International Journal of Modern Physics B

Some results are briefly reviewed and developments are presented on the study of Time in quantum mechanics as an observable, canonically conjugate to energy. Operators for the observable Time are investigated in particle and photon quantum theory. In particular, this paper deals with the hermitian (more precisely, maximal hermitian, but non-selfadjoint) operator for Time which appears: (i) for particles, in ordinary non-relativistic quantum mechanics; and (ii) for photons (i.e., in first-quantization quantum electrodynamics).

Professor Chen Ning Yang has made seminal and influential contributions in many different areas in theoretical physics. This talk focuses on his contributions in statistical mechanics, a field in which Professor Yang has held a continual interest for over sixty years. His Master's thesis was on the theory of binary alloys with multi-site interactions, some 30 years before others studied the problem. Likewise, his other works opened the door and led to subsequent developments in many areas of modern day statistical mechanics and mathematical physics. He made seminal contributions in a wide array of topics, ranging from the fundamental theory of phase transitions, the Ising model, Heisenberg spin chains, lattice models, and the Yang–Baxter equation, to the emergence of Yangian in quantum groups. These topics and their ramifications will be discussed in this talk.

In this paper, we propose integrable discretizations of a two-dimensional Hamiltonian system with a quartic potential. Using either the method of separation of variables or the method based on bilinear forms, we construct the corresponding integrable mappings for the first three among four integrable cases.

The influence of a perpendicular magnetic field on a bound polaron near the interface of a polar–polar semiconductor with Rashba effect has been investigated. The material is based on a GaAs/Al_xGa_1-xAs heterojunction and the Al concentration varying from 0.2 ≤ x ≤ 0.4 is the critical value below which the Al_xGa_1-xAs is a direct band gap semiconductor.The external magnetic field strongly altered the ground state binding energy of the polaron and the Rashba spin–orbit (SO) interaction originating from the inversion asymmetry in the heterostructure splitting of the ground state binding energy of the bound polaron. How the ground state binding energy will be with the change of the external magnetic field, the location of a single impurity and the electron area density have been shown in this paper, taking into account the SO coupling. The contribution of the phonons are also considered. It is found that the spin-splitting states of the bound polaron are more stable, and, in the condition of weak magnetic field, the Zeeman effect can be neglected.

Structural changes induced by heat treatment of yttrium-aluminosilicate glasses doped with gadolinium were studied by thermal differential analysis, X-ray diffraction and Gd³⁺ electron paramagnetic resonance (EPR). A small amount of yttrium was replaced by gadolinium in the host glass because yttrium and gadolinium cations are quite similar, and gadolinium can be used as a structural sensor by electron paramagnetic resonance measurements. EPR results evidence small changes in the surroundings of Gd³⁺ ions in the heat treated samples, as compared with the as prepared ones.

The afterpulse probability has been measured using the photon statistical method on the base of theoretical analysis for single-photon detection. It is found that the measured afterpulses obey Gaussian distribution, and the Gauss curves are left shifted with increasing incident photon intensity. We have analyzed the physical process of the phenomenon and obtained the afterpulse probability of our single-photon detector. Compared with the common start–stop method, this robust photon statistical method has the advantages of direct measurement and not requiring additional equipment.

The reaction-diffusion process is generalized by including spatiotemporal delay effects. As a first example, we study the influence of a constant production term which is switched off after a finite time. In a second case, all diffusion-reaction processes within a distance R(t) = κt^α around a certain spatial point are assumed to contribute to the instantaneous dynamics of the system. There occurs a competition between reaction-diffusion and the accumulation process which leads to a non-trivial stationary state. The evolving concentration profiles are calculated analytically for both a ballistic behavior with α = 1 and a diffusion-like transport with α = 1/2. Because the spatiotemporal delay breaks the reflection symmetry, the profiles reveal an anisotropic behavior. The exact solution in one dimension is supported by numerical simulations.

This paper reports a systematic study of tungsten bronze morphotropic phase boundary (MPB) system Pb_2-2X-3Y/2Ba_2xRE_yK_1-xNa_xNb₅O₁₅, where, x = 0.20, 0.25, 0.30, RE = Pr and Bi and y = 0.05 and their structure, microstructure, hysteresis, dielectric, piezoelectric, and Pyroelectric properties. Enhanced piezoelectric constants k_p, k_t, k₃₁, d₃₁, d₃₃, g₃₁, g₃₃, as 30.8%, 47.6%, 18.9%, 57 × 10^-12C/N, 159 × 10^-12C/N, 6.89 × 10^-3mV/N, 19.23 × 10^-3mV/N, and 13.88 × 10^-12m²/N respectively are observed in the composition for which y = 0, and x = 0.30, which is above MPB. Also, a change in thickness, 0.0159 μm has been developed for a thickness of the sample 1.2 mm, d₃₃ = 159 × 10^-12C/N and for an applied voltage of 100 V. The same material produces a length extension, 0.0475 μm for d₃₁ = 57 × 10^-12C/N, l = 10 mm, t = 1.2 mm, for an applied voltage of 100 V. Thus the material may be useful for a piezoelectric transducer. Enhanced piezoelectric coefficients, d₃₁ = 96 × 10^-12C/N and g₃₃ = 12.95 × 10^-3mV/N are also observed in the composition for which RE = Pr and x = 0.25.

This paper presents a tracking control strategy for a class of chaotic systems. A general tracking controller is designed. It is proved theoretically that the error signal can exponentially converge to zero. Numerical simulations show that the controller can make the output signal track all kinds of reference signals. Besides, a better effect can be obtained via changing the control parameters properly.

Numerical simulation of optical confinement in simple double heterostructure of ZnO/Mg_xZn_1-xO and hybrid double heterostructure of Al_xGa_1-xN/ZnO have been carried out at 375 nanometer wavelength using MATLAB. Field distribution along the junction plane has been studied as a function of mole fractions of Mg and Al for different thickness of active layers. The spread of field has been estimated as a function of mole fractions and articulated as Full Width at Half Maximum (FWHM). It was found to be decreasing nonlinearly with increase of Mg mole fraction in simple heterostructure and increasing in a nonlinear manner with increase of Al mole fraction in hybrid heterostructure. FWHM deduced from our analysis was 0.265 micron for 9% and 0.16 micron for 30% Mg mole fraction. For hybrid heterostructure, FWHM values estimated were 0.13 micron and 0.1475 micron for corresponding Al mole fraction values of 9% and 30%, respectively. The narrower confinement of field intensity around the center of the active layer for the higher values of Mg mole fraction has been attributed to an increase of refractive index step between active and barrier layers. The confinement factor as a function of mole fractions and active layer thickness has been explored, and it was found to be increasing with active layer thickness. Our analysis explores the optical confinement of mode 0 in simple and hybrid heterostructures of ZnO.

The electronic properties of ZnS/CdS (001) superlattices (SLs) are investigated using the sp³s* tight-binding method versus substrate composition and valence-band offset (VBO). The results show that the electron is always confined within the CdS slabs; and also show a more striking feature due to the prominent localization of the top hole state near the interface region independently from the substrate composition (strain state). Theoretically, we have varied the VBO and inspected its effect on the interface state, and found that this latter persists to exist for VBO values within the interval [-1.4 eV, 0.6 eV]. This interface state is a manifestation of strong band mixing effects induced by the biaxial strain, and is expected to enhance the radiative efficiency of the SLs. The modelling of some available PL data, obtained for thin CdS quantum well embedded inside ZnS, has shown that the samples are of type-I with high energy bandgaps lying within the blue to ultraviolet spectral region.

The dynamical equation for the kinetic spherical model of a system of spins that is initially in an arbitrary equilibrium state of a given temperature and an external magnetic field is solved. The properties of the non-equilibrium process which ensues when the temperature and field are suddenly changed are studied. The scaling hypotheses by introducing three characteristic functions are generalized. It is found that the process is scale invariant in the low temperature phase while finite-scale invariant in the high temperature phase. The characteristic functions governing the renormalization group trajectories are obtained. The diagram of renormalization group flow reveals a scaling violating point at 3T_c.