TY - JOUR A1 - Goychuk, Igor T1 - Quantum ergodicity breaking in semi-classical electron transfer dynamics JF - Physical chemistry, chemical physics : a journal of European Chemical Societies N2 - Can the statistical properties of single-electron transfer events be correctly predicted within a common equilibrium ensemble description? This fundamental in nanoworld question of ergodic behavior is scrutinized within a very basic semi-classical curve-crossing problem. 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. Namely, a common description based on the ensemble reduced density matrix with an initial equilibrium distribution of the reaction coordinate is not able to reproduce the statistics of single-trajectory events in this seemingly classical regime. For sufficiently large activation barriers, the ensemble survival probability in a state remains nearly exponential with the inverse rate given by the sum of the adiabatic curve crossing (Kramers) time and the inverse MLD rate. In contrast, near to the adiabatic regime, the single-electron survival probability is clearly non-exponential, even though it possesses an exponential tail which agrees well with the ensemble description. Initially, it is well described by a Mittag-Leffler distribution with a fractional rate. Paradoxically, the mean transfer time in this classical on the ensemble level regime is well described by the inverse of the nonadiabatic quantum tunneling rate on a single particle level. An analytical theory is developed which perfectly agrees with stochastic simulations and explains our findings. Y1 - 2016 U6 - https://doi.org/10.1039/c6cp07206b SN - 1463-9076 SN - 1463-9084 VL - 19 SP - 3056 EP - 3066 PB - Royal Society of Chemistry CY - Cambridge ER - TY - JOUR A1 - Goychuk, Igor T1 - Sensing magnetic fields with magnetosensitive ion channels JF - Sensors N2 - Magnetic nanoparticles are met across many biological species ranging from magnetosensitive bacteria, fishes, bees, bats, rats, birds, to humans. They can be both of biogenetic origin and due to environmental contamination, being either in paramagnetic or ferromagnetic state. The energy of such naturally occurring single-domain magnetic nanoparticles can reach up to 10-20 room k(B)T in the magnetic field of the Earth, which naturally led to supposition that they can serve as sensory elements in various animals. This work explores within a stochastic modeling framework a fascinating hypothesis of magnetosensitive ion channels with magnetic nanoparticles serving as sensory elements, especially, how realistic it is given a highly dissipative viscoelastic interior of living cells and typical sizes of nanoparticles possibly involved. KW - magnetic nanoparticles KW - ion channels KW - viscoelastic effects and anomalous diffusion KW - non-exponential statistics KW - influence of weak magnetic fields on living systems Y1 - 2018 U6 - https://doi.org/10.3390/s18030728 SN - 1424-8220 VL - 18 IS - 3 PB - MDPI CY - Basel ER - TY - JOUR A1 - Goychuk, Igor T1 - Viscoelastic subdiffusion in a random Gaussian environment JF - Physical chemistry, chemical physics : a journal of European Chemical Societies N2 - 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 (5–10kBT) 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 compared 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. Y1 - 2018 U6 - https://doi.org/10.1039/c8cp05238g SN - 1463-9076 SN - 1463-9084 VL - 20 IS - 37 SP - 24140 EP - 24155 PB - Royal Society of Chemistry CY - Cambridge ER - TY - JOUR A1 - Goychuk, Igor T1 - Perfect anomalous transport of subdiffusive cargos by molecular motors in viscoelastic cytosol JF - Biosystems : journal of biological and information processing sciences N2 - Multiple experiments show that various submicron particles such as magnetosomes, RNA messengers, viruses, and even much smaller nanoparticles such as globular proteins diffuse anomalously slow in viscoelastic cytosol of living cells. Hence, their sufficiently fast directional transport by molecular motors such as kinesins is crucial for the cell operation. It has been shown recently that the traditional flashing Brownian ratchet models of molecular motors are capable to describe both normal and anomalous transport of such subdiffusing cargos by molecular motors with a very high efficiency. This work elucidates further an important role of mechanochemical coupling in such an anomalous transport. It shows a natural emergence of a perfect subdiffusive ratchet regime due to allosteric effects, where the random rotations of a "catalytic wheel" at the heart of the motor operation become perfectly synchronized with the random stepping of a heavily loaded motor, so that only one ATP molecule is consumed on average at each motor step along microtubule. However, the number of rotations made by the catalytic engine and the traveling distance both scale sublinearly in time. Nevertheless, this anomalous transport can be very fast in absolute terms. KW - Brownian motors KW - Flashing ratchets KW - Memory effects KW - Viscoelasticity KW - Subdiffusion KW - Generalized Langevin equation KW - Multi-dimensional Markovian embedding of non-Markovian dynamics KW - Anomalous transport KW - Thermodynamic efficiency Y1 - 2019 U6 - https://doi.org/10.1016/j.biosystems.2018.11.004 SN - 0303-2647 SN - 1872-8324 VL - 177 SP - 56 EP - 65 PB - Elsevier CY - Oxford ER - TY - JOUR A1 - Goychuk, Igor T1 - Fractional electron transfer kinetics and a quantum breaking of ergodicity JF - Physical review : E, Statistical, nonlinear and soft matter physics N2 - The dissipative curve-crossing problem provides a paradigm for electron-transfer (ET) processes in condensed media. It establishes the simplest conceptual test bed to study the influence of the medium's dynamics on ET kinetics both on the ensemble level, and on the level of single particles. Single electron description is particularly important for nanoscaled systems like proteins, or molecular wires. Especially insightful is this framework in the semiclassical limit, where the environment can be treated classically, and an exact analytical treatment becomes feasible. Slow medium's dynamics is capable of enslaving ET and bringing it on the ensemble level from a quantum regime of nonadiabatic tunneling to the classical adiabatic regime, where electrons follow the nuclei rearrangements. This classical adiabatic textbook picture contradicts, however, in a very spectacular fashion to the statistics of single electron transitions, even in the Debye, memoryless media, also named Ohmic in the parlance of the famed spin-boson model. On the single particle level, ET always remains quantum, and this was named a quantum breaking of ergodicity in the adiabatic ET regime. What happens in the case of subdiffusive, fractional, or sub-Ohmic medium's dynamics, which is featured by power-law decaying dynamical memory effects typical, e.g., for protein macromolecules, and other viscoelastic media? Such a memory is vividly manifested by anomalous Cole-Cole dielectric response in such media. We address this question based both on accurate numerics and analytical theory. The ensemble theory remarkably agrees with the numerical dynamics of electronic populations, revealing a power-law relaxation tail even in a profoundly nonadiabatic electron transfer regime. In other words, ET in such media should typically display fractional kinetics. However, a profound difference with the numerically accurate results occurs for the distribution of residence times in the electronic states, both on the ensemble level and the level of single trajectories. Ergodicity is broken dynamically even in a more spectacular way than in the memoryless case. Our results question the applicability of all the existing and widely accepted ensemble theories of electron transfer in fractional, sub-Ohmic environments, on the level of single molecules, and provide a real challenge to face, both for theorists and experimentalists. Y1 - 2019 U6 - https://doi.org/10.1103/PhysRevE.99.052136 SN - 2470-0045 SN - 2470-0053 VL - 99 IS - 5 PB - American Physical Society CY - College Park ER - TY - JOUR A1 - Goychuk, Igor T1 - Fractional Hydrodynamic Memory and Superdiffusion in Tilted Washboard Potentials JF - Physical review letters N2 - 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, proportional to t(3) and ballistic supertransport, proportional to t(2), is revealed. Y1 - 2019 U6 - https://doi.org/10.1103/PhysRevLett.123.180603 SN - 0031-9007 SN - 1079-7114 VL - 123 IS - 18 PB - American Physical Society CY - College Park ER - TY - GEN A1 - Goychuk, Igor T1 - Comment on "Anomalous Escape Governed by Thermal 1/f Noise" Reply (R. K. Singh) T2 - Physical review letters Y1 - 2019 U6 - https://doi.org/10.1103/PhysRevLett.123.238902 SN - 0031-9007 SN - 1079-7114 VL - 123 IS - 23 PB - American Physical Society CY - College Park ER - TY - JOUR A1 - Goychuk, Igor T1 - Fractional Bhatnagar-Gross-Krook kinetic equation JF - The European physical journal : B, Condensed matter and complex systems N2 - The linear Boltzmann equation approach is generalized to describe fractional superdiffusive transport of the Levy 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. Also a phenomenological fractional BGK equation without retardation effects is proposed in the limit of infinite scattering rates. It cannot be, however, rigorously derived from a scattering model, being rather clever postulated. It this respect, this retardationless equation is similar to the fractional KFP by Barkai and Silbey. However, it corresponds to the opposite, much more physical limit and, therefore, also presents a viable alternative. Y1 - 2017 U6 - https://doi.org/10.1140/epjb/e2017-80297-x SN - 1434-6028 SN - 1434-6036 VL - 90 PB - Springer CY - New York ER - TY - JOUR A1 - Goychuk, Igor T1 - Molecular machines operating on the nanoscale: from classical to quantum JF - Beilstein journal of nanotechnology N2 - The main physical features and operating principles of isothermal nanomachines in the microworld, common to both classical and quantum machines, are reviewed. Special attention is paid to the dual, constructive role of dissipation and thermal fluctuations, the 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. This work examines some common fallacies that continue to plague the literature. In particular, the erroneous beliefs that one should minimize friction and lower the temperature for high performance of Brownian machines, and that the thermodynamic efficiency at maximum power cannot exceed one-half are discussed. The emerging topic of anomalous molecular motors operating subdiffusively but very efficiently in the viscoelastic environment of living cells is also discussed. KW - anomalous dynamics with memory KW - Brownian nanomachines KW - nanoscale friction and thermal noise KW - quantum effects KW - thermodynamic efficiency Y1 - 2016 U6 - https://doi.org/10.3762/bjnano.7.31 SN - 2190-4286 VL - 7 SP - 328 EP - 350 PB - Beilstein-Institut zur Förderung der Chemischen Wissenschaften CY - Frankfurt, Main ER - TY - GEN A1 - Goychuk, Igor A1 - Kharchenko, Vasyl O. T1 - Rocking subdiffusive ratchets BT - origin, optimization and efficiency T2 - Mathematical Modelling of Natural Phenomena N2 - 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. It grows sublinearly with time and the corresponding thermodynamic efficiency decays algebraically in time because the energy supplied by the driving field scales with time linearly. However, it compares well with the efficiency of normal diffusion rocking ratchets on an appreciably long time scale. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 622 KW - anomalous Brownian motion KW - generalized Langevin equation KW - memory effects KW - viscoelasticity KW - ratchet transport KW - stochastic Y1 - 2019 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-416138 SN - 1866-8372 IS - 622 ER -