International Journal of Modern Physics B

The thermodynamic limit in statistical thermodynamics of many-particle systems is an important but often overlooked issue in the various applied studies of condensed matter physics. To settle this issue, we review tersely the past and present disposition of thermodynamic limiting procedure in the structure of the contemporary statistical mechanics and our current understanding of this problem. We pick out the ingenious approach by Bogoliubov, who developed a general formalism for establishing the limiting distribution functions in the form of formal series in powers of the density. In that study, he outlined the method of justification of the thermodynamic limit when he derived the generalized Boltzmann equations. To enrich and to weave our discussion, we take this opportunity to give a brief survey of the closely related problems, such as the equipartition of energy and the equivalence and nonequivalence of statistical ensembles. The validity of the equipartition of energy permits one to decide what are the boundaries of applicability of statistical mechanics. The major aim of this work is to provide a better qualitative understanding of the physical significance of the thermodynamic limit in modern statistical physics of the infinite and "small" many-particle systems.

The vortex hopping motion in a type-II superconductor determines the current-carrying ability and consequently, the application fields of the superconductor. However, it is not clear how the vortices hop between the different pinning regions in the superconductor. Here, we proposed that there should be magnetic flux exchange between two contacting pinning regions. A system of differential equations was constructed to describe the flux exchange phenomenon. The qualitative analysis methods and approximate methods were used. The approximate solutions of the system were obtained. The results show that the flux exchange reduces the internal field in a weak pinning region, but increases the internal field in a strong pinning region. Moreover, the flux exchange is strongly influenced by the superconductor's geometrical size.

The electronic and optical properties of X-doped (X = Rh, Pd, Ag) cubic SrTiO₃ in perovskite structure are investigated using first-principles calculations. The strength of the Ti–O bonds near the substitutional X impurity is found to be weakened by the shorter X–O bonds. Three types of electronic characteristics due to X-doping are demonstrated. X-doping decreases the band gap of SrTiO₃, extending the optical absorption edge to visible light. Although Pd-doped SrTiO₃ has the greatest absorption in the visible light region, its photocatalytic activity is lower than that of Rh-doped SrTiO₃, because the intermediate bands from the 4d orbitals of the Pd dopant act as recombination centers. The theoretical results coincide with the available experimental results.

ZnO and Co-doped ZnO have been synthesized by co-precipitation technique. X-ray diffraction (XRD) patterns and absorption spectra show that Co ions are doped into the lattice positions of ZnO. Photoluminescence (PL) experiments on the samples have been performed in order to study the sp–d interaction in ZnO:Co. Room temperature measurements show two additional emissions related to Co besides the ZnO exciton-related and trap emissions. The two emissions are attributed to the transitions from Co⁺ to the excited Co²⁺ state and from ²E(G) to ⁴ A₂(F), respectively. The charge-transfer transitions related to Co²⁺ exciting 3d intrashell luminescence at 1.78 eV has been observed. A blue-shift in the exciton-related emission, a red-shift in the blue emission and no shift in the green emission were revealed and interpreted by the sp–d interaction.

The DC and AC transport properties are investigated in multi-terminal graphene nanoribbon (GNR) devices. The devices are composed of three or four graphene ribbons connected with different angles. It is found that DC and AC conductances depend on the structural configurations and ribbon properties. In the vicinity of Dirac point, the intersection of graphene ribbons forms band mixing and results in resonant or anti-resonant states. The edge and width, as well as, the angles of the graphene ribbons influence the DC and AC transport properties drastically. These properties can be used to build future graphene-based nanoelectronics.

We consider a restricted three-body problem, where two interacted particles are located in a two-dimensional (2D) plane and interact with the third one located in the parallel spatially separated plane. The system of such type can be formed in the semiconductor coupled quantum wells, where the electrons (holes) and direct excitons spatially separated in different parallel neighboring quantum wells are sufficiently close to interact and form negative X^- or positive X⁺ indirect trions. It is shown that at large interwell separations, when the interwell separation is much greater than the exciton Bohr radius, this problem can be solved analytically using the cluster approach. Analytical results for the energy spectrum and the wavefunctions of the spatially indirect trion are obtained, their dependencies on the interwell separations is analyzed and a conditional probability distribution is calculated. The formation of 2D Wigner crystal of trions at the low densities is predicted. It is shown that the critical density of the formation of the trion Wigner crystal is sufficiently greater than the critical density of the electron Wigner crystal in the same material.

The thermoelectric properties of LaCo_1-xCu_xO_3-δ ceramics are theoretically analyzed, it is observed that thermoelectric figure of merit ZT ( = S²σT/κ) is maximized by Cu substitution in LaCo_1-xCu_x O_3-δ at x = 0.15. The lattice thermal conductivity (κ_ph) and phonon drag thermoelectric power were estimated by the scattering of phonons with defects, grain boundaries, electrons and phonon umklapp scattering to evaluate the thermoelectric figure of merit ZT. The Mott expression is used to estimate the electron diffusive thermoelectric power using Fermi energy as electron free parameter, shows linear temperature dependence. The electron contribution to thermal conductivity (κ_e) is estimated using temperature-dependent electron relaxation time. We found that Cu substitution increases the phonon scattering with grain boundaries and defects which significantly decrease the thermal conductivity and subsequently increase the thermoelectric power. The present numerical analysis of thermoelectric properties will help in designing more efficient thermoelectric materials for thermoelectric applications.

Various properties of substitutional alloys formed from aluminium and the platinum group metals (PGMs) are examined using density functional (D-F) theory and show strong variations depending on metal type. A similar pattern for the binary alloys is observed using molecular dynamics modeling employing Sutton Chen potentials. All results suggest that several of the PGMs could have superior properties to the presently used Ni₃Al alloy for high temperature applications. Some phases are predicted to be stable with extremely high melting temperatures (MTs).

In this paper, we review some results obtained in our works with extension. The new type of braiding matrices called type-II has been extended to the solutions of Yang–Baxter equations (YBE). It is related to quantum entangling states. The four-dimensional realization is connected with Majorana fermions and the two-dimensional realization for the topological basis is the wigner D^J-function with J = 1/2. The YBE leads to the conclusion that the additivity rule of velocities for two anyons obeys Lorentz rather than Galilean. The discussion is extended to three body S-matrix formed by three two-body S-matrices. The three-qubit entanglement based on two-qubit entanglements is discussed.