Four-wave mixing in a liquid suspension of transparent dielectric microspheres

The process of four-wave mixing in an artificial heterogeneous nonlinear medium—a liquid suspension of transparent dielectric microspheres—is considered. The dynamics of the concentration response to gradient forces that act on microspheres in the interference field of interacting waves are investigated on the basis of the Smolukhovskii equation. Kinetic equations for the amplitudes of light-induced concentration gratings that take part in the four-wave mixing are obtained with the use of the Fourier series expansion of the distribution function of microspheres. The ratios of the microsphere radius to the grating periods are obtained under which the resultant gradient force vanishes and, hence, a suspension of dielectric microspheres does not exhibit nonlinear properties irrespective of the intensities of the interacting waves. The kinetics of the process of four-wave mixing is investigated under efficient energy exchange between reference, signal, and reversed waves. It is shown that a liquid suspension of transparent dielectric spheres is a highly effective wideband nonlinear medium for reversing the wave front of low-intensity radiation of continuous-wave lasers.     

Ion larmour radius effect on rf ponderomotive forces and induced poloidal flow in tokamak plasmas

Analytical approximations are used to clarify the effect of Larmour radius on rf ponderomotive forces and on poloidal flows induced by them in tokamak plasmas. The electromagnetic force is expressed as a sum of a gradient part and of a wave momentum transfer force, which is proportional to wave dissipation. The first part, called the gradient electromagnetic stress force, is combined with fluid dynamic (Reynolds) stress force, and gyroviscosity is included into viscosity force to model finite ion Larmour radius effects in the momentum response to the rf fields in plasmas. The expressions for the relative magnitude of different forces for kinetic Alfven waves and fast waves are derived.     

A STOCHASTIC OPTIMAL SEMI-ACTIVE CONTROL STRATEGY FOR ER/MR DAMPERS

A stochastic optimal semi-active control strategy for randomly excited systems using electrorheological/magnetorheological (ER/MR) dampers is proposed. A system excited by random loading and controlled by using ER/MR dampers is modelled as a controlled, stochastically excited and dissipated Hamiltonian system with n degrees of freedom. The control forces produced by ER/MR dampers are split into a passive part and an active part. The passive control force is further split into a conservative part and a dissipative part, which are combined with the conservative force and dissipative force of the uncontrolled system, respectively, to form a new Hamiltonian and an overall passive dissipative force. The stochastic averaging method for quasi-Hamiltonian systems is applied to the modified system to obtain partially completed averaged Itô stochastic differential equations. Then, the stochastic dynamical programming principle is applied to the partially averaged Itô equations to establish a dynamical programming equation. The optimal control law is obtained from minimizing the dynamical programming equation subject to the constraints of ER/MR damping forces, and the fully completed averaged Itô equations are obtained from the partially completed averaged Itô equations by replacing the control forces with the optimal control forces and by averaging the terms involving the control forces. Finally, the response of semi-actively controlled system is obtained from solving the final dynamical programming equation and the Fokker-Planck-Kolmogorov equation associated with the fully completed averaged Itô equations of the system. Two examples are given to illustrate the application and effectiveness of the proposed stochastic optimal semi-active control strategy.     

Virtual photon exchange,intermolecular interactions and optical response functions

According to molecular quantum electrodynamics, coupling between material particles occurs due to an exchange of one or more virtual photons. In this work, the relationship between polarisability and hyperpolarisability tensors of atoms and molecules that feature in linear and nonlinear optical processes, and their analytically continued form in the complex frequency domain that appear in formulae describing fundamental inter-particle interactions, is studied. Examples involving a single virtual photon exchange, which are linearly proportional to electric dipole moments at each centre, include the electrostatic energy and the resonant transfer of excitation energy. The Casimir–Polder dispersion potential, and its discriminatory counterpart applicable to coupled chiral molecules, are used to illustrate response properties depending on the exchange of two virtual photons. Meanwhile, the energy shift between two hyperpolarisable species, a higher order discriminatory contribution to the dispersion potential, is employed to represent forces arising from the three virtual photon exchange. It is shown that for energy shifts that are quadratic or bilinear or cubic in the transition dipole moment, it is necessary to account for all two- and three-photon optical processes, such as absorption, emission and linear and nonlinear scattering of light in order to arrive at the correct form of the molecular response tensor.     

The combined influence of the Pauli principle and saturation on the effectiveα andα α interactions

The recently developed fish bone optical model with saturation has been applied tonα. andαα scattering. Short ranged nucleon-nucleon correlations, which are responsible for nuclear saturation, have an influence both on the local potential part and on the exchange potential. The local potential becomes less attractive in the inner region and steeper in the surface region; it is better represented by a Woods Saxon shape than by a gaussian. A modification of the exchange potential is caused by the effect of short range correlations on the resonating group norm kernel. It is seen that short ranged nucleonnucleon correlations have no dramatic effect on two-cluster optical potentials. The present calculations rather support conventional phenomenological approaches. Together with older results one may conclude that, in multicluster systems, saturation is predominantly carried by three- and multicluster forces.     

Ortho- and Para-helium in Relativistic Schrödinger Theory

The characteristic features of ortho- and para-helium are investigated within the framework of Relativistic Schr?dinger Theory (RST). The emphasis lies on the conceptual level, where the geometric and physical properties of both RST field configurations are inspected in detail. From the geometric point of view, the striking feature consists in the splitting of the -valued bundle connection into an abelian electromagnetic part (organizing the electromagnetic interactions between the two electrons) and an exchange part, which is responsible for their exchange interactions. The electromagnetic interactions are mediated by the usual four-potentials A _μ and thus are essentially the same for both types of field configurations, where naturally the electrostatic forces (described by the time component A ₀ of A _μ) dominate their magnetostatic counterparts (described by the space part A of A _μ). Quite analogously to this, the exchange forces are as well described in terms of a certain vector potential (B _μ), again along the gauge principles of minimal coupling, so that also the exchange forces split up into an “electric” type ( ) and a “magnetic” type ( ). The physical difference of ortho- and para-helium is now that the first (ortho-) type is governed mainly by the “electric” kind of exchange forces and therefore is subject to a stronger influence of the exchange phenomenon; whereas the second (para-) type has vanishing “electric” exchange potential (B ₀ ≡ 0) and therefore realizes exclusively the “magnetic” kind of interactions ( ), which, however, in general are smaller than their “electric” counterparts. The corresponding ortho/para splitting of the helium energy levels is inspected merely in the lowest order of approximation, where it coincides with the Hartree–Fock (HF) approximation. Thus RST may be conceived as a relativistic generalization of the HF approach where the fluid-dynamic character of RST implies many similarities with the density functional theory.     

On nuclear energy levels and elementary particles

Considering only exchange forces, the binding energies and excited states of nuclei up to ²⁴ Mg are predicted to within charge independence, and there is no reason why the model should not be extended to cover all of the elements. A comparison of theory with experiment shows that the energy of one exchange is 2.56 MeV. Moreover, there is an attractive well of depth 30 MeV, corresponding to the helium nucleus, before exchange forces become operative. A possible explanation of the origin of mesons is also presented.     

Energy flow of moving dissipative topological solitons

We study the energy flow due to the motion of topological solitons in nonlinear extended systems in the presence of damping and driving. The total field momentum contribution to the energy flux, which reduces the soliton motion to that of a point particle, is insufficient. We identify an additional exchange energy flux channel mediated by the spatial and temporal inhomogeneity of the system state. In the well-known case of a dc external force the corresponding exchange current is shown to be small but nonzero. For the case of ac driving forces, which lead to a soliton ratchet, the exchange energy flux mediates the complete energy flow of the system. We also consider the case of combination of ac and dc external forces, as well as spatial discretization effects.     

Soft-core correlations and three body forces in nuclear matter

We show that, when nucleon-nucleon correlations are taken into account using correlation functions derived. from the Reid soft core potential, the contribution of three body forces to the binding energy of nuclear matter is enhanced. The two pion exchange three body forces contributes 6 MeV attraction.     

Superconductivity in crystals with covalent bonds

Novel types of ground states associated with properties of heavy fermion systems are derived for crystals with covalent bonds generated by short-range exchange forces between valence electrons of atoms localized at lattice sites. It is shown that the short-range exchange forces can give rise to a narrow energy band in which electrons can exhibit an enormous effective mass. The same exchange forces provide the microscopic mechanism for spin-singlet pairing of electrons into Cooper pairs which are responsible for superconductivity in these systems. This superconductivity exhibits several different anisotropic superconducting states. The effective mass, Fermi energy, specific heat, Pauli susceptibility, critical temperatures and critical magnetic field of heavy fermion systems are calculated and compared with experimental data.The authors thank Dr. . Jano for discussions.     

Model Study of Three-Body Forces in the Three-Body Bound State

The Faddeev equation for the three-body bound state with two- and three-body forces is solved directly as three-dimensional integral equation. The numerical feasibility and stability of the algorithm, which does not employ partial wave decomposition is demonstrated. The three-body binding energy and the full wave function are calculated with Malfliet-Tjon-type two-body potentials and scalar two-meson exchange three-body forces. For two- and three- body forces of ranges and strengths typical of nuclear forces the single-particle momentum distribution and the two-body correlation function are similar to the ones found for realistic nuclear forces.     

Nucleon-nucleon interaction in the three-nucleon system

The three-nucleon system is reconsidered. The Faddeev equations are given leading to a set of integral equations. Solving these integral equations, suitable forms are considered for the nucleon-nucleon interaction. In the bound state of three-nucleon system, the form of the nuclear forces from the nucleon-nucleon interaction is important. In the present calculations, we consider the nuclear forces resulting from the nucleon-nucleon interaction by the exchange of a scalar meson, a pseudoscalar meson, and a massless vector meson. With this different meson exchange nucleon-nucleon interaction, the binding energy of the three-nucleon system is calculated by solving the Faddeev integral equations giving a value of 8.452 MeV.     

Three-body forces and4He

Some two-pion exchange three-body forces are examined as effective two-body potentials in the framework of exp(S) many-body theory. Each effective potential is added to the Reid soft core potential and a fully self-consistent calculation carried out. The most reasonable three-body forces give remarkably good agreement with experiment.     

Relations between the Skyrme force parameters and the nucleon-nucleon forces within the quasi-Hartree-Fock-theory

The energy-density for the Skyrme forces in the Hartree-Fock-approximation is compared with the energy-density in the quasi-Hartree-Fock-approximation for two-body nucleon-nucleon forces with hard-core repulsion. From these expressions the magnitudes of the corresponding Hartree-Fock parameters of the nucleon-nucleon force are estimated. As an example, a simple nucleon-nucleon force is constructed, which reproduces the results of the Skyrme force SII. The ambiguities of such an comparison are discussed. The Skyrme forces SII-SIV correspond to potentials with hard-core radii ≈0.5–0.7 F. Smaller hard-core radii correspond to larger exchange contributions.     

Implications of duality,unitarity and SU6 symmetry for baryons and baryonium

It is shown that there exists a limit, involving both an exactly SU₆ symmetric spectrum and exactly exchange degenerate Regge trajectories, in which the OZI like selection rule for baryonium is exact. Deviations from the rule occur when SU₆ is broken and when unitarity forces the breaking of exchange degeneracy. By combining both of these latter effects we can qualitatively account for the observed pattern of broken exchange degeneracy among baryons. The strength of the baryonium coupling to mesons is related to the breaking of exchange degeneracy.     

Magnon-mediated binding between holes in an antiferromagnet

The long-range forces between holes in an antiferromagnet are due to magnon exchange. The one-magnon exchange potential between two holes is proportional to cos(2 ϕ)/r ² where r is the distance vector of the holes and ϕ is the angle between r and an axis of the square crystal lattice. One-magnon exchange leads to bound states of holes with antiparallel spins resembling d-wave symmetry.     

Van der Waals Forces and Photon-Less Effective Field Theory

In the ultra-cold regime Van der Waals forces between neutral atoms can be represented by short range effective interactions. We show that universal low energy scaling features of the underlying vdW long range force stemming from two photon exchange impose restrictions on an Effective Field Theory without explicit photons. The role of naively redundant operators, relevant to the definition of three body forces, is also analyzed.     

Derivation of a pion-rho' exchange three-body force and application to the trinucleon system

The pion-rho exchange three-body force is derived by means of lagrangians which are approximately invariant under chiral and gauge transformations. The leading contribution to the potential arises from a seagull diagram, which corresponds to forces that are dominantly repulsive and comparable to those due to the exchange of two pions. The qualitative features of our results are analysed by means of plots of the energy of the trinucleon system.     

Remarks on the forces generated by two-neutrino exchange

A brief up-to-date review of the long-range forces generated by two neutrino exchange is presented. The potential due to exchange of a massive neutrino–antineutrino pair between particles carrying weak charge might be larger than expected if the neutrinos have not only masses but also magnetic moments close to the present experimental bounds. It still remains too small to be observable.     

Nucleon core size and nuclear forces

Knowledge of nuclear forces is used to obtain information on the size of the quark core of nucleons. A RMS radius of 0.3–0.5 fm appears to be favored by a quark model of the nucleon-nucleon spin-orbit forces, with both one-gluon and ϱ-, ω-meson exchange qq interactions, depending on the relative strength of these qq interactions. The limitations of this estimate are briefly discussed.