Perturbation theory for large Stokes number particles in random velocity fields

We derive a perturbative approach to study, in the large inertia limit, the dynamics of solid particles in a smooth, incompressible and finite-time correlated random velocity field. We carry on an expansion in powers of the inverse square root of the Stokes number, defined as the ratio of the relaxation time for the particle velocities and the correlation time of the velocity field. We describe in this limit the residual concentration fluctuations of the particle suspension, and determine the contribution to the collision velocity statistics produced by clustering. For both concentration fluctuations and collision velocities, we analyze the differences with the compressible one-dimensional case.     

Diffusion in a collisional standard map

Test particle evaluation of the diffusion coefficient in the presence of magnetic field fluctuations and binary collisions is presented. Chaotic magnetic field lines originate from resonant magnetic perturbations (RMPs). To lowest order, charged particles follow magnetic field lines. Drifts and interaction (collisions) with other particles decorrelate particles from the magnetic field lines. We model the binary collision process by a constant collision frequency. The magnetic field configuration including perturbations on the integrable Hamiltonian part is such that the single particle motion can be followed by a collisional version of a Chirikov-Taylor (standard) map. Frequent collisions are allowed for. Scaling of the diffusion beyond the quasilinear and subdiffusive behaviour is investigated in dependence on the strength of the magnetic perturbations and the collision frequency. The appearance of the so called Rechester-Rosenbluth regime is verified. It is further shown that the so called Kadomtsev-Pogutse diffusion coefficient is the strong collisional limit of the Rechester-Rosenbluth formula. The theoretical estimates are supplemented by numerical simulations.     

Random Motion of a Charged Test Particle with a Constant Classical Velocity in a Spacetime with a Plane Boundary

We study the random motion of a charged test particle coupled to electromagnetic vacuum fluctuations near a perfectly reflecting plane boundary with a nonzero classical constant velocity in a direction parallel to the plane. We calculate the mean squared fluctuations in the velocity and position of the test particle taking into account both fluctuating electric and magnetic forces. Our results show that the influence of fluctuating magnetic fields is, in general, of the higher order than that caused by fluctuating electric fields and is thus negligible.     

Mesoscopic fluctuations of tunneling and cotunneling in quantum dots

Recent measurements of mesoscopic tunneling and cotunneling fluctuations in Coulomb blockaded ballistic quantum dots are presented. The statistics and parametric fluctuations (as a function of magnetic field) of Coulomb blockade peak heights are found to be consistent with random-matrix-theory predictions. Mesoscopic fluctuations of elastic cotunneling, measured in the valleys between blockade peaks, are also presented along with a semiclassical explanation of the observed enhancement of the magnetic field scale of cotunneling fluctuations compared to resonant tunneling fluctuations.     

Universal fluctuations in orbital diamagnetism

Bohr–van Leuween theorem has attracted the notice of physicists for more than 100 years. The theorem states about the absence of magnetisation in classical systems in thermal equilibrium. In this paper, we discuss about fluctuations of magnetic moment in classical systems. In recent years, this topic has been investigated intensively and it is not free from controversy. We have considered a system consisting of a single particle moving in a plane. A magnetic field is applied perpendicular to the plane. The system is in contact with a thermal bath. We have considered three cases: (a) particle moving in a homogeneous medium, (b) particle moving in a medium with space-dependent friction and (c) particle moving in a medium with space-dependent temperature. For all the three cases, the average magnetic moment and fluctuations in magnetic moment have been calculated. Average magnetic moment saturates to a finite value in the case of free particle but goes to zero when the particle is confined by a 2D harmonic potential. Fluctuations in magnetic moment shows universal features in the presence of arbitrary friction inhomogeneity. For this case, the system reaches equilibrium asymptotically. In the case of space-dependent temperature profile, the stationary distribution is non-Gibbsian and fluctuations deviate from universal value for the bounded system only.     

Anisotropic diffusion of a magnetically torqued ellipsoidal microparticle

We study the dynamics of an overdamped paramagnetic ellipsoidal particle confined above a plane and subjected to an external rotating magnetic field. Without magnetic forcing, the Brownian ellipsoid exhibits a crossover from a short time anisotropic diffusion to a long time isotropic one. Application of an external static or rotating magnetic field enables controlling and varying the crossover time depending on the field frequency and amplitude. We combine analytical results and numerical simulations in order to explore the diffusive properties of the forced ellipsoid.     

Role of nonlinear coupling and density fluctuations in magnetic-fluctuation-induced particle transport

Three-wave nonlinear coupling among spatial Fourier modes of density and magnetic fluctuations is directly measured in a magnetically confined toroidal plasma. Density fluctuations are observed to gain (lose) energy from (to) either equilibrium or fluctuating fields depending on the mode number. Experiments indicate that nonlinear interactions alter the phase relation between density and magnetic fluctuations, leading to strong particle transport.     

Two-dimensional motion of a parabolically confined charged particle in a perpendicular magnetic field

The classical two-dimensional motion of a parabolically confined charged particle in presence of a perpendicular magnetic is studied. The resulting equations of motion are solved exactly by using a mathematical method which is based on the introduction of complex variables. The two-dimensional motion of a parabolically charged particle in a perpendicular magnetic field is strikingly different from either the two-dimensional cyclotron motion, or the oscillator motion. It is found that the trajectory of a parabolically confined charged particle in a perpendicular magnetic field is closed only for particular values of cyclotron and parabolic confining frequencies that satisfy a given commensurability condition. In these cases, the closed paths of the particle resemble Lissajous figures, though significant differences with them do exist. When such commensurability condition is not satisfied, path of particle is open and motion is no longer periodic. In this case, after a sufficiently long time has elapsed, the open paths of the particle fill a whole annulus, a region lying between two concentric circles of different radii.     

Far Forward Scattering from Plasma Fluctuations Using a Detector Array and Coherent Signal Processing at 10 ?m

A far forward scattering experiment with a CO2 laser is described which uses a linear array of five photoconductive detector elements allowing the simultaneous measurement of the amplitude and phase of the scattered signals in one single shot. The direction of propagation of fluctuations can be determined from the spatial phase profile of the scattered light. The method described here is equivalent to a time resolved holographic diagnostic of electron density fluctuations. The plasma source used is a traveling wave experiment. Broad frequency and wavenumber spectra of electron density fluctuations associated with the excitation of strong nonlinear compressional Alfvén waves were measured. Two representative regimes of operation with low and high axial magnetic fields were investigated with wavenumber spectra ranging from k = 2 to 60 cm-1. The orientation of the array allowed observation of waves propagating either parallel or perpendicular to the magnetic field.     

Quantum quenches in a spinor condensate

We discuss the ordering of a spin-1 condensate when quenched from its paramagnetic phase to its ferromagnetic phase by reducing the magnetic field. We first elucidate the nature of the equilibrium quantum phase transition. Quenching rapidly through this transition reveals XY ordering either at a specific wave vector, or the "light-cone" correlations familiar from relativistic theories, depending on the end point of the quench. For a quench proceeding at a finite rate the ordering scale is governed by the Kibble-Zurek mechanism. The creation of vortices through growth of the magnetization fluctuations is also discussed. The long-time dynamics again depends on the end point, conserving the order parameter in a zero field, but not at a finite field, with differing exponents for the coarsening of magnetic order. The results are discussed in the light of a recent experiment by Sadler et al.     

Effects of magnetic field on the evolution of the wave function of a charged particle with an angular momentum

We have calculated the effect of a magnetic field on the evolution of angular momentum eigenfunctions of a charged particle. An additional harmonic potential is supplemented to trap the wave packet. We find the probability density of the wave function is oscillating in the radial direction with a time period determined by the strength of the effective harmonic potential. When the magnetic field is along the z direction, if the initial wave function is an eigenfunction of ${\hat{L}}_{z}$, the probability density of the particle remains axis-symmetric. While for the case of an eigenfunction of ${\hat{L}}_{x}$, it is anisotropic in the x−y plane and rotates with a time period inverse proportional to the strength of the external magnetic field. We also extend the results in a phenomenological way to the case with an external magnetic field that varies harmonically in time.     

Particle acceleration and magnetic field amplification in supernova shells: A nonlinear Monte Carlo model

A nonlinear model of particle spectra and nonadiabatic magnetic field amplification in supernova shells is presented. The effect super-diffusive particle propagation in the vicinity of a shock wave has on the spectra of accelerated particles and magnetic field fluctuations is studied in a Monte Carlo simulation.     

Perturbations of the Motion of a Charged Particle in a Noisy Magnetic Field

We consider deterministic and stochastic perturbations of the motion of a charged particle in a noisy magnetic field. The noise in the magnetic field leads to the mixing on the energy surfaces and allows to apply averaging principle. We describe long-time energy evolution and its metastable states for a given initial energy and a time scale.     

Simulation of induction at low magnetic Prandtl number

We consider the induction of a magnetic field in flows of an electrically conducting fluid at low magnetic Prandtl number and large kinetic Reynolds number. Using the separation between the magnetic and kinetic diffusive length scales, we propose a new numerical approach. The coupled magnetic and fluid equations are solved using a mixed scheme, where the magnetic field fluctuations are fully resolved and the velocity fluctuations at small scale are modeled using a large eddy simulation (LES) scheme. We study the response of a forced Taylor-Green flow to an externally applied field: topology of the mean induction and time fluctuations at fixed locations. The results are in remarkable agreement with existing experimental data; a global 1/f behavior at long times is also evidenced.     

Localized and delocalized motion of colloidal particles on a magnetic bubble lattice

We study the motion of paramagnetic colloidal particles placed above magnetic bubble domains of a uniaxial garnet film and driven through the lattice by external magnetic field modulation. An external tunable precessing field propels the particles either in localized orbits around the bubbles or in superdiffusive or ballistic motion through the bubble array. This motion results from the interplay between the driving rotating signal, the viscous drag force and the periodic magnetic energy landscape. We explain the transition in terms of the incommensurability between the transit frequency of the particle through a unit cell and the modulation frequency. Ballistic motion dynamically breaks the symmetry of the array and the phase locked particles follow one of the six crystal directions.     

Rapid alignment of velocity and magnetic field in magnetohydrodynamic turbulence

We show that local directional alignment of the velocity and magnetic field fluctuations occurs rapidly in magnetohydrodynamics for a variety of parameters and is seen both in direct numerical simulations and in solar wind data. The phenomenon is due to an alignment between magnetic field and gradients of either pressure or kinetic energy, and is similar to alignment of velocity and vorticity in Navier-Stokes turbulence. This rapid and robust relaxation process leads to a local weakening of nonlinear terms.     

Nonlinear conductance fluctuations in a mesoscopic ring

We study the conductance of a single particle on a ring subject to an arbitrary dc electric field, which is generated by a linearly in time increasing magnetic flux. The full quantum mechanical time development is calculated numerically by splitting the dynamics into independent consecutive Zener tunneling transitions and free motion on the ring. The Zener transitions occur near the avoided crossings of the bandstructure which arises from the adiabatic eigenstates as a function of flux in the presence of a static scattering potential. To account for the necessary dissipation the particle is coupled to an appropriate oscillator bath which is adjusted to give a strictly linear current-voltage characteristic for arbitrary voltage and temperature in the absence of scattering. Taking a single δ-function scatterer we find that the dissipative coupling eliminates the localization in energy space found previously and leads to a well defined resistive steady state. The scattering introduces reproducible fluctuations around the average Ohmic behavior which are caused by coherent backscattering. Their magnitude depends on the strength of the scattering potential and decays slowly for large voltages. The associated correlation energy is determined by the uncertainty of the eigenstates due to the dissipative bath coupling. Thermal averaging leads to a decrease of the conductance fluctuations proportional to T^?1.     

Quantum-classical transitions in Lifshitz tails with magnetic fields

We consider Lifshitz's model of a quantum particle subject to a repulsive Poissonian random potential and address various issues related to the influence of a constant magnetic field on the leading low-energy tail of the integrated density of states. In particular, we propose the magnetic analog of a 40-year-old landmark result of Lifshitz for short-ranged single-impurity potentials U. The Lifshitz tail is shown to change its character from purely quantum, through quantum classical, to purely classical with an increasing range of U. This systematics is explained by the increasing importance of the classical fluctuations of the particle's potential energy in comparison to the quantum fluctuations associated with its kinetic energy.     

Magnetic Field in a Screw Flow with Fluctuations

We consider the influence of fluctuations in a screw flow of a conducting liquid on the effect of magnetic field self-excitation; the solution of this problem is important for experimental realization of a turbulent dynamo. We propose a theoretical approach based on the solution of averaged equations obtained in the limit of a short correlation time. The applicability of this approach is confirmed by direct numerical simulation of the initial equations. We demonstrate the influence of the correlation of fluctuations on the dynamo effect threshold. It is shown that the solution of the mean-field equations differs from the solution based on direct numerical simulation for a finite correlation time. The advantages and disadvantages of the two approaches are estimates, as well as the importance of the discovered difference in the context of problems of magnetic field self-excitation. The influence of helicity and intermittency on the type of the solution is considered.     

Settling statistics of hard sphere particles

Direct imaging of settling, non-Brownian, hard sphere, particles allows measurement of particle occupancy statistics as a function of time and sampling volume dimension. Initially random relative particle number fluctuations, (2)>/ = 1, become suppressed, anisotropic, and dependent. Fitting to a simple Gaussian pair correlation model suggests a minute long ranged correlation leads to strong if not complete suppression of number fluctuations. Calflisch and Luke predict a divergence in velocity fluctuations with increasing sample volume size based on random (Poisson) statistics. Our results suggest this is not a valid assumption for settling particles.