Zitterbewegung of particles with arbitrary spin

The existence of zitterbewegung of particles with higher spins (s≥1) is proved. The investigation is based on the idea of Curie, Jordan, and Sudarshan that there are two aspects of relativistic invariance and also on the determination of the dynamical variables that describe systems with arbitrary spin obtained by Jordan and Mukunda. A number of new paradoxical properties of zitterbewegung unknown in Dirac theory is revealed. For example, particles with high spins (s≥1) can have a velocity greater than light. It is shown in a general form that elimination of zitterbewegung in all directions of space, or even only in a plane, is impossible. There can be only partial liquidation of zitterbewegung, in one of the directions of space, and then only at the price of violation of relativistic invariance of the theory. Finally, it is suggested that the paradoxical properties of zitterbewegung can be understood by redefining the momentum and mass operators. In this way, a connection between zitterbewgung and tachyons is established.     

Clustering of Fermi particles with arbitrary spin

A single l-shell model is investigated for a system of fermions of spin s and an attractive s-wave, spin channel independent, interaction. The spectra and eigenvectors are determined exactly for different l,s values and particle numbers N. As a generalization of Cooper pairing it is shown that when N=mu(2s+1), mu=1,2,..., 2l+1, the ground state consists of clusters of (2s+1) particles. The relevance of the results for more general situations including the homogeneous system is briefly discussed.     

Positivity properties in elastic scattering of particles with arbitrary spins

We prove the positivity of the coefficients of the expansion in Legendre polynomials of $\text{(}\text{dσ}{}^{\mathrm{A}}\text{dt}\text{)}$(s, cosθ), the absorptive contribution to the elastic unpolarized differential cross-section for particles with arbitrary spins.     

Quasi-probability distributions for arbitrary spin-j particles

Quasi-probability distribution functions f^j _WW, f^j _MM for quantum spin-j systems are derived based on the Wigner-Weyl, Margenau-Hill approaches. A probability distribution f^j _sph which is nonzero only on the surface of the sphere of radius j(j+1) is obtained by expressing the characteristic function in terms of the spherical moments. It is shown that the Wigner-Weyl distribution function turns out to be a distribution over the sphere in the classical limit.     

Successive defects asymmetric simple exclusion processes with particles of arbitrary size

This paper uses various mean-field approaches and the Monte Carlo simulation to calculate asymmetric simple exclusion processes with particles of arbitrary size in the successive defects system. In this system, the hopping probability p (p<1) and the size d of particles are not constant. Through theoretical calculation and computer simulation, it obtains the exact theoretical results and finds that the theoretical results are in agreement with the computer simulation. These results are helpful in analysing the effect of traffic with different hopping probabilities p and sizes d of particle.     

Two particle unitarity for helicity amplitudes with particles of arbitrary spin

The two particle unitarity contribution to the double spectral function of the scattering amplitude for any 2 → 2 process is explicitly calculated for the case of arbitrary spins of the initial, intermediate and final particles. A closed, simple result is obtained which is a generalization of the Mandelstam result for spinless particles. The results should be of value in calculations of the contribution of the exchange of pairs of high spin particles to the nucleon-nucleon force.     

Calculation of the rate constants of spin exchange between paramagnetic particles with arbitrary spins for their diffusion motion in nonviscous liquids

The rate constant of spin exchange between two paramagnetic particles with arbitrary spins is calculated within a model of diffusion passage through a region of exchange interaction that exponentially depends on the interparticle distance.     

Processes following thermalization of positive particles in condensed matter

In previous discussions of the details of the processes which can lead to the formation of muonium, Mu, and positronium, Ps, the two fields of study have often been compared. In this communication we discuss the various mechanisms of Mu and Ps formation and particular attention is given to some of the more important differences between the physical properties of muons and positrons in condensed matter. Also, we discuss possible Mu and Ps reactions with some of the transient species created during the slowing down of the muon or positron. The effect of these latter processes may be that part of the formed Mu or Ps will not be recognized by the normal experimental techniquies. Furthermore, it is emphasized that the kinetics of the various muon and positron reactions are those of non-homogeous-kinetics.     

Exact solution of the asymmetric exclusion model with particles of arbitrary size

A generalization of the simple exclusion asymmetric model is introduced. In this model an arbitrary mixture of molecules with distinct sizes s=0,1,2, ..., in units of lattice space, diffuses asymmetrically on the lattice. A related surface growth model is also presented. Variations of the distribution of the molecules sizes may change the excluded volume almost continuously. We solve the model exactly through the Bethe ansatz and the dynamical critical exponent z is calculated from the finite-size corrections of the mass gap of the related quantum chain. Our results show that for an arbitrary distribution of molecules, the dynamical critical behavior is on the Kardar-Parizi-Zhang universality.     

Mobility matrix for arbitrary spherical particles in solution

We review the theory of the extended mobility matrix for N arbitrary, spherically symmetric particles immersed in an incompressible fluid. The two-particle mobility functions can be evaluated to any desired order in the inverse interparticle distance by means of an algebraic computer program implementing exact recursion relations. We correct some earlier published expressions and summarize known results for the scattering coefficients which characterize the hydrodynamic properties of the particles. Explicit results are presented for stick and slip hard spheres, for permeable spheres and for fluid droplets.     

Dust particles in collisionless plasma sheath with arbitrary electron energy distribution function

Dust particles often appear in industrial plasmas as undesirable product of the plasma-wall interactions. Large particles of several micrometers in diameter are concentrated in a thin layer (the sheath) above the lower electrode of the rf driven parallel plate device, where the electric force is strong enough to compensate particle’s gravity. Experimental and theoretical uncertainties are significantly increased in the plasma sheath. Common models of dust charging in the plasma sheath suppose the Maxwellian electron energy distribution function (EEDF) in conjunction with a flux of cold ions satisfying classical Bohm criterion at the sheath edge. In this paper we generalize this model to arbitrary EEDF with adapted Bohm criterion. We limit our considerations to collisionless or slightly collisional plasma, where the EEDF inside the sheath is expressed through the EEDF in the plasma bulk. Derived theoretical formulas are incorporated into numerical model, describing collisionless radio frequency (rf) plasma sheath together with the electrical charge, various kinds of forces, balancing radius and oscillation frequency of particles.     

Conformal invariance of relativistic equations for arbitrary spin particles

We show that any Poincaré-invariant equation for particles of zero mass and of discrete spin provide a unitary representation of the conformal group, and find an explicit expression of the conformal group generators in terms of Poincaré group generators.     

Relativistic polarization density matrix for particles of arbitrary spin

The polarization density matrix for particles of arbitrary spin can be expressed as a linear function of the expectation values of the generators of the polarization symmetry group of the corresponding wave equations.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 84–88, April, 1984.