We present an exact diagrammatic approach for the problem of dimer-dimer scattering in 3D for dimers being a resonant bound state of two fermions in a spin singlet state, with corresponding scattering length a. We recover exactly the previously known result a(B) = 0.60a, where a(B) is the dimer-dimer scattering length. A detailed discussion of how one can "sum all the diagrams" in this case is presented. Applications to the study of 4-particle bound states of various complexes in 2D are briefly presented.

We present a diagrammatic approach for the dimer-dimer scattering problem in two or three spatial dimensions, within the resonance approximation where these dimers are in a weakly bound resonant state. This approach is first applied to the calculation of the dimer-dimer scattering length a(B) in three spatial dimensions, for dimers made of two fermions in a spin-singlet state, with corresponding scattering length a(F), and the already known result a(B)=0.60 a(F) is recovered exactly. Then we make use of our approach to obtain results in two spatial dimensions for fermions as well as for bosons. Specifically, we calculate bound-state energies for three bbb and four bbbb resonantly interacting bosons in two dimensions. We consider also the case of a resonant interaction between fermions and bosons, and we obtain the exact bound-state energies of two bosons plus one fermion bbf, two bosons plus two fermions bf(up arrow)bf(down arrow), and three bosons plus one fermion bbbf.

A theoretical model and numerical calculations are developed to estimate consequences of the impact of a 7 TeV proton beam on the physical-mechanical properties of materials used in the LHC, for example graphite used for collimators, and copper. Each 7 TeV proton beam consists of 2808 bunches with 1.1x10 11 protons per bunch. In our calculations we assume a bunch length of 0.5 ns and a bunch spacing of 25 ns. The high energy stored in each bunch can produce a shock wave in these materials. The theoretical model for the investigations of shock wave propagation in the collimator materials takes into account ionization, electronic excitation, and energy transfer from excited electronic subsystem of material to the ionic subsystem. The changes of some physical properties of the collimator materials during shock wave propagation are considered here. The deposited energy is calculated with FLUKA (1). The first numerical results are presented here to show the possibilities of developed computer program and to test it in the calculations of microstructure changes in materials produced by shock wave propagation for different numbers of bunches for some deposited energy. This allows investigating the changes of density and internal pressure, temperature profiles in electronic and ionic subsystems of materials near the front of shock wave. This program will be used in the future for the understanding of behaviour of collimator materials used in LHC under 7 TeV proton beam in accident cases.

We consider a possibility of the creation of composite fermions in optical traps and in high-T-c superconductors. For optical traps we study a model of Fermi-Bose mixture with resonant attraction between particles of different sorts. In this case a pairing between fermion and boson of the type bf is possible. This pairing corresponds to creation of composite fermions. At low temperatures and equal densities of fermions and bosons composite fermions are further paired in quartets. In the 2D case we exactly solve Skomiakov-Ter-Martirosian type of integral equations [1] and find the binding energies of two bosons plus one fermion fbb and two bosons plus two fermions fbfb. For high-Tc superconductors we consider a quartet - a bound state of two composite holes Delta =< hh >, where each composite hole h = fb consists of a spinon and a holon bound by the stringlike potential. Our investigations are important for recent experiments on the observation of weakly bound composite fermions and bosons in optical traps in the regime of Feshbach resonance.

We consider a model of Fermi-Bose mixture with strong hard-core repulsion between particles of the same sort and attraction between particles of different sorts. In this case, besides the standard anomalous averages of the type $$; $$ and $$, a pairing between fermion and boson of the type $bc$ is possible. This pairing corresponds to a creation of composite fermions in the system. At low temperatures and equal densities of fermions and bosons composite fermions are further paired in quartets. Our investigations are important for high-$T_c$ superconductors and in connection with recent observation of weakly bound dimers in magnetic traps at ultralow temperatures.

We present an exact diagrammatic approach for the problem of dimer-dimer scattering in 3D for dimers being a resonance bound state of two fermions in a spin-singlet state, with corresponding scattering length a F . Applying this approach to the calculation of the dimmer-dimer scattering length a B , we recover exactly the already known result a B = 0.6 a F . We use the developed approach to obtain new results in 2D for fermions and bosons. Namely, we calculate bound state energies for three bbb and four bbbb resonantly interacting bosons in 2D. For the case of resonance interaction between fermions and bosons, we exactly calculate bound state energies of the following complexes: two bosons plus one fermion bbf , two bosons plus two fermions bf ↑ bf ↓, and three bosons plus one fermion bbbf .

The experiments on electron irradiation of yttrium-stabilized zirconium oxide samples show the formation of strong elastic fields near interstitial dislocation loops. The fields increase with an increase in the loop radius and, when the loop radius reaches a certain critical value, the loops became unstable due to the beginning of plastic deformation and the formation of a dislocation network. The mechanism of the occurrence of this instability is suggested. It is based on the accumulation of charges at dislocation loops due to ionization processes in an electron-irradiated dielectric. It is shown that the accumulation of the electric charge at growing dislocation loops in dielectrics may be responsible for an increase in elastic stresses near dislocation loops and for their instability because of the beginning of plastic deformation near the loops when stresses at growing loops become close to the theoretical yield stress of the material.

Point defects in fusion ceramic materials under irradiation can have an effective charge due to ionization and covalent chemical bonding. The kinetics of charged point defects in these materials is determined by their effective charge and this kinetics is completely different from non-charged point defects in metals. The experimental investigation of point defect charge states in ceramic materials is rather difficult. In this paper, a new method is proposed for the investigation of charge states of point defects in irradiated ceramic materials. This method is based on a new theoretical model and experimental observations of defect cluster formation near permanent sinks, such as grain boundaries. Previous experimental investigations show that a denuded zone is formed in irradiated ceramic materials near free surfaces and grain boundaries. The effect of an applied electric field on the formation of interstitial-type point defect clusters (dislocation loops) near grain boundaries in irradiated ceramic materials is investigated. For this purpose a new theoretical model is suggested, which takes into account the effect of an applied electric field on the denuded zone formation. It is shown that the denuded zone size depends on point defect charge and direction of applied electric field. The obtained theoretical results are compared with experimental data.

The temperature and magnetic field dependence of the resistivity, magnetoresistance, and magnetic susceptibility of phase-separated manganites in the temperature range corresponding to nonmetallic behavior are considered within the framework of a model of inhomogeneous state with allowance for the existence of ferromagnetically correlated regions even in the absence of long-range magnetic order. The main attention is given to the interval of high temperatures and weak fields. The main characteristics of the phase-separated state of manganites are evaluated from a comparison of the theoretical results with available experimental data.

We consider a model of a Fermi-Bose mixture with strong hard-core repulsion between particles of the same sort and attraction between particles of different sorts. In this case, besides the standard anomalous averages of the type , , and , a pairing between fermions and bosons of the type bc is possible. This pairing corresponds to the creation of composite fermions in the system. At low temperatures and equal densities of fermions and bosons composite fermions are further paired in quartets. At higher temperatures trios, which consist of composite fermions and elementary bosons, are also present in the system. Our investigations are important in connection with the recent observation of weakly bound dimers in magnetic and optical dipole traps at ultralow temperatures and with the observation of the collapse of a Fermi gas in an attractive Fermi-Bose mixture of neutral particles.

Ceramic materials produced on the basis of SiC and SiC/SiC composites are considered, due to their high-temperature strength, pseudo-ductile fracture behavior and low-induced radioactivity, as candidate materials for fusion reactors. The radiation resistance of ceramic materials under neutron irradiation is one of the key problems, which determines the use of these materials in fusion reactor environment. The dimensional stability (radiation swelling) of SiC is an important problem for degradation of radiation resistance of SiC materials. In fusion reactor environment helium atoms will be produced in SiC in the first wall region up to very high concentrations (15,000 20,000 at. ppm) and therefore it is very important to understand the helium effect on radiation swelling of SiC.In the present paper the effect of helium on radiation swelling of SiC is investigated. Recent experimental results concerning the helium effect on radiation swelling of SiC under neutron, single-ion and dual-beam irradiation are presented. A new theoretical model is suggested for an explanation of the effect of helium on radiation swelling in ceramic materials. Point defects in ceramic materials can have an effective charge (e.g., an F-centre(+), vacancy with a single trapped electron). The suggested theoretical model is based on kinetic consideration of charged point defect accumulation and kinetic growth of dislocation loops in a matrix of ceramic material (SiC) taking into account the effect of internal electric fields formed under irradiation near dislocation loops on diffusion processes of charged point defects. In this theoretical model, vacancies and small vacancy clusters are considered as additional traps for helium atoms. This results in enhanced growth rate of dislocation loops and finally swelling increase. The obtained numerical and analytical theoretical results for radiation swelling in the presence of helium atoms are compared with the existing experimental data for irradiated SiC material containing helium atoms. It has been shown that helium atoms increase the radiation swelling of SiC.

SiC and SiC/SiC composites are considered as candidate materials for fusion reactors. In a fusion reactor environment, helium atoms will be produced in SiC up to very high concentrations (15000–20000 at.ppm) and therefore it is very important to understand how helium effects radiation swelling of SiC. In this paper a theoretical model of the helium effect on radiation swelling of SiC is suggested. This model is based on considering of kinetic growth of dislocation loops in the matrix taking into account the effect an internal electric field formed near dislocation loops has on diffusion processes of charged point defects. The trapping of helium atoms by vacancies results in an enhanced growth rate of dislocation loops and finally a swelling increase. The theoretical results for radiation swelling are compared with the existing experimental data. It is shown that helium atoms increase the radiation swelling of SiC, especially at high temperatures.

We consider the model of a Fermi-Bose mixture with strong hard-core repulsion between particles of the same sort and attraction between particles of different sorts. In this case, in addition to the standard anomalous averages of the type 〈b〉, 〈bb〉, and 〈cc〉, pairing between fermions and bosons of the type 〈bc〉 is possible. This pairing corresponds to creation of composite fermions in the system. At low temperatures and equal densities of fermions and bosons, composite fermions are further paired into quartets. At higher temperatures, trios consisting of composite fermions and elementary bosons are also present in the system. Our investigations are important in connection with the recent observation of weakly bound dimers in magnetic and optical dipole traps at ultralow temperatures and with the observation of collapse of a Fermi gas in an attractive Fermi-Bose mixture of neutral particles.

We study the possibility of nanoscale phase separation in manganites in the framework of the double-exchange model. The homogeneous canted state of this model is proved to be unstable towards the formation of small ferromagnetic droplets inside an antiferromagnetic insulating matrix. For the ferromagnetic polaronic state we analyse the quantum effects related to the tails of electronic wave function and a possibility of electron hopping in the antiferromagnetic background. We find that these effects lead to the formation of the threshold for the polaronic state.

One type of candidate materials for future fusion reactors is ceramics, which can be applied as radio frequency windows, toroidal insulating breaks and diagnostic probes. The degradation of physical and mechanical properties of these materials under neutron irradiation is determined by the kinetics of radiation defects including a point defect cluster formation (dislocation loops, voids and so on). The physical mechanisms of defect structure development in ceramic materials, where point defects and their clusters can have an effective charge, are completely different from those in metals. We have investigated the physical mechanisms of instability of extended interstitial defect clusters (charged dislocation loops), which were formed in stabilized cubic zirconia under electron irradiation with 100–1000 keV due to the selective displacement damage in oxygen sublattice. A new theoretical model is suggested for the explanation of the growth process and instability of the interstitial clusters. The suggested model takes into account an accumulation of effective charge on growing dislocation loops due to the trapping of electrons in dislocation cores. Our calculations show that the elastic stress and strain fields are much intense around charged dislocation loops than non-charged dislocation loops, due to an additional stress and strain fields driven by an electric field of accumulated charge. The stress induced by the charged dislocation loops with the density of trapped electrons per atom n=0.4 is found to be comparable with the theoretical yield stress of zirconia, which explains the multiplication of dislocation network at a critical size of the defect clusters observed by experiments.

The magnetoresistance and the noise power of non-metallic phase-separated manganites are studied. The material is modelled by a system of small ferromagnetic metallic droplets (magnetic polarons or ferrons) in an insulating matrix. The concentration of metallic phase is assumed to be far from the percolation threshold. The electron tunnelling between ferrons causes the charge transfer in such a system. The magnetoresistance is determined both by the increase in the volume of the metallic phase and by the change in the electron hopping probability. In the framework of such a model, the low-field magnetoresistance is proportional to H 2 and decreases with temperature as T −n , where n can vary from 1 to 5, depending on the parameters of the system. In the high-field limit, the tunnelling magnetoresistance grows exponentially. Different mechanisms of the voltage fluctuations in the system are analysed. The noise spectrum generated by the fluctuations of the number of droplets with extra electrons has a 1/ f form over a wide frequency range. In the case of strong magnetic anisotropy, the 1/ f noise can also arise due to fluctuations of the magnetic moments of ferrons. The 1/ f noise power depends only slightly on the magnetic field in the low field range whereas it can increase as H 6 in the high-field limit.

Ceramic materials produced on the basis of SiC and SiC/SiC composites are considered due to their high temperature strength, pseudo-ductile fracture behavior and low-induced radioactivity as candidate materials for fusion reactors. The radiation resistance of ceramic materials under neutron irradiation is the key problem which determines the use of these materials in fusion reactor environment. In the present paper the general physical mechanisms of radiation swelling of SiC are investigated. Recent experimental results concerning the effect of neutron and charged particle irradiation on radiation swelling of SiC are presented. A new theoretical model is suggested for the description of radiation swelling in ceramic materials. Point defects in ceramic materials can have an effective charge (e.g., an F+ center, vacancy with a single trapped electron). The theoretical model is based on kinetic consideration of charged point defect accumulation and kinetic growth of dislocation loops in the matrix taking into account the effect of internal electric field formed under irradiation in the matrix on diffusion processes of charged point defects. The theoretical results for radiation swelling are compared with the existing experimental data for irradiated SiC material.

We have investigated the physical mechanisms of the growth and stability of charged dislocation loops in ceramic materials with very strong different mass of atoms (stabilized cubic zirconia) under different energies and types of irradiation conditions: 100–1000 keV electrons, 100 keV He+ and 300 keV O+ ions. The anomalous formation of extended defect clusters (charged dislocation loops) has been observed by TEM under electron irradiation subsequent to ion irradiation. It is demonstrated that very strong strain field (contrast) near charged dislocation loops is formed. The dislocation loops grow up to a critical size and after then become unstable. The instability of the charged dislocation loop leads to the multiplication of dislocation loops and the formation of dislocation network near the charged dislocation loops. A theoretical model is suggested for the explanation of the growth and stability of the charged dislocation loop, taking the charge state of point defects. The calculated distribution of the modified strain field by the electrical field around the charged dislocation loops is stronger than that of noncharged dislocation loops. The obtained theoretical results for the modified strain field contrast and the critical radius of unstable charged dislocation loops are compared with observed experimental data.

Starting from the assumption that ferromagnetically correlated regions exist in manganites even in the absence of long-range magnetic order, we construct a model of charge transfer due to the spin-dependent tunnelling of charge carriers between such regions. This model allows us to analyze the temperature and magnetic field dependence of resistivity, magnetoresistance, and magnetic susceptibility of phase-separated manganites in the temperature range corresponding to non-metallic behavior. The comparison of theoretical and experimental results reveals the main characteristics of the phase-separated state.