On the stability of symmetric four-particle molecules

The stability of four-particle molecules m ₁⁺ m ₂⁺ m ₃⁻m₄⁻ with unit charges of particles is studied for different masses of the particles. It is shown that all molecules containing two like particles with masses m ₃ = m ₄ are stable against dissociation. Their stability results from the stability of symmetric molecules with m ₁ = m ₂ and m ₃ = m ₄ and from the stability of molecules with masses of particles m ₃ = m ₄ and m ₁ = ∞ containing one infinitely heavy particle.     

Precise calculation of coulomb binding energies of mesomolecules

The best variational energies obtained to date for the ground states of all -mesomolecules are presented. The results are of rather high accuracy and can serve as a theoretical basis for the experimental study of three-body systems. The energies of thee ^– e ⁺ e ^–,H^– and 1¹ S, 2³ S, 2³ P, 2³ P states ofHe are calculated using the same method.     

Three-dimensional Ising model with four-particle interactions

On the basis of the operational Pfaffian method it is shown that a three-dimensional Ising model with four-particle interactions is reduced to the problem of three interdependent planar lattices and its partition function is expressed through Pfaffian minors of a cyclic matrix.     

On the existence of four-particle Coulomb systems

Whether bound states of Coulomb systems composed of four particles with unit charges (quadrions), a ⁺ b ⁺ c ⁻ d ⁻, exist is demonstrated to be determined by the masses of the constituent particles. Relations that make it possible to establish the existence of a large number quadrions with different masses of the particles are derived. The energies of reference quadrions of different symmetry, a positronium molecule, a ⁺ a ⁺ a ⁻ a ⁻, a ⁺ b ⁺ a ⁻ b ⁻, a ⁺ b ⁺ a ⁻ b ⁻, and a ⁺ a ⁺ b ⁻ c ⁻, are determined and groups of stable asymmetric quadrions corresponding to them are identified. A relationship between the stability of a number of quadrions and three-particle systems (trions) was found. The results shows that, among all the 406 four-particle independent combinations of electrons, muons, pions, kaons, protons, deuterons, and tritium nuclei or their antiparticles, there are 227 bound quadrions.     

Constants of motion of the four-particle Calogero model

We present the explicit expressions of the complete set of constants of motion of four-particle Calogero model with excluded center of mass, i.e. of the A ₃ rational Calogero model. Then we find the constants of motion of its spherical part, defining two-dimensional 12-center spherical oscillator, with the force centers located at the vertexes of cuboctahedron.     

Three-dimensional Ising model with two-and four-particle interaction

The three-dimensional Ising model is investigated by the method of interdependent pfaffians. It is show that this model may be represented as two independent planar lattices.     

Integrals in the theory of four-particle atomic-molecular systems

Explicit expressions for four-particle Coulomb interaction integrals and overlap integrals for exponential basis functions dependent on five interparticle distances have been obtained. These formulas significantly simplify calculations in comparison with the general algorithm and are free from uncertainties arising in its application. The values of the integrals under consideration are calculated for a number of points forbidden in the general algorithm. The results obtained are applicable to analysis of four-particle integrals of the general form and calculation of four-particle atomic-molecular systems with partial allowance for the correlation of particle motion.     

The stability of triple junctions during the grain boundary diffusion process

The grain boundary diffusion in a system with triple junctions is considered in such a geometry, in which the flows of diffusing atoms meet at the triple line. The solutions of the diffusion equation is given in the frameworks of Fisher's model and under the assumption of quasi-stationary distribution of the diffusing atoms along the grain boundaries. The change of the mechanical equilibrium at the triple junction due to the increase of the concentration of solute atoms is considered. It is shown that under some circumstances the triple junction looses its stability with respect to migration in the direction to the diffusion source. The stability diagrams in the segregation-diffusivity parameter space are plotted.     

The stability boundary of synchronized states in globally coupled dynamical systems

The stability boundary of synchronized states in families of globally coupled map lattices and differential equations are studied. It is shown that this boundary may have a very complicated structure in a wide variety of systems. This explains why states can go through sequences of desynchronization and resynchronization as a parameter is varied: in `typical' systems, between any two parameter values at which synchronized states are unstable there are parameter values at which synchronized states are stable!     

Quantum teleportation of entanglement using four-particle entangled states

We present a model to realise a probabilistic quantum teleportation of two-particle mode entangled state through the four-photon quantum channel. Four modes of the two-photon mode entangled state are directly transferred to other spatial four modes of the quantum channel with success probability of 50%. The quantum protocol operates in space of photon number states. A Bell state measurement with four beam splitters and four pairs of detectors in the teleportation protocol is accomplished in the fourfold coincidence basis.     

Orientation-dependent morphological stability of grain boundary groove

Crystal orientation influences the morphological stability of solid–liquid interface during directional solidification of alloy, resulting in the variation of solidified microstructure. In this paper, the morphological evolution near grain boundary grooves（GBGs） with different crystal orientations in a dilute succinonitrile alloy under low temperature gradient and interface velocity is observed in situ. Under experimental conditions, the macroscopic solid–liquid interface is planar and keeps stable, while in GBGs there emerge protrusion and undulation. It is found that the morphological stability of GBG is dependent on crystal orientation. Specifically, for succinonitrile with a body-centered cubic crystal structure, GBGs around the 100 crystal orientation keep stable, while those apart from the 100 crystal orientation become unstable under the same conditions. So it is concluded that 100 crystal orientation favors the morphological stability of GBG.     

Symmetry and boundness of four-particle coulomb systems

The problem of boundness of a ⁺ b ⁺ c ⁻ d ⁻ four-particle Coulomb systems (quadrions) is studied versus the masses of the particles involved. Inequalities that make it possible to deduce that, if some reference quadrions form a bound state, the same is true for a large number of quadrions formed by particles having various masses were derived. A compendium of calculations for energies of reference systems that possess various symmetries [positronium molecules (e ⁺ e ⁺ e ⁻ e ⁻) and quadrions of the a ⁺ b ⁺ b ⁻ b ⁻, a ⁺ b ⁺ a ⁻ b ⁻, and a ⁺ a ⁺ b ⁻ c ⁻ types] is given, and groups of bound asymmetric quadrions corresponding to them are determined. An inequality for kinetic energies of particles that makes it possible to find out, by using asymmetric reference systems, whether specific quadrions are bound is obtained. It is shown that the boundness of many quadrions is ensured by the boundness of respective three-particle systems. The entire body of the present results permits proving that, of the total number of 406 quadrions containing electrons, muons, pions, kaons, protons, deuterons, and tritons and their antiparticles, 227 quadrions are bound.     

On four-particle system ground state with hyperspherical methods

The irregular energy dependence of the elastic scattering cross section at 180° is analysed assuming that the non-regular components of the partial amplitudes depend on the energy. Averaged quantities as well as the energy autocorrelation function are considered. The calculations were performed using the random number generator of the desk calculator TI-59.     

Plasmonic enhancement of four-particle radiative recombination in SiGe quantum wells

The influence of gold nanoparticles deposited on the surface of a Si_0.95Ge_0.05/Si quantum-well heterostructure with a thin Si cap layer on the spectra of low-temperature recombination radiation of biexcitons and an electron–hole liquid confined in the quantum well is investigated. The spectra of both visible and near-infrared radiation are recorded from a region on the sample surface without nanoparticles and regions coated with nanoparticles of different areal densities. It is found that the presence of gold nanoparticles causes strong plasmonic enhancement of collective emission processes in which two holes simultaneously recombine with two electrons from opposite valleys of the conduction band, with the energy of the four particles being transferred to a single photon in the visible spectral range.     

Deterministic assisted clone of an unknown four-particle entangled cluster-type state

Two deterministic schemes are proposed to realize the assisted clone of an unknown four-particle entangled cluster- type state. The schemes include two stages. The first stage requires teleportation via maximal entanglement as the quantum channel. In the second stages of the protocols, two novel sets of mutually orthogonal basis vectors are constructed, With the assistance of the preparer through a four-particle or two-step two-particle projective measurement under these bases, the perfect copy of an original state can be produced. Comparing with the previous protocols which produce the unknown state and its orthogonal complement state at the site of the sender, the proposed schemes generate the unknown state deterministically.     

Generation of a four-particle entangled state via cross-Kerr nonlinearity

We propose a scheme for generating a genuine four-particle polarisation entangled state ︱χ00 that has many interesting entanglement properties and potential applications in quantum information processing. In our scheme, we use the weak cross-Kerr nonlinear interaction between field-modes and the non-demolition measurement method based on highly efficient homodyne detection, which is feasible under the current experiment conditions.     

Projectile-charge sign dependence of four-particle dynamics in helium double ionization

Double ionization of helium by 6 MeV proton impact has been explored in a kinematically complete experiment using a "reaction microscope." For the first time, fully differential cross sections for positively charged projectiles have been obtained and compared with data from 2 keV electron impact. The significant differences observed in the angular distribution of the ejected electrons are attributed to the charge sign of the projectile, resulting in different dynamics of the four-particle Coulomb system, which is not considered in the first Born approximation.     

Field theory of collective excitations III condensation of four-particle clusters

For many fermions with arbitrary two-body forces we investigate the effective action Г[?, α] where ? is the density matrix including pair correlations and α is the four-particle vertex. The physical state including all radiative corrections is obtained by extremizing Г[?, α] with respect to ? and α. Just as ? ≠ 0 corresponds to non-zero density and condensation of pairs, α ≠ 0 signals the presence of a condensate of four-particle clusters. A simple loop expansion is given for Г[?, α]. To lowest order, the extremum amounts to the Hartree-Fock-Bogoliubov equations. The next two steps bring in the four-particle condensate.