International Journal of Modern Physics B

Yang and Yang in 1969 [J. Math. Phys. 10, 1115 (1969)] for the first time proposed a rigorous approach to the thermodynamics of the one-dimensional system of bosons with a delta-function interaction. This paper was a breakthrough in exact statistical mechanics, after Yang [Phys. Rev. Lett. 19, 1312 (1967)] published his seminal work on the discovery of the Yang–Baxter equation in 1967. Yang and Yang’s brilliant method yields significant applications in a wide range of fields of physics. In this paper, we briefly introduce the method of the Yang–Yang equilibrium statistical mechanics and demonstrate a fundamental application of the Yang–Yang method for the study of thermodynamics of the Lieb–Liniger model with strong and weak interactions in a whole temperature regime. We also consider the equivalence between the Yang–Yang’s thermodynamic Bethe ansatz equation and the thermodynamics of the ideal gas with the Haldane’s generalized exclusion statistics.

We review harmonic oscillator theory for closed, stable quantum systems. The H₂ potential energy curve (PEC) of Mexican hat-type, calculated with a confined Kratzer oscillator, is better than the Rydberg–Klein–Rees (RKR) H₂ PEC. Compared with QM, the theory of chemical bonding is simplified, since a confined Kratzer oscillator can also lead to the long sought for universal function, once called the Holy Grail of Molecular Spectroscopy. This is validated by reducing PECs for different bonds H₂, HF, I₂, N₂ and O₂ to a single one. The equal probability for H₂, originating either from $H_A+H_B$ or $H_B+H_A$, is quantified with a Gauss probability density function. At the Bohr scale, a confined harmonic oscillator behaves properly at the extremes of bound two-nucleon quantum systems.

Phoxonic crystal (PXC) is a promising artificial periodic material for optomechanical systems and acousto-optical devices. The multi-objective topology optimization of dual phononic and photonic max relative bandgaps in a kind of two-dimensional (2D) PXC is investigated to find the regular pattern of topological configurations. In order to improve the efficiency, a multi-level substructure scheme is proposed to analyze phononic and photonic band structures, which is stable, efficient and less memory-consuming. The efficient and reliable numerical algorithm provides a powerful tool to optimize and design crystal devices. The results show that with the reduction of the relative phononic bandgap (PTBG), the central dielectric scatterer becomes smaller and the dielectric veins of cross-connections between different dielectric scatterers turn into the horizontal and vertical shape gradually. These characteristics can be of great value to the design and synthesis of new materials with different topological configurations for applications of the PXC.

We study a model of resonant point-contact tunneling of a single Luttinger-liquid lead, using the boundary state formulation. The model is described by a single chiral Fermion in one-dimensional space with one point contact interaction at the origin. It is the simplest model of this type. By folding the infinite line, we map the model onto a nonchiral model on the half infinite line and transcribe the point-contact tunneling interaction into a boundary interaction. The tunneling interaction yields a nonlocal effective action at the boundary. We explicitly construct the boundary state and evaluate the current correlation functions. The contact interaction is shown to act on the lower frequency modes more strongly.

An explicit calculation of the quantum nonlocal (QNL) polarizability of a metallic nanoparticle is presented, where two quantum longitudinal plasma waves are excited. The QNL generalization of the classical Clausius–Mossotti factor of the system is derived, by means of the quantum hydrodynamic theory in conjunction with the Poisson equation and applying the appropriate additional quantum boundary conditions.

For the evacuation dynamics in indoor space, a novel crowd flow model is put forward based on Linear Fractional Stable Motion. Based on position attraction and queuing time, the calculation formula of movement probability is defined and the queuing time is depicted according to linear fractal stable movement. At last, an experiment and simulation platform can be used for performance analysis, studying deeply the relation among system evacuation time, crowd density and exit flow rate. It is concluded that the evacuation time and the exit flow rate have positive correlations with the crowd density, and when the exit width reaches to the threshold value, it will not effectively decrease the evacuation time by further increasing the exit width.

Theoretical as well as experimental studies in the literature suggest that defect sites associated with the threading dislocation lines within $n$-type gallium nitride (GaN) act to trap free electrons from the bulk of this semiconductor material. As a result, the core of the threading dislocation lines become negatively charged. The charge accumulated along the core of a threading dislocation line should be screened by a charge of opposite polarity and equal in absolute value per unit length along the dislocation line. In the present work, we model this screened charge buildup along the threading dislocation lines by two concentric space-charge cylinders. Quantum mechanical theory of scattering in cylindrical coordinates is then employed in order to numerically compute the electron mobility limited by scattering from the charged threading dislocation lines. The dependence of the computed electron mobility on the dislocation line density and on the amount of charge accumulated per unit length along the core of the dislocation lines is also investigated in this work. Our computed electron mobility results are compared with results from existing calculations of the GaN dislocation scattering limited electron mobility in the literature.

Social networks have attracted remarkable attention from both academic and industrial societies and it is of great importance to understand the formation of social networks. However, most existing research cannot be applied directly to investigate social networks, where relationships are heterogeneous and structural balance is a common phenomenon. In this paper, we take both positive and negative relationships into consideration and propose a model to characterize the process of social network formation under the impact of structural balance. In this model, a new node first establishes a link with an existing node and then tries to connect to each of the newly connected node’s neighbors. If a new link is established, the type of this link is determined by structural balance. Then we analyze the degree distribution of the generated network theoretically, and estimate the fractions of positive and negative links. All analysis results are verified by simulations. These results are of importance to understand the formation of social networks, and the model can be easily extended to consider more realistic situations.

The temperature and pressure dependence of the static dielectric permittivity in the isotropic phase of the isotropic to cholesteric phase transition is calculated using Landau–de Gennes’s fluctuation theory, allowing spatial variation of the orientational order parameter. A comparison is made with experimental data available in the isotropic phase of the isotropic to cholesteric phase transition.

The localization of the valence electron of $H$, $Li$ and $Na$ atoms enclosed by three different fullerene molecules is studied. The structure of the fullerene molecules is used to calculate the equilibrium position of the endohedrally atom as the minimum of the classical $(N+1)$-body Lennard–Jones potential. Once the position of the guest atom is determined, the fullerene cavity is modeled by a short range attractive shell according to molecule symmetry, and the enclosed atom is modeled by an effective one-electron potential. In order to examine whether the endohedral compound is formed by a neutral atom inside a neutral fullerene molecule $X$@$C_N$ or if the valence electron of the encapsulated atom localizes in the fullerene giving rise to a state with the form $X^{+}$@$C_N^{-}$, we analyze the electronic density, the projections onto free atomic states and the weights of partial angular waves.