecular complex. A tractable analytical expression is obtained for the relaxation of the donor population (in the Laplace-transformed time domain) averaged over the stationary conformational fluctuations. The corresponding mean transfer time is also obtained in an analytical form. The case of two-state fluctuations is studied in detail for a model incorporating substate diffusion within one of the conformations. It is shown that an increase of the conformational diffusion time results in a gradual transition from the regime of fast modulation characterized by the averaged ET rate to the regime of quasi-static disorder. This transition occurs at the...

Stochastic Wilson-Cowan models of neuronal network dynamics with memory and delay

We consider a simple Markovian class of the stochastic Wilson-Cowan type models of neuronal netwo... more We consider a simple Markovian class of the stochastic Wilson-Cowan type models of neuronal network dynamics, which incorporates stochastic delay caused by the existence of a refractory period of neurons. From the point of view of the dynamics of the individual elements, we are dealing with a network of non-Markovian stochastic two-state oscillators with memory which are coupled globally in a mean-field fashion. This interrelation of a higher-dimensional Markovian and lower-dimensional non-Markovian dynamics is discussed in its relevance to the general problem of the network dynamics of complex elements possessing memory. The simplest model of this class is provided by a three-state Markovian neuron with one refractory state, which causes firing delay with an exponentially decaying memory within the two-state reduced model. This basic model is used to study critical avalanche dynamics (the noise sustained criticality) in a balanced feedforward network consisting of the excitatory an...

Modeling magnetosensitive ion channels in viscoelastic environment of living cells

We propose and study a model of hypothetical magnetosensitive ionic channels which are long thoug... more We propose and study a model of hypothetical magnetosensitive ionic channels which are long thought to be a possible candidate to explain the influence of weak magnetic fields on living organisms ranging from magnetotactic bacteria to fishes, birds, rats, bats and other mammals including humans. The core of the model is provided by a short chain of magnetosomes serving as a sensor which is coupled by elastic linkers to the gating elements of ion channels forming a small cluster in the cell membrane. The magnetic sensor is fixed by one end on cytoskeleton elements attached to the membrane and is exposed to viscoelastic cytosol. Its free end can reorient stochastically and subdiffusively in viscoelastic cytosol responding to external magnetic field changes and open the gates of coupled ion channels. The sensor dynamics is generally bistable due to bistability of the gates which can be in two states with probabilities which depend on the sensor orientation. For realistic parameters, it...

Molecular machines operating on nanoscale: from classical to quantum

The main physical features and operating principles of isothermal nanomachines in microworld are ... more The main physical features and operating principles of isothermal nanomachines in microworld are reviewed, which are common for both classical and quantum machines. Especial attention is paid to the dual and constructive role of dissipation and thermal fluctuations, fluctuation-dissipation theorem, heat losses and free energy transduction, thermodynamic efficiency, and thermodynamic efficiency at maximum power. Several basic models are considered and discussed to highlight generic physical features. Our exposition allows to spot some common fallacies which continue to plague the literature, in particular, erroneous beliefs that one should minimize friction and lower the temperature to arrive at a high performance of Brownian machines, and that thermodynamic efficiency at maximum power cannot exceed one-half. The emerging topic of anomalous molecular motors operating sub-diffusively but highly efficiently in viscoelastic environment of living cells is also discussed.

Subdiffusive Brownian ratchets rocked by a periodic force

This work puts forward a generalization of the well-known rocking Markovian Brownian ratchets to ... more This work puts forward a generalization of the well-known rocking Markovian Brownian ratchets to the realm of antipersistent non-Markovian subdiffusion in viscoelastic media. A periodically forced subdiffusion in a parity-broken ratchet potential is considered within the non-Markovian generalized Langevin equation (GLE) description with a power-law memory kernel η(t)∝ t^-α (0<α<1). It is shown that subdiffusive rectification currents, defined through the mean displacement and subvelocity v_α, <δ x(t)>∼ v_α t^α/ Γ(1+α), emerge asymptotically due to the breaking of the detailed balance symmetry by driving. The asymptotic exponent is α, the same as for free subdiffusion, <δ x^2(t)>∝ t^α. However, a transient to this regime with some time-dependent α_ eff(t) gradually decaying in time, α≤α_ eff(t)≤ 1, can be very slow depending on the barrier height and the driving field strength. In striking contrast to its normal diffusion counterpart, the anomalous rectification cur...

Molecular motors transporting cargos in viscoelastic cytosol: how to beat subdiffusion with a power stroke?

Anomalously slow passive diffusion, 〈δ x^2(t)〉≃ t^α, with 0<α<1, of larger tracers such as ... more Anomalously slow passive diffusion, 〈δ x^2(t)〉≃ t^α, with 0<α<1, of larger tracers such as messenger RNA and endogenous submicron granules in the cytoplasm of living biological cells has been demonstrated in a number of experiments and has been attributed to the viscoelastic physical nature of the cellular cytoplasm. This finding provokes the question to which extent active intracellular transport is affected by this viscoelastic environment: does the subdiffusion of free submicron cargo such as vesicles and organelles always imply anomalously slow transport by molecular motors such as kinesins, that is, directed transport characterized by a sublinear growth of the mean distance, 〈 x(t)〉≃ t^α_ eff, with 0<α_ eff<1? Here we study a generic model approach combining the commonly accepted two-state Brownian ratchet model of kinesin motors based on the continuous-state diffusion along microtubule driven by a flashing binding potential. The motor is elastically coupled to a ca...

Anomalous transport of subdiffusing cargos by single kinesin motors: the role of mechanochemical coupling and anharmonicity of tether

Here we generalize our previous model of molecular motors trafficking subdiffusing cargos in visc... more Here we generalize our previous model of molecular motors trafficking subdiffusing cargos in viscoelastic cytosol by (i) including mechanochemical coupling between cyclic conformational fluctuations of the motor protein driven by the reaction of ATP hydrolysis and its translational motion within the simplest two-state model of hand-over-hand motion of kinesin, and also (ii) by taking into account the anharmonicity of the tether between the motor and cargo (its maximally possible extension length). It is shown that the major earlier results such as occurrence of normal versus anomalous transport depending on the amplitude of binding potential, cargo size and the motor turnover frequency not only survive in this more realistic model, but the results also look very similar for the correspondingly adjusted parameters. However, this more realistic model displays a substantially larger thermodynamic efficiency due to a bidirectional mechanochemical coupling. For realistic parameters, the ...

Quantum dynamics with non-Markovian fluctuating parameters

A stochastic approach to the quantum dynamics randomly modulated in time by a discrete state non-... more A stochastic approach to the quantum dynamics randomly modulated in time by a discrete state non-Markovian noise, which possesses an arbitrary non-exponential distribution of the residence times, is developed. The formally exact expression for the Laplace-transformed quantum propagator averaged over the stationary realizations of such N-state non-Markovian noise is obtained. The theory possesses a wide range of applications. It includes some previous Markovian and non-Markovian theories as particular cases. In the context of stochastic theory of spectral line shape and relaxation, the developed approach presents a non-Markovian generalization of the Kubo-Anderson theory of sudden modulation. In particular, the exact analytical expression is derived for the spectral line shape of optical transitions described by a Kubo-oscillator with randomly modulated frequency which undergoes jump-like non-Markovian fluctuations in time.

Persistent Sinai type diffusion in Gaussian random potentials with decaying spatial correlations

Logarithmic or Sinai type subdiffusion is usually associated with random force disorder and non-s... more Logarithmic or Sinai type subdiffusion is usually associated with random force disorder and non-stationary potential fluctuations whose root mean squared amplitude grows with distance. We show here that extremely persistent, macroscopic ultraslow logarithmic diffusion also universally emerges at sufficiently low temperatures in stationary Gaussian random potentials with spatially decaying correlations, known to exist in a broad range of physical systems. Combining results from extensive simulations with a scaling approach we elucidate the physical mechanism of this unusual subdiffusion. In particular, we explain why with growing temperature and/or time a first crossover occurs to standard, power-law subdiffusion, with a time-dependent power law exponent, and then a second crossover occurs to normal diffusion with a disorder-renormalized diffusion coefficient. Interestingly, the initial, nominally ultraslow diffusion turns out to be much faster than the universal de Gennes-Baessler-Z...

Life and death of stationary linear response in anomalous continuous time random walk dynamics

Linear theory of stationary response in thermal systems subjected to external perturbations requi... more Linear theory of stationary response in thermal systems subjected to external perturbations requires to find equilibrium correlation function of the responding system variable in the absence of external perturbations. Studies of the response of the systems exhibiting anomalously slow dynamics are often based on the continuous time random walk description (CTRW) with divergent mean waiting times. The bulk of the literature on anomalous response contains linear response functions like one by Cole-Cole calculated from such a CTRW theory and applied to thermal systems. Here we show within a fairly simple and general model that for the systems with divergent mean waiting times the stationary response is absent, in accordance with some recent studies. The absence of stationary response at thermal equilibrium (or dying to zero non-stationary response in aging experiments) would confirm CTRW with divergent mean waiting times as underlying physical relaxation mechanism, but reject it otherwi...

Anomalous features of diffusion in corrugated potentials with spatial correlations: faster than normal, and other surprises

Normal diffusion in corrugated potentials with spatially uncorrelated Gaussian energy disorder fa... more Normal diffusion in corrugated potentials with spatially uncorrelated Gaussian energy disorder famously explains the origin of non-Arrhenius [-σ^2/(k_BT^2)] temperature-dependence in disordered systems. Here we show that unbiased diffusion remains asymptotically normal also in the presence of spatial correlations decaying to zero. However, due to a temporal lack of self-averaging transient subdiffusion emerges on mesoscale, and it can readily reach macroscale even for moderately strong disorder fluctuations of σ∼ 4-5 k_BT. Due to its nonergodic origin such subdiffusion exhibits a large scatter in single trajectory averages. However, at odds with intuition, it occurs essentially faster than one expects from the normal diffusion in the absence of correlations. We apply these results to diffusion of regulatory proteins on DNA molecules and predict that such diffusion should be anomalous, but much faster than earlier expected on a typical length of genes for a realistic energy disorder ...

Fractional Brownian motors and Stochastic Resonance

We study fluctuating tilt Brownian ratchets based on fractional subdiffusion in sticky viscoelast... more We study fluctuating tilt Brownian ratchets based on fractional subdiffusion in sticky viscoelastic media characterized by a power law memory kernel. Unlike the normal diffusion case the rectification effect vanishes in the adiabatically slow modulation limit and optimizes in a driving frequency range. It is shown also that anomalous rectification effect is maximal (stochastic resonance effect) at optimal temperature and can exhibit a surprisingly good quality. Moreover, subdiffusive current can flow in the counter-intuitive direction upon a change of temperature or driving frequency. The dependence of anomalous transport on load exhibits a remarkably simple universality.

Rocking Subdiffusive Ratchets: Origin, Optimization and Efficiency

We study origin, parameter optimization, and thermodynamic efficiency of isothermal rocking ratch... more We study origin, parameter optimization, and thermodynamic efficiency of isothermal rocking ratchets based on fractional subdiffusion within a generalized non-Markovian Langevin equation approach. A corresponding multi-dimensional Markovian embedding dynamics is realized using a set of auxiliary Brownian particles elastically coupled to the central Brownian particle (see video on the journal web site). We show that anomalous subdiffusive transport emerges due to an interplay of nonlinear response and viscoelastic effects for fractional Brownian motion in periodic potentials with broken space-inversion symmetry and driven by a time-periodic field. The anomalous transport becomes optimal for a subthreshold driving when the driving period matches a characteristic time scale of interwell transitions. It can also be optimized by varying temperature, amplitude of periodic potential and driving strength. The useful work done against a load shows a parabolic dependence on the load strength....