Hysteresis from dynamically pinned sliding states

We report a surprising hysteretic behavior in the dynamics of a simple one-dimensional nonlinear model inspired by the tribological problem of two sliding surfaces with a thin solid lubricant layer in between. In particular, we consider the frictional dynamics of a harmonic chain confined between two rigid incommensurate substrates which slide with a fixed relative velocity. This system was previously found, by explicit solution of the equations of motion, to possess plateaus in parameter space exhibiting a remarkable quantization of the chain center-of-mass velocity (dynamic pinning) solely determined by the interface incommensurability. Starting now from this quantized sliding state, in the underdamped regime of motion and in analogy to what ordinarily happens for static friction, the dynamics exhibits a large hysteresis under the action of an additional external driving force F_ext. A critical threshold value F_c of the adiabatically applied force F_ext is required in order to alter the robust dynamics of the plateau attractor. When the applied force is decreased and removed, the system can jump to intermediate sliding regimes (a sort of “dynamic” stick-slip motion) and eventually returns to the quantized sliding state at a much lower value of F_ext. Hysteretic behavior is also observed as a function of the external driving velocity.     

Active transport and cluster formation on 2D networks

We introduce a model for active transport on inhomogeneous networks embedded in a diffusive environment which is motivated by vesicular transport on actin filaments. In the presence of a hard-core interaction, particle clusters are observed that exhibit an algebraically decaying distribution in a large parameter regime, indicating the existence of clusters on all scales. The scale-free behavior can be understood by a mechanism promoting preferential attachment of particles to large clusters. The results are compared with a diffusion-limited aggregation model and active transport on a regular network. For both models we observe aggregation of particles to clusters which are characterized by a finite size scale if the relevant time scales and particle densities are considered.     

Localization of quasiparticles in a disordered vortex

We study the diffusive motion of low-energy normal quasiparticles along the core of a single vortex in a dirty, type-II, s-wave superconductor. The physics of this system is argued to be described by a one-dimensional supersymmetric non-linear σ model, which differs from the σ models known for disordered metallic wires. For an isolated vortex and quasiparticle energies less than the Thouless energy E_Th, we recover the spectral correlations that are predicted by random matrix theory for the universality class C. We then consider the transport problem of transmission of quasiparticles through a vortex connected to particle reservoirs at both ends. The transmittance at zero energy exhibits a weak localization correction reminiscent of quasi-one-dimensional metallic systems with symmetry index β = 1. Weak localization disappears with increasing energy over a scale set by E_Th This crossover should be observable in measurements of the longitudinal heat conductivity of an ensemble of vortices under mesoscopic conditions. In the regime of strong localization, the localization length is shown to decrease by a factor of 8 as the quasiparticle energy goes to zero.     

Forward gluon production in hadron–hadron scattering with pomeron loops

We discuss new physical phenomena expected in particle production in hadron–hadron collisions at high energy, as a consequence of pomeron loop effects in the evolution equations for the color glass condensate. We focus on gluon production in asymmetric, ‘dilute–dense’, collisions: a dilute projectile scatters off a dense hadronic target, whose gluon distribution is highly evolved. This situation is representative for particle production in proton–proton collisions at forward rapidities (say, at LHC) and admits a dipole factorization similar to that of deep inelastic scattering (DIS). We show that at sufficiently large forward rapidities, where the pomeron loop effects become important in the evolution of the target wavefunction, gluon production is dominated by ‘black spots’ (saturated gluon configurations) up to very large values of the transverse momentum, well above the average saturation momentum in the target. In this regime, the produced gluon spectrum exhibits diffusive scaling, so like DIS at sufficiently high energy.     

Two interacting particles in a random potential: mapping onto one parameter localization theories without interaction

We consider two models for a pair of interacting particles in a random potential: (i) two particles with a Hubbard interaction in arbitrary dimensions and (ii) a strongly bound pair in one dimension. Establishing suitable correspondences we demonstrate that both cases can be described in terms familiar from theories of non-interacting particles. In particular, these two cases are shown to be controlled by a single scaling variable, namely the pair conductance g ₂. For an attractive or repulsive Hubbard interaction and starting from a certain effective Hamiltonian we derive a supersymmetric nonlinear σ model. Its action turns out to be closely related to the one found by Efetov for noninteracting electrons in disordered metals. This enables us to describe the diffusive motion of the particle pair on scales exceeding the oneparticle localization length L ₁ and to discuss the corresponding level statistics. For tightly bound pairs in one dimension, on the other hand, we follow early work by Dorokhov and exploit the analogy with the transfer matrix approach to quasi-1d conductors. Extending our study to M particles we obtain a M-particle localization length scaling like the Mth power of the one-particle localization length.     

Tagged Particle Diffusion in One-Dimensional Gas with Hamiltonian Dynamics

We consider a one-dimensional gas of hard point particles in a finite box that are in thermal equilibrium and evolving under Hamiltonian dynamics. Tagged particle correlation functions of the middle particle are studied. For the special case where all particles have the same mass, we obtain analytic results for the velocity auto-correlation function in the short time diffusive regime and the long time approach to the saturation value when finite-size effects become relevant. In the case where the masses are unequal, numerical simulations indicate sub-diffusive behaviour with mean square displacement of the tagged particle growing as t/ln(t) with time t. Also various correlation functions, involving the velocity and position of the tagged particle, show damped oscillations at long times that are absent for the equal mass case.     

Crossover from diffusive to ballistic transport in periodic quantum maps

We derive an expression for the mean square displacement (MSD) of a particle whose motion is governed by a uniform, periodic, quantum multi-baker map. The expression is a function of both time, t, and Planck’s constant, h, and allows a study of both the long time, t→∞, and semi-classical, h→0, limits taken in either order. We evaluate the expression using random matrix theory as well as numerically, and observe good agreement between both sets of results. The long time limit shows that particle transport is generically ballistic for any fixed value of Planck’s constant. However, for fixed times, the semi-classical limit leads to diffusion. The mean square displacement for non-zero Planck’s constant, and finite time, exhibits a crossover from diffusive to ballistic motion, with crossover time on the order of the inverse of Planck’s constant. We argue that these results are generic for a large class of 1D quantum random walks, similar to the quantum multi-baker, and that a sufficient condition for diffusion in the semi-classical limit is classically chaotic dynamics in each cell. Some connections between our work and the other literature on quantum random walks are discussed. These walks are of some interest in the theory of quantum computation.     

The localization transition of the two-dimensional Lorentz model

We investigate the dynamics of a single tracer particle performing Brownian motion in a two-dimensional course of randomly distributed hard obstacles. At a certain critical obstacle density, the motion of the tracer becomes anomalous over many decades in time, which is rationalized in terms of an underlying percolation transition of the void space. In the vicinity of this critical density the dynamics follows the anomalous one up to a crossover time scale where the motion becomes either diffusive or localized. We analyze the scaling behavior of the time-dependent diffusion coefficient D(t) including corrections to scaling. Away from the critical density, D(t) exhibits universal hydrodynamic long-time tails both in the diffusive as well as in the localized phase.     

Electron-electron interaction in the magnetoresistance of graphene

We investigate the magnetotransport in large area graphene Hall bars epitaxially grown on silicon carbide. In the intermediate field regime between weak localization and Landau quantization, the observed temperature-dependent parabolic magnetoresistivity is a manifestation of the electron-electron interaction. We can consistently describe the data with a model for diffusive (magneto)transport that also includes magnetic-field-dependent effects originating from ballistic time scales. We find an excellent agreement between the experimentally observed temperature dependence of magnetoresistivity and the theory of electron-electron interaction in the diffusive regime. We can further assign a temperature-driven crossover to the reduction of the multiplet modes contributing to electron-electron interaction from 7 to 3 due to intervalley scattering. In addition, we find a temperature-independent ballistic contribution to the magnetoresistivity in classically strong magnetic fields.     

Semiclassical approach for multiparticle production in scalar theories

We propose a semiclassical approach to calculate multiparticle cross sections in scalar theories, which have been strongly argued to have the exponential form exp(λ⁻¹ F(λn, ϵ)) in the regime λ → 0, λn, ϵ = fixed, where λ is the scalar coupling, n is the number of produced particles, and ϵ is the kinetic energy per final particle. The formalism is based on singular solutions to the field equation, which satisfy certain boundary and extremizing conditions. At low multiplicities and small kinetic energies per final particle we reproduce in the framework of this formalism the main perturbative results. We also obtain a lower bound on the tree-level cross section in the ultra-relativistic regime.     

Viscous compressible hydrodynamics at planes,spheres and cylinders with finite surface slip

We consider the linearized time-dependent Navier-Stokes equation including finite compressibility and viscosity. We first constitute the Green's function, from which we derive the flow profiles and response functions for a plane, a sphere and a cylinder for arbitrary surface slip length. For high driving frequency the flow pattern is dominated by the diffusion of vorticity and compression, for low frequency compression propagates in the form of sound waves which are exponentially damped at a screening length larger than the sound wave length. The crossover between the diffusive and propagative compression regimes occurs at the fluid's intrinsic frequency w \omega ∼ c ² r₀ \rho_{0}^{}/h \eta , with c the speed of sound, r₀ \rho_{0}^{} the fluid density and h \eta the viscosity. In the propagative regime the hydrodynamic response function of spheres and cylinders exhibits a high-frequency resonance when the particle size is of the order of the sound wave length. A distinct low-frequency resonance occurs at the boundary between the propagative and diffusive regimes. Those resonant features should be detectable experimentally by tracking the diffusion of particles, as well as by measuring the fluctuation spectrum or the response spectrum of trapped particles. Since the response function depends sensitively on the slip length, in principle the slip length can be deduced from an experimentally measured response function.     

Size analysis and magnetic structure of nickel nanoparticles

The size distribution of an assembly of fcc nickel nanoparticles is studied by measuring the temperature dependent magnetization curves fitted by a uniform model and a core-shell model, both based on the Langevin function for superparamagnetism with a log-normal particle volume distribution. The uniform model fits lead to a spontaneous magnetization M_s much smaller than the M_s for bulk nickel and to particle sizes larger than the ones evaluated by transmission electron microscopy; the core-shell model fits can result in a correct size distribution but the M_s in the core becomes significantly greater than the M_s for bulk nickel. It is concluded that there is a core-shell magnetic structure in nickel particles. Although the enhanced M_s in the core may be related to the narrowing of the energy bands of 3d electrons in small fcc nickel particles, the modeling values of M_s are over large compared with previous calculations on nickel clusters of different structures, which implies possible existence of an exchange interaction between the core and the shell, which is not considered in the simple core-shell model.     

Fluctuation study of pionisation in ultrarelativistic nucleus-nucleus interaction

The scaled factorial moments and the multifractal moments have been investigated in different??-intervals to study the dynamical fluctuation of pions produced in 200 AGeV³²S-Ag/Br interaction. In order to investigate the detail characteristics of intermittency behaviour, theF-moments are extracted up to the eighth order of moments in differentM-intervals. The analysis indicates a non-thermal phase transition and different regime of particle production during the hadronisation process.     

Momentum distributions in the nucleus

The nuclear form factor F(q) and one particle momentum distribution p(q) can be shown to have a power law decrease for large momenta. For the form factor F(q) we show that it is q/A that must be large for this asymptotic behavior to be important. For only q large the form factor, in a simple model, is shown to decrease exponentially in q. A similar behavior for p(q) is proposed.     

Quantum ohmic dissipation: Particle on a one-dimensional periodic lattice

We investigate the dynamics of a particle on a periodic lattice, coupled to phonons with ohmic dissipation. At T = 0 a symmetry breaking appears, which corresponds to a transition between a localized and a delocalized regime. For T > 0 we recover a diffusive motion for which the diffusion coefficient is computed.     

Fluctuation study of pionisation in ultrarelativistic nucleus-nucleus interaction

The scaled factorial moments and the multifractal moments have been investigated in differentη-intervals to study the dynamical fluctuation of pions produced in 200 AGeV³²S-Ag/Br interaction. In order to investigate the detail characteristics of intermittency behaviour, theF-moments are extracted up to the eighth order of moments in differentM-intervals. The analysis indicates a non-thermal phase transition and different regime of particle production during the hadronisation process.     

Light scattering by an inhomogeneous spherical particle with intermediate layers

A model of a radially inhomogeneous multilayer spherical particle with a continuously varying refractive index in the intermediate layers between the shells of the particle and between the particle and the surroundings is proposed. Such a particle scatters light much like a dust particle with a rough and ragged surface of the layers, which is simulated with the help of the discrete dipole approximation method. For dust particles whose surface shape deviates from the spherical one, the refractive index profile and the behavior of the extinction Q _ext(x) and absorption Q _abs(x) efficiency factors with increasing thickness of the intermediate layers are studied. Properties of such particles in dependence on the number of layers are also studied. It is revealed that, as the number of shells increases, the order of the relative position of substances ceases to play a role, as is also the case for a multilayer spherical particle without intermediate layers. It is shown that, upon an increase in the number of shells at the same percentages of substances in the intermediate layers, the difference of the values of Q _ext(x) and Q _abs(x) from the corresponding values calculated with the model without intermediate layers decreases.     

Unified model of the temperature quenching of narrow-line and broad-band emissions

Temperature quenchings of narrow-line and broad-band emissions are pictured through the quantum-mechanical single-configurational-coordinate model. The model is taken in the thermal-Condon approximation with the overlap integrals evaluated through the Manneback recursion formulas. The multiple activation energies m?ω_υ to the initial vibrational states produce an increase in the non-radiative rate poorly described, in general, by a single activation energy. The model applies to energy parabolas with large Franck- Condon offset and a consequent crossover and to energy parabolas with small Franck- Condon offset and no relevant crossover. For large offset, the model gives approximately Mott's single-activation-energy rate A_M exp(-E_X/kT) for upward transitions but faster rates poorly described by a single activation energy for downward transitions. For small offset, the model gives approximately Kiel's multiphonon-emission rate A_K?^p[1+〈m〉_υ]^p for downward transitions. A numerical matrix method is described which can handle all cases and which explicitly exhibits the multiple activation energies m?ω_υ in every case. This method is used to work out examples of the various types of quenchings which can occur: a fast bottom crossover, an outside crossover, small-offset multiphonon emission, a tunneling crossover, and two-step quenchings through a higher offset state.