Activated drift motion of a classical particle with a dynamical pinning effect

A one dimensional trap model for a thermally activated classical particle is introduced to simulate driven dynamics in presence of “ageing” effects. The depth of each trap increases with the time elapsed since the particle has fallen into it. The consequences of this dynamical pinning are studied, and velocity-force characteristics are numerically obtained. A special attention is paid to the situation where the particle is pulled with a spring to ensure a finite average velocity. In the low velocity regime, the presence of a broad distribution of trapping times leads to suppression of linear response, replaced by a threshold or by sublinear dynamics. A regime of strong fluctuations is obtained when the particle is driven at intermediate velocities. Received: 12 December 1997 / Accepted: 25 February 1998     

Fractional Dynamics of Relativistic Particle

Fractional dynamics of relativistic particle is discussed. Derivatives of fractional orders with respect to proper time describe long-term memory effects that correspond to intrinsic dissipative processes. Relativistic particle subjected to a non-potential four-force is considered as a nonholonomic system. The nonholonomic constraint in four-dimensional space-time represents the relativistic invariance by the equation for four-velocity u _μ u ^μ +c ²=0, where c is a speed of light in vacuum. In the general case, the fractional dynamics of relativistic particle is described as non-Hamiltonian and dissipative. Conditions for fractional relativistic particle to be a Hamiltonian system are considered.     

Brownian motion near a liquid-like membrane

The dynamics of a tracer molecule near a fluid membrane is investigated, with particular emphasis given to the interplay between the instantaneous position of the particle and membrane fluctuations. It is found that hydrodynamic interactions creates memory effects in the diffusion process. The random motion of the particle is then shown to cross over from a “bulk” to a “surface” diffusive mode, in a way that crucially depends on the elastic properties of the interface.     

Entanglement and the process of measuring the position of a quantum particle

We explore the entanglement-related features exhibited by the dynamics of a composite quantum system consisting of a particle and an apparatus (here referred to as the “pointer”) that measures the position of the particle. We consider measurements of finite duration, and also the limit case of instantaneous measurements. We investigate the time evolution of the quantum entanglement between the particle and the pointer, with special emphasis on the final entanglement associated with the limit case of an impulsive interaction. We consider entanglement indicators based on the expectation values of an appropriate family of observables, and also an entanglement measure computed on particular exact analytical solutions of the particle–pointer Schrödinger equation. The general behavior exhibited by the entanglement indicators is consistent with that shown by the entanglement measure evaluated on particular analytical solutions of the Schrödinger equation. In the limit of instantaneous measurements the system’s entanglement dynamics corresponds to that of an ideal quantum measurement process. On the contrary, we show that the entanglement evolution corresponding to measurements of finite duration departs in important ways from the behavior associated with ideal measurements. In particular, highly localized initial states of the particle lead to highly entangled final states of the particle–pointer system. This indicates that the above mentioned initial states, in spite of having an arbitrarily small position uncertainty, are not left unchanged by a finite-duration position measurement process.     

Gravitational geometric phase in the presence of torsion

We investigate the relativistic and non-relativistic quantum dynamics of a neutral spin-1/2 particle subject to an external electromagnetic field in the presence of a cosmic dislocation. We analyze the explicit contribution of the torsion in the geometric phase acquired in the dynamics of this neutral spinorial particle. We discuss the influence of the torsion in the relativistic geometric phase. Using the Foldy–Wouthuysen approximation, the non-relativistic quantum dynamics is studied and the influence of the torsion on the Aharonov–Casher and He–McKellar–Wilkens effects are discussed. An erratum to this article can be found at     

On the Mean-Field Limit of Bosons with Coulomb Two-Body Interaction

In the mean-field limit the dynamics of a quantum Bose gas is described by a Hartree equation. We present a simple method for proving the convergence of the microscopic quantum dynamics to the Hartree dynamics when the number of particles becomes large and the strength of the two-body potential tends to 0 like the inverse of the particle number. Our method is applicable for a class of singular interaction potentials including the Coulomb potential. We prove and state our main result for the Heisenberg- picture dynamics of “observables”, thus avoiding the use of coherent states. Our formulation shows that the mean-field limit is a “semi-classical” limit.     

About bursty behaviour, coherent structures, wide scrape-off layer and large parallel flows in the edge of the Tore Supra tokamak

We present the measurements of plasma characteristics in the scrape-off layer (SOL) of the Tore Supra tokamak performed by means of reciprocating Langmuir probe. The probe is inserted into the machine from top. As the radial distance from last closed flux surface (LCFS) increases, ion saturation current exhibits stronger bursty character and its probability density function becomes increasingly skewed towards positive values. At the same time, burst duration and inter-burst time increase dramatically. We explain this phenomenon by radial propagation and dynamics of the ensemble of coherent turbulent structures of different size. The results of two-dimensional fluid modelling based of flux-driven interchange instability mechanism are in excellent agreement with experimental results. We obtained clear experimental evidence that most of the coherent structures are formed in poloidally localized region of the SOL around the outboard midplane. If the probe is magnetically connected to this region, the SOL is very wide and we detect bursty behaviour in the far SOL. On the other hand, if the probe is not magnetically connected to the outboard midplane region (magnetic field lines are intercepted by the outboard limiter), then the SOL is very thin and bursty behaviour is much less prominent. Detection of bursty behaviour in the far SOL is correlated with existence of wide SOL pointing on important role of bursty transport by means of coherent turbulent structures in establishing the width of the SOL in tokamaks. The measurements of parallel flow in the SOL shows that plasma particle radial flux coming from confinement region to the SOL is mostly poloidally localized around the outboard midplane. Our estimations show that more than 80% of plasma particle radial flux is coming from confinement region to the SOL in poloidally localized region — approximately ±15° — around the outboard midplane. Presented at the Workshop “Electric Fields, Structures and Relaxation in Edge Plasmas”, Roma, Italy, June 26–27, 2006.     

The kinetics of homogeneous nucleation of silver nanoparticles stabilized by polymers

The formation of Ag nanoparticles synthesized by homogeneous nucleation, stabilized by polymers (PVA and PVP) was monitored by UV–Vis spectrophotometry and transmission electron microscopy. Our aim was to differentiate between the two main phases of particle formation, i.e. nucleation and growth and to characterize their rates with the help of appropriate kinetic equations. Time resolved spectrophotometric measurements revealed that particle formation is an autocatalytic process: a slow, continuous nucleation phase (3–5 min) is followed by a rapid, autocatalytic growth phase where the maximal particle size is 5–7 nm. By freezing the reaction mixture, the process of particle growth can be followed from 5 to 40 min on TEM pictures. The first order rate constants were calculated and they are strongly depend on the polymer concentration. If the growing particles are attached by PEI to the surface of a solid support, the formation of silver nanoparticles can also be followed by atomic force microscopy (AFM) and we can control the particle growth on mica surface. The cross section analysis of the pictures show, that the particle growing process can be also monitored at solid–liquid interface.     

Mixing Properties for Mechanical Motion¶of a Charged Particle in a Random Medium

We study a one-dimensional semi-infinite system of particles driven by a constant positive force F which acts only on the leftmost particle of mass M, called the heavy particle (the h.p.), and all other particles are mechanically identical and have the same mass m < M. Particles interact through elastic collisions. At initial time all neutral particles are at rest, and the initial measure is such that the interparticle distances ξ _i are i.i.d. r.v. Under conditions on the distribution of ξ which imply that the minimal velocity obtained by each neutral particle after the first interaction with the h.p. is bigger than the drift of an associated Markovian dynamics (in which each neutral particle is annihilated after the first collision) we prove that the dynamics has a strong cluster property, and as a consequence, we prove existence of the discrete time limit distribution for the system as seen from the first particle, a ψ-mixing property, a drift velocity, as well as the central limit theorem for the tracer particle. Received: 22 March 2000 / Accepted: 8 December 2000     

An analytic perturbation approach for classical spinning particle dynamics

A perturbation method to analytically describe the dynamics of a classical spinning particle, based on the Mathisson–Papapetrou–Dixon (MPD) equations of motion, is presented. By a power series expansion with respect to the particle’s spin magnitude, it is shown how to obtain in general form an analytic representation of the particle’s kinematic and dynamical degrees of freedom that is formally applicable to infinite order in the expansion. Within this formalism, it is possible to identify a classical analogue of radiative corrections to the particle’s mass and spin due to spin–gravity interaction. The robustness of this approach is demonstrated by showing how to explicitly compute the first-order momentum and spin tensor components for arbitrary particle motion in a general space–time background. Potentially interesting applications based on this perturbation approach are outlined.     

Noncommutative gravity, a ‘no strings attached’ quantum-classical duality, and the cosmological constant puzzle

There ought to exist a reformulation of quantum mechanics which does not refer to an external classical spacetime manifold. Such a reformulation can be achieved using the language of noncommutative differential geometry. A consequence which follows is that the ‘weakly quantum, strongly gravitational’ dynamics of a relativistic particle whose mass is much greater than Planck mass is dual to the ‘strongly quantum, weakly gravitational’ dynamics of another particle whose mass is much less than Planck mass. The masses of the two particles are inversely related to each other, and the product of their masses is equal to the square of Planck mass. This duality explains the observed value of the cosmological constant, and also why this value is nonzero but extremely small in Planck units. Second Award in the 2008 Essay Competition of the Gravity Research Foundation.     

Velocity measurement of a settling sphere

We study experimentally the motion of a solid sphere settling under gravity in a fluid at rest. The particle velocity is measured with a new acoustic method. Variations of the sphere size and density allow measurements at Reynolds numbers, based on limit velocity, between 40 and 7 000. At all Reynolds numbers, our observations are consistent with the presence of a memory-dependent force acting on the particle. At short times it has a t ^-1/2 behaviour as predicted by the unsteady Stokes equations and as observed in numerical simulations. At long times, the decay of the memory (Basset) force is better fitted by an exponential behaviour. Comparison of the dynamics of spheres of different densities for the same Reynolds number show that the density is an important control parameter. Light spheres show transitory oscillations at Re∼ 400, but reach a constant limit speed. Received 12 April 2000 and Received in final form 13 July 2000     

A Geometrical Representation of Entanglement as Internal Constraint

We study a system of two entangled spin 1/2, were the spin's are represented by a sphere model developed within the hidden measurement approach which is a generalization of the Bloch sphere representation, such that also the measurements are represented. We show how an arbitrary tensor product state can be described in a complete way by a specific internal constraint between the ray or density states of the two spin 1/2. We derive a geometrical view of entanglement as a “rotation” and “stretching” of the sphere representing the states of the second particle as measurements are performed on the first particle. In the case of the singlet state entanglement can be represented by a real physical constraint, namely by means of a rigid rod.     

Phase propagation of localized surface plasmons probed by time-resolved photoemission electron microscopy

In combining time-resolved two-photon photoemission (TR-2PPE) and photoemission electron microscopy (PEEM) the ultra-fast dynamics of collective electron excitations in silver nanoparticles (localized surface plasmons – LSPs) is probed at fs and nm resolution. Here we demonstrate that the sampling of the LSP dynamics by means of time-resolved PEEM enables detailed insight into the propagation processes associated with these excitations. In phase-integrated as well as phase-resolved measurements we observe spatio-temporal modulations in the photoemission yield from a single nanoparticle. These modulations are assigned to local variations in the electric near field as a result of the phase propagation of a plasmonic excitation through the particle. Furthermore, the control of the phase between the fs pump and probe laser pulses used for these experiments can be utilized for an external manipulation of the nanoscale electric near-field distribution at these particles. PACS 78.47.+p; 78.67.Bf; 79.60.-i; 73.20.Mf     

Glimmers of a Pre-geometric Perspective

Spacetime measurements and gravitational experiments are made by using objects, matter fields or particles and their mutual relationships. As a consequence, any operationally meaningful assertion about spacetime is in fact an assertion about the degrees of freedom of the matter (i.e. non gravitational) fields; those, say for definiteness, of the Standard Model of particle physics. As for any quantum theory, the dynamics of the matter fields can be described in terms of a unitary evolution of a state vector in a Hilbert space. By writing the Hilbert space as a generic tensor product of “subsystems” we analyse the evolution of a state vector on an information theoretical basis and attempt to recover the usual spacetime relations from the information exchanges between these subsystems. We consider generic interacting second quantized models with a finite number of fermionic degrees of freedom and characterize on physical grounds the tensor product structure associated with the class of “localized systems” and therefore with “position”. We find that in the case of free theories no spacetime relation is operationally definable. On the contrary, by applying the same procedure to the simple interacting model of a one-dimensional Heisenberg spin chain we recover the tensor product structure usually associated with “position”. Finally, we discuss the possible role of gravity in this framework.     

Nelsonian mechanics revisited

In de Broglie and Bohm’s pilot-wave theory, as is well known, it is possible to consider alternative particle dynamics while still preserving the |ψ|² distribution. I present the analogous result for Nelson’s stochastic theory, thus characterising the most general diffusion processes that preserve the quantum equilibrium distribution, and discuss the analogy with the construction of the dynamics for Bell’s beable theories. I briefly comment on the problem of convergence to |ψ|² and on possible experimental constraints on the alternative dynamics.     

On the determination of the particle interaction potential in a dusty plasma from a pair correlation function

The effect of confinement on the pair correlation function of microparticles whose interaction is described by a screened Coulomb potential (Yukawa potential) has been investigated by the molecular dynamics simulations. The data are used to solve the inverse problem of the reconstruction of the particle interaction potential. It has been shown that such a reconstruction is likely impossible for a strongly nonideal system (with the coupling parameter Γ > 1). For systems with Γ ≤ 1, reconstruction is possible if confinement does not lead to the strong inhomogeneity of the system of microparticles.     

Transport induced by large scale convective structures in a dipole-confined plasma

Convective structures characterized by E×B motion are observed in a dipole-confined plasma. Particle transport rates are calculated from density dynamics obtained from multipoint measurements and the reconstructed electrostatic potential. The calculated transport rates determined from the large-scale dynamics and local probe measurements agree in magnitude, show intermittency, and indicate that the particle transport is dominated by large-scale convective structures.     

An approach to introducing fractional integro-differentiation in classical electrodynamics

Analogs for Maxwell’s equations with fractional derivatives are obtained using the concepts of an effective current and the velocity of a charged particle in a medium. The calibration invariance is considered and a diffusion-wave equation is found and analyzed for scalar and vector potentials. It is shown that the stochastic nature of charged particle motion in a medium influences the dynamics of an electromagnetic field.     

Brownian motion in a solitary potential well in a bounded solid structure

The motion of a heavy Brownian particle in a low-dimensional bounded solid structure under the effect of a phonon’s excitation fluctuations is considered. Because of the finiteness of the system, the fluctuation spectrum has zero spectral density at zero frequency. The effect of this kind of noise, which is conditionally called “green” noise, is studied both analytically by using the averaging method and numerically on the basis of predictor-corrector algorithms. The effective potential is introduced, and its form is shown to govern the particle dynamics. Considering a Gaussian potential well (a trap) as an example, it is demonstrated that green noise leads to abrupt phase transitions in the system as a result of very small parameter variations (a catastrophe-type effect). The results are compared with the case of white noise in an unbounded structure. From numerical calculations, it follows that the boundedness of the structure, which changes the noise spectrum, favors a considerable increase in the lifetime of the particle in the trap.