International Journal of Modern Physics B

In this chapter, I will briefly review, from my own perspective, the situation within theoretical physics at the beginning of the 1970s, and the advances that played an important role in providing a solid theoretical and experimental foundation for the Berezinskii–Kosterlitz–Thouless theory (BKT). Over this period, it became clear that the Abelian gauge symmetry of the 2D-XY model had to be preserved to get the right phase structure of the model. In previous analyses, this symmetry was broken when using low order calculational approximations. Duality transformations at that time for two-dimensional models with compact gauge symmetries were introduced by José, Kadanoff, Nelson and Kirkpatrick (JKKN). Their goal was to analyze the phase structure and excitations of XY and related models, including symmetry breaking fields which are experimentally important. In a separate context, Migdal had earlier developed an approximate Renormalization Group (RG) algorithm to implement Wilson’s RG for lattice gauge theories. Although Migdal’s RG approach, later extended by Kadanoff, did not produce a true phase transition for the XY model, it almost did asymptotically in terms of a non-perturbative expansion in the coupling constant with an essential singularity. Using these advances, including work done on instantons (vortices), JKKN analyzed the behavior of the spin–spin correlation functions of the 2D XY-model in terms of an expansion in temperature and vortex-pair fugacity. Their analysis led to a perturbative derivation of RG equations for the XY model which are the same as those first derived by Kosterlitz for the two-dimensional Coulomb gas. JKKN’s results gave a theoretical formulation foundation and justification for BKT’s sound physical assumptions and for the validity of their calculational approximations that were, in principle, strictly valid only at very low temperatures, away from the critical $T_{\mathrm{\text{BKT}}}$ temperature. The theoretical predictions were soon tested successfully against experimental results on superfluid helium films. The success of the BKT theory also gave one of the first quantitative proofs of the validity of the RG theory.

Detailed Mössbauer studies carried out in liquid sodium (Na)-exposed austenitic stainless steel (SS-316) show that there is a partial formation of ferromagnetically (FM)-ordered ferritic zones in the paramagnetic austenitic matrix. Results of low energy positron beam-based Doppler broadening studies imply the occurrence of vacancy kind of defects in the liquid Na-exposed SS-316. Correlating these results, the partial occurrence of FM-ordered zones in the liquid Na-exposed SS-316 is understood to be due to open volume defects, predominantly that of Ni vacancies occurring at the surface and upto a certain depth of liquid Na-exposed stainless steel. These results are elucidated in terms of hyperfine parameters associated with ferritic zones.

This paper concentrates on construction of new nonbinary quantum error-correcting codes (QECCs) from three classes of narrow-sense imprimitive BCH codes over finite field ${𝔽}_{q^2}$ ($q\ge 3$ is an odd prime power). By a careful analysis on properties of cyclotomic cosets in defining set $T$ of these BCH codes, the improved maximal designed distance of these narrow-sense imprimitive Hermitian dual-containing BCH codes is determined to be much larger than the result given according to Aly et al. [S. A. Aly, A. Klappenecker and P. K. Sarvepalli, IEEE Trans. Inf. Theory 53, 1183 (2007)] for each different code length. Thus families of new nonbinary QECCs are constructed, and the newly obtained QECCs have larger distance than those in previous literature.

The magnetic properties of zigzag metallic chains have been calculated based on the Monte Carlo simulation. The reduced transition temperatures and the magnetization have been obtained for different exchange interactions and for different crystal fields. The hysteresis cycle is obtained for different exchange interactions, temperatures and crystal field. The superparamagnetic behavior is obtained for a specific value of temperatures and crystal field. The second-order phase transitions are also observed. The obtained results are comparable with some given by experiment results and theoretical calculations.

Codopant is an effective approach to modify the bandgap and band edge positions of transition metal oxide. Here, the electronic structures as well as the optical properties of pristine, mono-doped (N/P/Sb) and codoped (Sb, N/P) anatase TiO₂ have been systematically investigated based on density functional theory calculations. It is found that mono-doped TiO₂ exhibits either unoccupied or partially occupied intermediate state within the energy gap, which promotes the recombination of electron-hole pairs. However, the presence of (Sb, N/P) codopant not only effectively reduces the width of bandgap by introducing delocalized occupied intermediate states, but also adjusts the band edge alignment to enhance the hydrogen evolution activity of TiO₂. Moreover, the optical absorption spectrum for (Sb, N/P) codoped TiO₂, which is favored under oxygen-rich condition, demonstrates the improvement of its visible light absorption. These findings will promote the potential application of (Sb, N/P) codoped TiO₂ photocatalysis for water splitting under visible light irradiation.

In this paper, we give a microscopic view concerning influence of the growth conditions on the physical properties of nanocrystals (NCs) thin films made of CdS, prepared using chemical bath deposition CBD technique. We show a crystalline phase transformation of CdS NCs from hexagonal wurtzite (W) structure to cubic zincblende (ZB) when the growth conditions change, particularly the solution pH values. This effect was confirmed using X-ray diffraction (XRD), transmission electron microscopy (TEM), optical absorption and photoluminescence (PL) measurements. The optical absorption spectra allow calculation of the bandgap value, $E_g$, where significant increase $\sim$200 meV in the CdS bandgap when transforming from Hexagonal to Cubic phase was found.

In this paper, the acoustic wave propagation in a two-dimensional phononic crystal composed of rotational multiple scatterers is investigated. The dispersion relationships, the transmission spectra and the acoustic modes are calculated by using finite element method. In contrast to the system composed of square tubes, there exist a low-frequency resonant bandgap and two wide Bragg bandgaps in the proposed structure, and the transmission spectra coincide with band structures. Specially, the first bandgap is based on locally resonant mechanism, and the simulation results agree well with the results of electrical circuit analogy. Additionally, increasing the rotation angle can remarkably influence the band structures due to the transfer of sound pressure between the internal and external cavities in low-order modes, and the redistribution of sound pressure in high-order modes. Wider bandgaps are obtained in arrays composed of finite unit cells with different rotation angles. The analysis results provide a good reference for tuning and obtaining wide bandgaps, and hence exploring the potential applications of the proposed phononic crystal in low-frequency noise insulation.

Employing the state-to-state time-dependent quantum wave packet method, the Au${}^{+}+$H₂ reactive scattering with initial states $v=0$, $j=0$ and 1 were investigated. Total reaction probabilities, product state-resolved integral cross-sections (ICSs) and differential cross-sections (DCSs) were calculated up to collision energy of 4.5 eV. The numerical results show that total reaction probabilities and ICSs increase with increasing collision energies, and there is little effect to the reactive scattering processes from the rotational excitation of H₂ molecule. Below collision energy of around 3.0 eV, the role of the potential well in the entrance channel is significant and the reactive scattering proceeds dominantly by an indirect process, which leads to a nearly symmetric shape of the DCSs. With collision energy higher than 4.0 eV, the reactive scattering proceeds through a direct process, which leads to a forward biased DCSs, and also a hotter rotational distributions of the products. Total ICS agrees with the results by the quasi-classical trajectories theory very well, which suggests that the quantum effects in this reactive process are not obvious. However, the agreement between the experimental total cross-section and our theoretical result is not so good. This may be due to the uncertainty of the experiment or/and the inaccuracy of the potential energy surface.

The principle and theory of quantum computation are investigated by researchers for many years, and further applied to improve the efficiency of classical machine learning algorithms. Based on physical mechanism, a quantum version of AdaBoost (Adaptive Boosting) training algorithm is proposed in this paper, of which purpose is to construct a strong classifier. In the proposed scheme with cluster state in quantum mechanism is to realize the weak learning algorithm, and then update the corresponding weight of examples. As a result, a final classifier can be obtained by combining efficiently weak hypothesis based on measuring cluster state to reweight the distribution of examples.

The study of community structure is a primary focus of network analysis, which has attracted a large amount of attention. In this paper, we focus on two famous functions, i.e., the Hamiltonian function $H$ and the modularity density measure $D$, and intend to uncover the effective thresholds of their corresponding resolution parameter $\gamma$ without resolution limit problem. Two widely used example networks are employed, including the ring network of lumps as well as the ad hoc network. In these two networks, we use discrete convex analysis to study the interval of resolution parameter of $H$ and $D$ that will not cause the misidentification. By comparison, we find that in both examples, for Hamiltonian function $H$, the larger the value of resolution parameter $\gamma$, the less resolution limit the network suffers; while for modularity density $D$, the less resolution limit the network suffers when we decrease the value of $\gamma$. Our framework is mathematically strict and efficient and can be applied in a lot of scientific fields.

In this work, Bi${}_{2-x}$Na${}_x$Ba₂Co₂O${}_y$ ($x$=0.00, 0.05, 0.10, 0.15, 0.20, 0.25 and 0.30) ceramic samples were prepared by the conventional solid phase method. The influence of Na element doping on the thermoelectric properties of samples was investigated from 300 K to 950 K. Compared with undoped sample, the Seebeck coefficients of Na-doped samples have only a slight decrease. While, the electrical resistivity of the Na-doped samples reduces, for Bi${}_{2-x}$Na${}_x$Ba₂Co₂O${}_y$ ceramic samples with $x$$\le$0.15, the electrical resistivity decreases with increasing Na doping amounts due to the hole-doping effect. In addition, its temperature-dependent resistivity exhibits metallic electrical conductivity behavior. While, the samples with $x$$>$0.20 exhibit semiconductor electrical conductivity behavior at the temperature range of 473–823 K, because of the significant reduction of the electrical resistivity and the slight decrease of Seebeck coefficients, the power factors of the doped samples get a significant improvement. For the most suitable doped sample Bi${}_{1.8}$Na${}_{0.2}$Ba₂Co₂O${}_y$, its ZT value can reach a better value of 0.2 at 873 K.

The transmission properties of armchair- and zigzag-edged graphene nanoribbon junctions between graphene electrodes are examined by means of the standard nonequilibrium Green’s function (NEGF) technique. The quantum transport of electrons is studied through a monolayer graphene strip in the presence of Rashba spin–orbit coupling that acts as a barrier between the two normal leads. The present work compares the conductances of nanoribbons with zigzag and armchair edges. Since the nature of induced gap for zigzag edge is different from armchair, it is expected to give rise to different types of conductance for each edge. Findings indicate that the Rashba strength has more pronounced influence on armchair ribbons than on zigzag ribbons, and the minimum conductance of $2G_0$ for nanoribbon remains intact even in the presence of the Rashba spin–orbit coupling. It is predicted that controllability of spin transport in the monolayer graphene may contribute to the development of well-known spintronics.

We compare the irreversible work produced in an infinitesimal sudden quench of a quantum system at zero temperature with its ground state fidelity susceptibility, giving an explicit relation between the two quantities. We find that the former is proportional to the latter but for an extra term appearing in the irreversible work which includes also contributions from the excited states. We calculate explicitly the two quantities in the case of the quantum Ising chain, showing that at criticality they exhibit different scaling behaviors. The irreversible work, rescaled by square of the quench’s amplitude, exhibits a divergence slower than that of the fidelity susceptibility. As a consequence, the two quantities obey also different finite-size scaling relations.