Rearrangement collisions for high energies (linear model)

The high energy behaviour of the cross section for particle exchange in a three particle collision is investigated for arbitrary masses and a rather general class of potentials. For convenience we use a linear model. It is shown that in general the first and second Born approximation provide the leading terms for high energies. If the exchanged mass is “small” the interaction between the two heavy masses cancels. The wave treatment and the impact parameter version give identical results. For particular mass ratios either the first or the second Born approximation provides the leading term. Then even backscattering can be dominant. The high energy results agree with the asymptotic expansion for two exactly solvable cases.     

Initial data for two Kerr-like black holes

We prove the existence of a family of initial data for the Einstein vacuum equation which can be interpreted as the data for two Kerr-like black holes in an arbitrary location and with spins pointing in arbitrary directions. We also provide a method to compute them. If the mass parameter of one of the black holes is zero, then this family reduces exactly to the Kerr initial data. The existence proof is based on a general property of the Kerr metric which can be used in other constructions as well. Further generalizations are also discussed.     

New critical matrix models and generalized universality

We study a class of one-matrix models with an action containing nonpolynomial terms. By tuning the coupling constants in the action to criticality we obtain that the eigenvalue density vanishes as an arbitrary real power at the origin, thus defining a new class of multicritical matrix models. The corresponding microscopic scaling law is given and possible applications to the chiral phase transition in QCD are discussed. For generic coupling constants off-criticality we prove that all microscopic correlation functions at the origin of the spectrum remain in the known Bessel universality class. An arbitrary number of Dirac mass terms can be included and the corresponding massive universality is maintained as well. We also investigate the critical behavior at the edge of the spectrum: there, in contrast to the behavior at the origin, we find the same critical exponents as derived from matrix models with a polynomial action.     

Thermodynamic anomalies in the presence of general linear dissipation: from the free particle to the harmonic oscillator

A free particle coupled to a heat bath can exhibit a number of thermodynamic anomalies like a negative specific heat, reentrant classicality or a nonmonotonic entropy. These low-temperature phenomena are expected to be modified at very low temperatures where finite-size effects associated with the discreteness of the energy spectrum become relevant. In this paper, we explore in which form the thermodynamic anomalies visible in the specific heat and the entropy of the free damped particle appear for a damped harmonic oscillator. Since the discreteness of the oscillator’s energy spectrum is fully accounted for, the results are valid for arbitrary temperatures. As expected, they are in agreement with the third law of thermodynamics and indicate how the thermodynamic anomalies of the free damped particle can be reconciled with the third law. Particular attention is paid to the transition from the harmonic oscillator to the free particle when the limit of the oscillator frequency to zero is taken.     

Wegner Estimate and Anderson Localization for Random Magnetic Fields

We consider a two dimensional magnetic Schrödinger operator with a spatially stationary random magnetic field. We assume that the magnetic field has a positive lower bound and that it has Fourier modes on arbitrarily short scales. We prove the Wegner estimate at arbitrary energy, i.e. we show that the averaged density of states is finite throughout the whole spectrum. We also prove Anderson localization at the bottom of the spectrum.     

Short-wave excitations in non-local Gross-Pitaevskii model

We show that a non-local form of the Gross-Pitaevskii equation describes not only long-wave excitations, but also the short-wave ones in Bose-condensate systems. At certain parameter values, the excitation spectrum mimics the Landau spectrum of quasi-particle excitations in superfluid helium with roton minimum. The excitation wavelength, at which the roton minimum exists, is close to the inter-particle interaction range. We determine how the roton gap and the effective roton mass depend on the interaction potential parameters, and show that the existence domain of the spectrum with a roton minimum is reduced if one accounts for an inter-particle attraction.     

Particle structure analysis of soliton sectors in massive lattice field theories

We discuss the particle structure in the soliton sectors of massive lattice field theories by means of convergent cluster expansions. In several models we prove that the soliton field operator with lowest charge couples the vacuum to a stable one-particle state, in a suitable region of the coupling parameter space. Both local and stringlike solitons are analyzed. We also show that the mass of the local soliton equals the surface tension.     

Collective oscillations of the magnetic moments of a chain of spherical magnetic nanoparticles with uniaxial magnetic anisotropy

Magnetic particles moving freely in a fluid can organize dense phases (3D clusters or linear chains). We analyze the spectrum of magnetic oscillations of a chain of spherical magnetic particles taking into account the magnetic anisotropy of an individual particle for an arbitrary relation between the anisotropy energy and the energy of the dipole interaction of particles. For any relation between these energies, the spectrum contains three branches of collective oscillations: a high-frequency branch and a weakly split doublet of low-frequency branches. The frequency of the high-frequency branch is determined by a stronger interaction, while the frequencies of the low-frequency branches are determined by the weakest interaction. Accordingly, the dispersion is maximal for oscillations formed by the dipole-dipole interaction of particles, which have high frequencies in the case of a strong dipole interaction or low frequencies in the case of a strong anisotropy.     

Decoherence and Bare Mass Induced by Nonconformal Metric Fluctuations

The effects, upon the Klein–Gordon field, of nonconformal stochastic metric fluctuations, are analyzed. It will be shown that these fluctuations allow us to consider an effective mass, i.e., the mass detected in a laboratory is not the parameter appearing in the Klein–Gordon equation, but a function of this parameter and of the fluctuations of the metric. In other words, in analogy to the case of a nonrelativistic electron in interaction with a quantized electromagnetic field, we may speak of a bare mass, where the observed mass shows a dependence upon the stochastic terms included in the metric. Afterwards, we prove, resorting to the influence functional, that the energy–momentum tensor of the Klein–Gordon field inherites this stochastic behavior, and that this feature provokes decoherence upon a particle immersed in the region where this tensor is present.     

Monte Carlo simulation of lower hybrid current drive in tokamaks

In this paper, we present a method for noninductive current drive studies based on three-dimensional simulation of test particle orbits. A Monte Carlo momentum diffusion operator is developed to model the wave-particle interaction. The scheme can be utilized in studies of current drive efficiency as well as in examining the current density profiles caused by waves with a finite parallel wave number spectrum and a nonuniform power deposition profile in a toroidal configuration space of arbitrary shape. Calculations performed with a uniform power deposition profile of lower hybrid waves for axisymmetric magnetic configurations having different aspect ratios and poloidal cross-section shape confirm the semianalytic estimates for the current drive efficiency based on the solutions of the flux surface averaged Fokker-Planck equation for configurations with circular poloidal cross section. The consequences of the combined effect of radial diffusion, magnetic trapping and radially nonhomogeneous power deposition and background plasma parameter profiles are investigated     

The effects of self-interaction on constructing relativistic point particles

We introduce a framework for studying the effects of self-interaction on the construction of point particle initial data in General Relativity. Within this framework we rigorously prove the vanishing mass result of Arnowitt et al. (Phys Rev Lett 4: 375, 1960) regarding point sources. We identify a geometric structure and a scaling parameter that allow one to determine, by controlling the effects of self-interaction, when one does or does not obtain a non-zero mass.     

Correlation inequalities for antiferromagnets

We prove several correlation inequalities for a class of antiferromagnets with pair interaction and arbitrary fields. To do this we use the Ginibre-Percus method of double variables.     

Superdiffusive Behaviour of a Passive Ornstein–Uhlenbeck Tracer in a Turbulent Shear Flow

In this paper, we are interested in the study of the diffusion of a passive particle with positive mass by a divergence free velocity field. We consider here the very simple turbulent shear flow case, in which we will prove the superdiffusive behaviour of the motion for large enough values of the energy spectrum of the velocity field. For small values, the proof of the diffusive behaviour of the model is also new, and it is shown that this diffusion is strictly greater than the one obtained with a non-massive particle. One interesting point to insist on is that we are able to obtain explicit hydrodynamic equations without even having the stationary measure of the studied processes     

Electrostatic fluctuations in nonequilibrium plasmas with particle collisions

We present a method for calculation of plasma fluctuations in a nonequilibrium plasma with stable particle distribution functions. The method takes into account particle collisions and collective particle interactions which affect the collision process. In contrast to the known approaches, our method makes no reference to a specific form of the collision integrals and distribution functions. Using the developed method, we calculate the high-frequency spectrum of the electric field fluctuations in a collisional plasma with arbitrary particle distribution functions.     

Numerical Analysis of Unsteady Magneto-Biphase Williamson Fluid Flow with Time Dependent Magnetic Field

Numerical investigation of the dusty Williamson fluid with the dependency of time has been done in current disquisition. The flow of multiphase liquid/particle suspension saturating the medium is caused by stretching of porous surface. The influence of magnetic field and heat generation/absorption is observed. It is assumed that particle has a spherical shape and distributed uniformly in fluid matrix. The unsteady two-dimensional problems are modeled for both fluid and particle phase using conservation of mass, momentum and heat transfer. The finalized model generates the non-dimensioned parameters, namely Weissenberg number, unsteadiness parameter, magnetic parameter,heat generation/absorption parameter, Prandtl number, fluid particle interaction parameter, and mass concentration parameters. The numerical solution is obtained. Locality of skin friction and Nusselt number is deliberately focused to help of tables and graphs. While inferencing the current article it is clearly observed that increment of Williamson parameter, unsteadiness parameter, magnetic parameter, volume fraction parameter, and mass concentration parameter reduces the velocity profile of fluid and solid particles as well. And increment of Prandtl number, unsteadiness parameter,volume fraction parameter, and mass concentration parameter reduces the temperature profile of fluid and solid particles as well.     

Ring diagrams,Landau parameters,pion condensation and the binding energy of nuclear matter

We calculate all direct π-exchange ring diagrams to arbitrary orders in nuclear matter. Our model incorporates intermediate Δ(1236) resonances, correlations, ρ- as well as π-meson exchange and mesonic form factors. We find that the convergence of the diagram summation is governed by two quantities which have an immediate physical interpretation: the Landau parameter G'₀ and the threshold for pion condensation. The contribution to the energy of nuclear matter from terms of third and higher order is 2 MeV/particle (repulsion) at normal density, with a strong density dependence.     

A Mechanical Model of Brownian Motion for One Massive Particle Including Slow Light Particles

We provide a connection between Brownian motion and a classical mechanical system. Precisely, we consider a system of one massive particle interacting with an ideal gas, evolved according to non-random mechanical principles, via interaction potentials, without any assumption requiring that the initial velocities of the environmental particles should be restricted to be “fast enough”. We prove the convergence of the (position, velocity)-process of the massive particle under a certain scaling limit, such that the mass of the environmental particles converges to 0 while the density and the velocities of them go to infinity, and give the precise expression of the limiting process, a diffusion process.     

Spontaneous photon emission from a non-relativistic free charged particle in collapse models: A case study

We study the photon emission rate of a non-relativistic charged particle interacting with an external classical noise through its position. Both the particle and the electromagnetic field are quantized. Under only the dipole approximation, the equations of motion can be solved exactly for a free particle, or a particle bounded by an harmonic potential. The physical quantity we will be interested in is the spectrum of the radiation emitted by the particle, due to the interaction with the noise. We will highlight several properties of the spectrum and clarify some issues appearing in the literature, regarding the exact mathematical formula of a spectrum for a free particle.