Control of electron and electron-hole pair dynamics on nonlinear lattice bilayers by strong solitons.

We consider the dynamics of electrons and holes moving in two-dimensional lattice layers and bilayers. As an example, we study triangular lattices with units interacting via anharmonic Morse potentials and investigate the dynamics of excess electrons and electron-hole pairs according to the Schrödinger equation in the tight binding approximation. We show that when single-site lattice solitons or M-solitons are excited in one of the layers, those lattice deformations are capable of trapping excess electrons or electron-hole pairs, thus forming quasiparticle compounds moving approximately with the velocity of the solitons. We study the temporal and spatial nonlinear dynamical evolution of localized excitations on coupled triangular double layers. Furthermore, we find that the motion of electrons or electron-hole pairs on a bilayer is slaved by solitons. By case studies of the dynamics of charges bound to solitons, we demonstrate that the slaving effect may be exploited for controlling the motion of the electrons and holes in lattice layers, including also bosonic electron-hole-soliton compounds in lattice bilayers, which represent a novel form of quasiparticles.

About electron transfer over long distances with tunable sub/supersonic velocities.

Provided in this paper is a theory of long-range electron transfer with near sound (supersonic or subsonic) velocity along one-dimensional crystal lattices. The theory represents the development of an earlier work by introducing Marcus formulation. To illustrate its application to a realistic case, the theory is used to offer an explanation of two puzzling observations made by Donovan and Wilson in transient photoconduction experiments with non-dopable perfectly crystalline polydiacetylene crystals in the presence of an electric field: transport velocity value close to sound velocity being independent of field for four orders of magnitude of field (102 V/m-106 V/m) and, in the low field values, an ultra-high mobility greater than 20 m2/V s. We also study factors eventually leading to lowering of the transport velocity.

Discrete-breather-assisted charge transport along DNA-like molecular wires.

Mobile discrete breathers (MDBs) are here suggested as localized excitations underlying the trapping and transport of charged particles (electron or hole) along a DNA-like molecular wire with anchored ends such as attached to two electrodes. For illustration the Peyrard-Bishop-Dauxois-Holstein (PBDH) model is used. MDBs are excited by imposing appropriate disturbances to velocities or space positions of adjacent nucleotide pairs or lattice units of the wire. They can be directed either towards or away from the wire hence transverse to it. Numerical computer simulations show that a rather stable quasiparticle MDB + electron is possible when just a few of the nucleotide pairs near one of the fixed ends of the wire are excited. For the process to be effective, the charge, e.g., the electron, must be initially placed around the disturbed region of the molecule. Once the MDB + electron quasiparticle is formed it may be transported to quite a long distance up to ca. 60-70 nm in real space. Our findings show that such process does not demand intervention of an externally applied electric field and hence it may be considered as alternative to the polaron transport process.

Studies on Manfred Eigen's model for the self-organization of information processing.

In 1971, Manfred Eigen extended the principles of Darwinian evolution to chemical processes, from catalytic networks to the emergence of information processing at the molecular level, leading to the emergence of life. In this paper, we investigate some very general characteristics of this scenario, such as the valuation process of phenotypic traits in a high-dimensional fitness landscape, the effect of spatial compartmentation on the valuation, and the self-organized transition from structural to symbolic genetic information of replicating chain molecules. In the first part, we perform an analysis of typical dynamical properties of continuous dynamical models of evolutionary processes. In particular, we study the mapping of genotype to continuous phenotype spaces following the ideas of Wright and Conrad. We investigate typical features of a Schrödinger-like dynamics, the consequences of the high dimensionality, the leading role of saddle points, and Conrad's extra-dimensional bypass. In the last part, we discuss in brief the valuation of compartment models and the self-organized emergence of molecular symbols at the beginning of life.

Comment on "Direct linear term in the equation of state of plasmas".

In a recent paper [Phys. Rev. E 91, 013108 (2015)], Kraeft et al. criticize known exact results on the equation of state of quantum plasmas, which have been obtained independently by several authors. They argue about a difference in the definition of the direct two-body function Q(x), which appears in virial expansions of thermodynamical quantities, but Q(x) is not a measurable quantity in itself. Differences in definitions of intermediate quantities are irrelevant, and only differences in physical quantities are meaningful. Beyond Kraeft et al.'s broad statement that there is no agreement at order ρ(5/2) in the virial equation for the pressure, we show that their published results for this quantity are in fact in perfect agreement with previous existing expressions.

Compounds of paired electrons and lattice solitons moving with supersonic velocity.

We study the time evolution of two correlated electrons of opposite spin in an anharmonic lattice chain. The electrons are described quantum mechanically by the Hubbard model while the lattice is treated classically. The lattice units are coupled via Morse-Toda potentials. Interaction between the lattice and the electrons arises due to the dependence of the electron transfer-matrix element on the distance between neighboring lattice units. Localized configurations comprising a paired electron and a pair of lattice deformation solitons are constructed such that an associated energy functional is minimized. We investigate long-lived, stable pairing features. It is demonstrated that traveling pairs of lattice solitons serve as carriers for the paired electrons realizing coherent transport of the two correlated electrons. We also observe dynamical narrowing of the states, that is, starting from an initial double-peak profile of the electron probability distribution, a single-peak profile is adopted going along with enhancement of localization of the paired electrons. Interestingly, a parameter regime is identified for which supersonic transport of paired electrons is achieved.

Electron capture and transport mediated by lattice solitons.

We study electron transport in a one-dimensional molecular lattice chain. The molecules are linked by Morse interaction potentials. The electronic degree of freedom, expressed in terms of a tight binding system, is coupled to the longitudinal displacements of the molecules from their equilibrium positions along the axis of the lattice. More specifically, the distance between two sites influences in an exponential fashion the corresponding electronic transfer matrix element. We demonstrate that when an electron is injected in the undistorted lattice it causes a local deformation such that a compression results leading to a lowering of the electron's energy below the lower edge of the band of linear states. This corresponds to self-localization of the electron due to a polaronlike effect. Then, if a traveling soliton lattice deformation is launched a distance apart from the electron's position, upon encountering the polaronlike state it captures the latter dragging it afterwards along its path. Strikingly, even when the electron is initially uniformly distributed over the lattice sites a traveling soliton lattice deformation gathers the electronic amplitudes during its traversing of the lattice. Eventually, the electron state is strongly localized and moves coherently in unison with the soliton lattice deformation. This shows that for the achievement of coherent electron transport we need not start with the polaronic effect.

Temperature-dependent quantum pair potentials and their application to dense partially ionized hydrogen plasmas.

Extending our previous work [J. Phys. A 36, 5957 (2003)]], we present a detailed discussion of accuracy and practical applications of finite-temperature pseudopotentials for two-component Coulomb systems. Different pseudopotentials are discussed: (i) the diagonal Kelbg potential, (ii) the off-diagonal Kelbg potential, (iii) the improved diagonal Kelbg potential, (iv) an effective potential obtained with the Feynman-Kleinert variational principle, and (v) the "exact" quantum pair potential derived from the two-particle density matrix. For the improved diagonal Kelbg potential, a simple temperature-dependent fit is derived which accurately reproduces the "exact" pair potential in the whole temperature range. The derived pseudopotentials are then used in path integral Monte Carlo and molecular-dynamics (MD) simulations to obtain thermodynamical properties of strongly coupled hydrogen. It is demonstrated that classical MD simulations with spin-dependent interaction potentials for the electrons allow for an accurate description of the internal energy of hydrogen in the difficult regime of partial ionization down to the temperatures of about 60 000 K. Finally, we point out an interesting relationship between the quantum potentials and the effective potentials used in density-functional theory.

Mode transitions and wave propagation in a driven-dissipative Toda-Rayleigh ring.

A circular lattice (ring) of N electronic elements with Toda-type exponential interactions and Rayleigh-type dissipation is used to illustrate wave formation, propagation, and switching between wave modes. A methodology is provided to help controlling modes, thus allowing it to realize any of (N-1) different wave modes (including soliton-type modes) and the switching between them by means of a single control parameter.

Correction algorithm for finite sample statistics.

Assume in a sample of size M one finds M(i) representatives of species i with i = 1..N*. The normalized frequency pi* triple bond Mi/M, based on the finite sample, may deviate considerably from the true probabilities p(i). We propose a method to infer rank-ordered true probabilities r(i) from measured frequencies M(i). We show that the rank-ordered probabilities provide important informations on the system, e.g., the true number of species, the Shannon- and the Renyi-entropies.

Kramers problem in evolutionary strategies.

We calculate the escape rates of different dynamical processes for the case of a one-dimensional symmetric double-well potential. In particular, we compare the escape rates of a Smoluchowski process, i.e., a corresponding overdamped Brownian motion dynamics in a metastable potential landscape, with the escape rates obtained for a biologically motivated model known as the Fisher-Eigen process. The main difference between the two models is that the dynamics of the Smoluchowski process is determined by local quantities, whereas the Fisher-Eigen process is based on a global coupling (nonlocal interaction). If considered in the context of numerical optimization algorithms, both processes can be interpreted as archetypes of physically or biologically inspired evolutionary strategies. In this sense, the results discussed in this work are utile in order to evaluate the efficiency of such strategies with regard to the problem of surmounting various barriers. We find that a combination of both scenarios, starting with the Fisher-Eigen strategy, provides a most effective evolutionary strategy.

Rotational kinetics of absorbing dust grains in neutral gas.

We study the rotational and translational kinetics of massive particulates (dust grains) absorbing the ambient gas. Equations for microscopic phase densities are deduced resulting in the Fokker-Planck equation for the dust component. It is shown that although there is no stationary distribution, the translational and rotational temperatures of dust tend to certain values, which differ from the temperature of the ambient gas. The influence of the inner structure of grains on rotational kinetics is also discussed.

Entropy and local uncertainty of data from sensory neurons.

We present an empirical comparison between neural interspike interval sequences obtained from two different kinds of sensory receptors. Both differ in their internal structure as well as in the strength of correlations and the degree of predictability found in the respective spike trains. As a further tool in this context, we suggest the local uncertainty, assigning a well-defined predictability to individual spikes. The local uncertainty is demonstrated to reveal significant patterns within the interspike interval sequences, even when its overall structure is (almost) random. Our approach is based on the concept of symbolic dynamics and information theory.

Evolution of induced axial magnetization in a two-component magnetized plasma.

In this paper, the evolution of the induced axial magnetization due to the propagation of an electromagnetic (em) wave along the static background magnetic field in a two-component plasma has been investigated using the Block equation. The evolution process induces a strong magnetic anisotropy in the plasma medium, depending nonlinearly on the incident wave amplitude. This induced magnetic anisotropy can modify the dispersion relation of the incident em wave, which has been obtained in this paper. In the low frequency Alfven wave limit, this dispersion relation shows that the resulting phase velocity of the incident wave depends on the square of the incident wave amplitude and on the static background magnetic field of plasma. The analytical results are in well agreement with the numerically estimated values in solar corona and sunspots.

Dissipative Toda-Rayleigh lattice and its oscillatory modes.

A detailed theoretical and experimental analysis of the possible oscillatory regimes of the dissipative Toda-Rayleigh lattice system is provided. It is shown that the system has (N-1) oscillatory modes with different space-time scales and two rotatory modes. Using its analog electronic circuit implementation we also show with a simple and robust method how switching between modes occurs.

Statistical mechanics of canonical-dissipative systems and applications to swarm dynamics.

We develop the theory of canonical-dissipative systems, based on the assumption that both the conservative and the dissipative elements of the dynamics are determined by invariants of motion. In this case, known solutions for conservative systems can be used for an extension of the dynamics, which also includes elements such as the takeup/dissipation of energy. This way, a rather complex dynamics can be mapped to an analytically tractable model, while still covering important features of nonequilibrium systems. In our paper, this approach is used to derive a rather general swarm model that considers (a) the energetic conditions of swarming, i.e., for active motion, and (b) interactions between the particles based on global couplings. We derive analytical expressions for the nonequilibrium velocity distribution and the mean squared displacement of the swarm. Further, we investigate the influence of different global couplings on the overall behavior of the swarm by means of particle-based computer simulations and compare them with the analytical estimations.

Isentropes and Hugoniot curves for dense hydrogen and deuterium.

Multiple-shock experiments with fluid hydrogen have shown that a transition from semiconducting behavior to metal-like conductivity occurs at pressures (p) of about 140 GPa and temperatures (T) near 3000 K. We model the p-T pathway by Hugoniot curves (initial shock) and isentropes (subsequent shocks). For the calculation of these curves we apply an expression for the free energy developed recently for dense hydrogen and deuterium plasma in the regions of partial dissociation and partial ionization. Furthermore, we discuss the relations between Hugoniot curves, isentropes and the coexistence line of the plasma phase transition.

Stochastic multiresonance in a chaotic map with fractal basins of attraction.

Noise-free stochastic resonance in a chaotic kicked spin model at the edge of the attractor merging crisis is considered. The output signal reflects the occurrence of crisis-induced jumps between the two parts of the attractor. As the control parameter-the amplitude of the magnetic field pulses-is varied, the signal-to-noise ratio shows plateaus and multiple maxima, thus stochastic multiresonance is observed. It is shown that the multiresonance occurs due to a fractal structure of the precritical attractors and their basins. In the adiabatic approximation theoretical expression for the signal-to-noise ratio is derived, based on the theory of oscillations in average crisis-induced transient lifetimes. Numerical and theoretical results agree quantitatively just above the threshold for crisis and qualitatively in a wide range of the control parameter.

Self-oscillations in ring Toda chains with negative friction.

We study here the different modes of self-oscillations in ring Toda chains with Rayleigh-type negative friction. Assuming that at small friction the shape of self-oscillations is close to one of the known Toda solitonlike solutions we use analytical methods in combination with numerical ones for study of the self-oscillations. We calculate explicitly for a Toda chain consisting of N elements the N+1 different modes of self-oscillations. Among them two modes correspond to left and right rotations of the chain as a whole with a constant velocity Each of the other N-1 modes represents a combination of solitonlike oscillations and a rotation with a velocity depending on the mode number. Only for the mode corresponding to antiphase oscillations of the chain neighboring elements (such oscillations are possible for an even N) the constant component of the velocity is equal to zero.

Active Brownian particles with energy depots modeling animal mobility.

In the model of active motion studied here, Brownian particles have the ability to take up energy from the environment to store it in an internal depot and to convert internal energy into kinetic energy. Considering also internal dissipation, we derive a simplified model of active biological motion. For the take-up of energy two different examples are discussed: (i) a spatially homogeneous supply of energy, and (ii) the supply of energy at spatially localized sources (food centers). The motion of the particles is described by a Langevin equation which includes an acceleration term resulting from the conversion of energy. Dependent on the energy sources, we found different forms of periodic motion (limit cycles), i.e. periodic motion between 'nest' and 'food'. An analytic approximation allows the description of the stationary motion and the calculation of critical parameters for the take-up of energy. Finally, we derive an analytic expression for the efficiency ratio of energy conversion, which considers the take-up of energy, compared to (internal and external) dissipation.